This book was produced in EPUB format by the Internet Archive.

The book pages were scanned and converted to EPUB format automatically. This process relies on optical character recognition, and is somewhat susceptible to errors. The book may not offer the correct reading sequence, and there may be weird characters, non-words, and incorrect guesses at structure. Some page numbers and headers or footers may remain from the scanned page. The process which identifies images might have found stray marks on the page which are not actually images from the book. The hidden page numbering which may be available to your ereader corresponds to the numbered pages in the print edition, but is not an exact match; page numbers will increment at the same rate as the corresponding print edition, but we may have started numbering before the print book's visible page numbers. The Internet Archive is working to improve the scanning process and resulting books, but in the meantime, we hope that this book will be useful to you.

The Internet Archive was founded in 1996 to build an Internet library and to promote universal access to all knowledge. The Archive's purposes include offering permanent access for researchers, historians, scholars, people with disabilities, and the general public to historical collections that exist in digital format. The Internet Archive includes texts, audio, moving images, and software as well as archived web pages, and provides specialized services for information access for the blind and other persons with disabilities.

Created with hocr-to-epub (v.1.0.0)

The text on this page is estimated to be only 0.00% accurate

Ico ilte

The text on this page is estimated to be only 24.08% accurate

ELEMENTARY MATHEMATICAL TABLES. BY ALEXANDER MACFAKLAXE, D.Sc., LL.D., PROFESSOR OF PHYSICS IN THE UNIVERSITY OF TEXAS. BOSTON, U.S.A., AND LONDON: GIXN & COMPANY, PUBLISHERS, 1890.

The text on this page is estimated to be only 26.50% accurate

ENTERED AT STATIONERS' HALL. Entered, according to Act of Congress, in the year 1889, by ALEXANDER MACFABLANE, in the Office of the Librarian of Congress, at Washington ALL RIGHTS RESERVED. TYPOGRAPHY BY J. 8. CTJSHING & Co., BOSTON, U.S.A. PRESSWORK BY GINN & Co., BOSTON, U.S.A.

The text on this page is estimated to be only 28.10% accurate

PREFACE. rpHESE tables are designed to be useful not only in com•*- puting and in tlie graphic method, but also in the teaching of arithmetic and in the illustration of the theorems of algebra. I have arranged the several tables 011 a uniform decimal plan, so that the entries for a particular number are generally found in the same position on the page. The arrangement is that of double entry, so that in general the order of reading is the same as for ordinary print. The argument and entry are so expressed that it is easy to find the entry corresponding to any other position of the decimal point in the argument. In most cases the whole of a table is seen at one opening of the pages, and the tenth compartment, when not required for the main table, is filled with a short table which is in general auxiliary to the main table. Special acknowledgments are due to Prof. Hastings of Yale University, and Prof. Halsted of this University. In the proof-reading and independent computation, I have received aid from D. W. Spence and J. C. Nagle, science students of this University. ALEXANDER, MACFARLANE. UNIVERSITY OF TEXAS, April, 1889.

The text on this page is estimated to be only 27.03% accurate

CONTENTS. PAGES I. Common logarithms. Proportional parts,* 4-23 . 2-3 The same for 1000-1900. Logarithms for interest . 4-5 II. Antilogarithms . 6-7 III. Addition logarithms . . . . . . 8-9 IV. Subtraction logarithms. Proportio nal parts, 1-38 . 10-13 V. Logarithmic sines and cosines. Proportional parts, 11-30. 14-15 The same for 0°.00 to 9°. 00. Equivalent of degrees in minutes. Table of S for degrees . . . 16-17 VI. Logarithmic tangents and cotangents. Proportional parts, 31-50 18-19 The same for 0°.00 to 9°.00. Equivalent of minutes in degrees. Table of T for degrees . . . 20-21 VII. Logarithmic sines and cosines for minutes. Proportional parts, 1-49. Table of S for minutes . 22-23 VIII. Logarithmic tangents and cotangents for minutes. Proportional parts, 50-99. Table of T for minutes . . - . 24-25 IX. Natural sines and cosines. Proportional parts to six, 1-19 . . . . ... . . . 26-27 X. Natural tangents and cotangents. Proportional parts to six, 20-59 28-29 XI. Natural secants and cosecants. Proportional parts to six, 60-99 . . . . . . . . 30-31 XII. Radians equivalent to degrees. Radians equivalent to minutes. Fraction of period, and time, equivalent to degrees . . .f . . . 32-33 * A caption in Italics indicates a small table appended to the main table.

The text on this page is estimated to be only 26.92% accurate

CONTENTS. PAGES Reciprocals. Multiples of £ to T^ . . . . 34-35 Squares. Square of reciprocal ..... 36-37 Cubes. Cube of reciprocal 38-39 Square roots. Square root of reciprocal . . . 40-43 Cube roots. Cube root of reciprocal . . . 44-49 Multiples of 100-999 50-67 Circumference of circle. Constants involving v . 68-69 Area of circle. Multiples of ^ and ^ . . . 70-71 Content of sphere. Logarithms of factorials and of powers of '2 72-73 Hyperbolic logarithms. Multiples of the modulus . 74-75 Amount at the end of n years .... 76 PresenUvalue of 1000 77 Amount of an annuity paid at the end of each year 78 Present value of the preceding . . . . 79 Amount of an annuity paid at the beginning of each year 80 Sum to be paid at the end of each of n years to extinguish a debt of 1000 .... 81 Least divisors 82-85 Exponentials 86 Explanation of Tables 87-105 Folding leaf XIII. XIV. XV. XVI. XVII. XVIII. XIX. XX. XXI. XXII. XXIII. XXIV. XXV. XXVI. XXVII. XXVIII. XXIX. XXX. XXXI. Multiples of 1-100

The text on this page is estimated to be only 28.57% accurate

I, COMMON LOGAEITHMS, logn n 0 123 456 7 8 9 (1 10 0000 0043 0086 0128 0170 0212 0253; 0294 0334 0374 40 11 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 37 12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 33 13 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 31 14 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 29 15 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 27 16 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 25 17 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 24 18 2553 2577 2601 2625 2648 2672 2695 2718 2742 2765 23 19 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 21 20 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 21 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 20 22 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 19 28 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 18 24 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 17 25 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 17 26 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 16* 27 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 16 28 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 15 29 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 14 80 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 14 31 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 13 32 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 13 33 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 13 34 5315. 5328 5340 5353 5366 5378 5391 5403 5416 5428 13. 35 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 12 36 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 12 37 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 12 38 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 12 39 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 11 40 6021. 6031 6042 6053 6064 6075 6085 6096 6107 6117 11 41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 10 42 6232 6243 6253 6265 6274 6284 6294 6304 6314 6325 10 43 6335 6345 6355 6365 6375 6385 6395 6405. 6415 6425 10 44 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 10 45 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 10 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 9 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 9 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 9 49 6902 6911 6920 6928' 6937 6946 6955 6964 6972 6981 9 50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 9 51 7076" 7084 7093 7101 7110 7118 7126 7135 7143 7152 8 52 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 8 53 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 8 54 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 8 55 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 8 56 7482 7490 7497- 7505 7513 7520 7528 7536 7543 7551 8 57 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 7 58 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 8 59 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 8

The text on this page is estimated to be only 27.30% accurate

logn I, COMMON LOGABITHMS, 11 0 1 2 3 456 78 9 •9 60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 7 61 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 7 62 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 6 63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 7 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 7 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 6 66 8195 8202 8 P 8215 8222 8228 8235 8241 8248 8254 7 67 8261 8267 81 >74 8287 8293 8299 8306 8312 8319 6 68 8325 8331 8331 8344 8351 8357 8363 8370 8376 8382 6 69 8388 8395 840f $407 8414 8420 8426 8432 8439 8445 6 70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 7 71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 6 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 6 73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 6 74 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 6 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 6 76 8808 8814' 8820 8825 8831 8837 8842 8848 8854 8859 6 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 6 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 5 79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 6 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 6 81 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 5 82 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 5 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 5 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 5 85 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 5 86 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 5 87 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 5 88 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 5 89 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 4 90 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 4 91 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 5 92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 5 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 4 94 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 4 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 5 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 5 97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 4 98 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 4 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 4 pp. 456 789 10 11 1218-14 15 16 17 18 19 20 21 22 23 1 Oil 111 1 111 1222222 222 2 111 122 2 2233333444 4 4 5 3 1 2 2 223 3 3444555566 677 4 222334 4 4556667788 899 5 233 -1-45 5 667 788 99 10 10 11 11 12 6 234455 6 7 7 8 8 9 10 10 11 11 12 13 13 14 7 34-4 566 7 8 8 9 10 11 11 12 13 13 14 15 15 16 8 345 667 8 9 10 10 11 12 13 14 14 15 16 17 18 18 9 455678 9 10 11 12 13 14 14 15 16 17 18 19 20 21

The text on this page is estimated to be only 28.67% accurate

I. COMMON LOGAEITHMS logn n 0 123456789 d pp. 100 0000 0004 0009 0013 0017 0022 0026 0030 0035 0039 4 5 101 0043 0048 0052 0056 0060 0065 0069 0073 0077 0082 4 1 102 0086 0090 0095 0099 0103 0107 0111 0116 0120 0124 4 1 103 0128 0133 0137 0141 0145 0149 0154 0158 0162 0166 4 2 104 0170 0175 0179 0183 0187 0191 0195 0199 0204 0208 4 2 105 0212 0216 0220 0224 0228 0233 0237 0241 0245 0249 4 3 106 0253 0257 0261 0265 0269 0273 0278 0282 0286 0290 4 3 107 0294 0298 03J2 0306 0310 0314 0318 0322 0326 0330 4 4 108 0334 0338 0342 0346 0350 0354 0358 0362 0366 0370 4 4 109 0374 0378 0382 0386 0390 0394 0398 0402 0406 0410 4 5 110 0414 0418 0422 0426 0430 0434 0438 0441 0445 0449 4 111 0453 0457 0461 0465 0469 0473 0477 0481 0484 0488 4 112 0492 0496 0500 0504 0508 0512 0515 0519 0523 0527 4 113 0531 0535 0538 0542 0546 0550 0554 0558 0561 0565 4 114 0569 0573 0577 0580 0584 0588 0592 0596 0599 0603 4 115 0607 0611 0615 0618 0622 0626 0630 0633 0637 0641 4 116 0645 0648 0652 0656 0660 0663 0667 0671 0674 0678 4 117 0682 0686 0689 0693 0697 0700 0704 0708 0711 0715 4 118 0719 0722 0726 0730 0734 0737 0741 0745 0748 0752 3 119 0755 0759 0763 0766 0770 0774 0777 0781 0785 0788 4 120 0792 0795 0799 0803 0806 0810 0813 0817 0821 0824 4 T 121 0828 0831 0835 0839 0842 0846 0849 0853 0856 0860 4 0 122 0864 0867 0871 0874 0878 0881 0885 0888 0892 0896 3 i 123 0899 0903 0906 0910 0913 0917 0920 0924 0927 0931 3 i 124 0934 0938 0941 0945 0948 0952 0955 0959 0962 0966 3 2 125 0969 0973 0976 0980 0983 0986 0990 0993 0997 1000 4 2 126 1004 1007 1011 1014 1017 1021 1024 1028 1031 1035 3 2 127 1038 1041 1045 1048 1052 1055 1059 1062 1065 1069 3 3 128 1072 1075 1079 1082 1086 1089 1092 1096 1099 1103 3 3 129 1106 1109 1113 1116 1119 1123 1126 1129 1133 1136 3 4 130 1139 1143 1146 1149 1153 1156 1159 1163 1166 1169 4 131 1173 1176 1179 1183 1186 1189 1193 1196 1199 1202 4 132 1206 1209 1212 1216 1219 1222 1225 1229 1232 1235 4 133 1239 1242 1245 1248 1252 1255 1258 1261 1265 1268 3 134 1271 1274 1278 1281 1284 1287 1290 1294 1297 1300 3 135 1303 1307 1310 1313 1316 1319 1323 1326 1329 1332 3 136 1335 1339 1342 1345 1348 1351 1355 1358 1361 1364 3 137 1367 1370 1374 1377 1380 1383 1386 1389 1392 1396 3 138 1399 1402 1405 1408 1411 1414 1418 1421 1424 1427 3 139 1430 1433 1436 1440 1443 1446 1449 1452 1455 1458 3 140 1461 1464 1467 1471 1474 1477 1480 1483 1486 1489 3 IT 141 1492 1495 1498 1501 1504 1508 1511 1514 1517 1520 3 0 142 1523 1526 1529 1532 1535 1538 1541 1544 1547 1550 3 i 143 1553 1556 1559 1562 1565 1569 1572 1575 1578 1581 3 i 144 1584 1587 1590 1593 1596 1599 1602 1605 160S 1611 3 i 145 1614 1617 1620 1623 1626 1629 1632 1635 1638 1641 3 2 146 1644 1647 1649 1652 1655 1658 1661 1664 1667 1670 3 2 147 1673 1676 1679 1682 1685 1688 1691 1694 1697 1700 3 2 148 1703 1706 1708 1711 1714 1717 1720 1723 1726 1729 3 2 149 1732 1735 1738 1741 1744 1746 1749 1752 1755 1758 3 3

The text on this page is estimated to be only 28.52% accurate

log" n CONTINUED. n 0 1 23 4 5 6 7 8 9 d pp. 150 1761 1764 1767 1770 1772 1775 1778 1781 1784 1787 3 3 151 1790 1793 1796 1798 1801 1804 1807 1810 1813 1816 2 0 152 1818 1821 1824 1827 1830 1833 1836 1838 1841 1844 3 1 153 1847 1850 1853 1855 1858 1861 1864 1867 1870 1872 3 1 154 1875 1878 1881 1884 1886 1889 1892 1895 1898 1901 2 1 155 1903 1906 1909 1912 1915 1917 1920 1923 1926 1928 3 2 156 1931 1934 1937 1940 1942 1945 1948 1951 1953 1956 3 2 157 1959 1962 1965 1967 1970 1973 1976 1978 1981 1984 3 2 158 1987 1989 1992 1995 1998 2000 2003 2006 2009 2011 3 2 159 2014 2017 2019 2022 2025 2028 2030 2033 2036 2038 3 3 160 2041 2044 2047 2049 2052 2055 2057 2060 2063 2066 2 161 2068 2071 2074 2076 2079 2082 2084 2087 2090 2092 3 162 2095 2098 2101 2103 2106 2109 2111 2114 2117 2119 3 163 2122 2125 2127 2130 2133 2135 2138 2140 2143 2146 2 164 2148 2151 2154 2156 2159 2162 2164 2167 2170 2172 3 165 2175 2177 2180 2183 2185 2188 2191 2193 2196 2198 3 166 2201 2204 $206 2209 2212 2214 2217 2219 2222 2225 2 167 2227 2230 2232 2235 2238 2240 2243 2245 2248 2251 2 168 2253 2256 2258 2261 2263 2266 2269 2271 2274 2276 3 169 2279 2281 2284 2287 2289 2292 2294 2297 2299 2302 2 170 2304 2307 2310 2312 2315 2317 2320 2322 2325 2327 3 2 171 2330 2333 2335 2338 2340 2343 2345 2348 2350 2353 2 0 172 2355 2358 2360 2363 2365 2368 2370 2373 2375 2378 2 0 173 2380 2383 2385 2388 2390 2393 2395 2398 2400 2403 2 1 174 2405 2408 2410 2413 2415 2418 2420 2423 2425 2428 2 1 175 2430 2433 2435 2438 2440 2443 2445 2448 2450 2453 2' 1 176 2455 2458 2460 2463 2465 2467 2470 2472 2475 2477 3 1 177 2480 2482 2485 2487 2490 2492 2494 2497 2499 2502 2 1 178 2504 2507 2509 2512 2514 2516 2519 2521 2524 2526 3 2 179 2529 2531 2533 2536 2538 2541 2543 2545 2548 2550 3 2 180 2553 2555 2558 2560 2562 2565 2567 2570 2572 2574 ~T 181 2577 2579 2582 2584 2586 2589 2591 2594 2596 2598 3 182 2601 2603 2605 2608 2610 2613 2615 2617 2620 2622 3 183 2625 2627 2629 2632 2634 2636 2639 2641 2643 2646 2 184 2648 2651 2653 2655 2658 2660 2662 2665 2667 2669 3 185 2672 2674 2676 2679 2681 2683 2686 2688 2690 2693 2 186 2695 2697 2700 2702 2704 2707 2709 2711 2714 2716 2 187 2718 2721 2723 2725 2728 2730 2732 2735 2737 2739 3 188 2742 2744 2746 2749 2751 2753 2755 2758 2760 2762 3 189 2765 2767 2769 2772 2774 2776 2778 2781 2783 2785 3 n 0 | 1 2 3 4 5 6 789 d 1.00 000000 0434 0868 1301 1734 2166 2598 3029 3461 3891 430 1.01 004321 4751 5181 5609 6038 6466 6894 7321 7748 8174 426 1.02 008600 9026 9451 9876 *0300*0724*1147 *1570*1993*2415 422 1.03 01 2837 3259 3680 4100 4521 4940 5360 5779 6197 6616 417 1.04 .01 7033 7451 7868 8284 8700 9116 9532 9947*0361*0775 414 1.05 .02 1189 1603 2016 2428 2841 3252 3664 4075 4486 4896 410 1.06 .025306 571561256533 694273507757 8164 8571 8978 406 1.07 .029384 ! 9789*0195*0600 *1004*1408*1812 *22 16*2619*3021 403 1.08 .03 3424 i 3826 4227 4628 5029 5430 5830 6230 6629 7028 398 1.09 .03 7426 7825 8223 8620 9017 9414 9811 *0207*0602*0998 395

The text on this page is estimated to be only 28.46% accurate

II, ANTILOaAKITHMS, 1O-* n 0 123 456 7 8 9 (1 pp. 00 1000 1002 1005 1007 1009 1012 1014 1016 1019 1021 2 234 01 1023 1026 1028 1030 1033 1035 1038 1040 1042 1045 2 000 02 1047 1050 1052 1054 1057 1059 1062 1064 1067 1069 3 01 1 03 1072 1074 1076 1079 1081 1084 1086 1089 1091 1094 2 1 1 1 04 1096 1099 1102 1104 1107 1109 1112 1114 1117 1119 3 1 12 05 1122 1125 1127 1130 1132 1135 1138 1140 1143 1146 2 122 06 1148 1151 1153 1156 1159 1161 1164 1167 1169 1172 3 122 07 1175 1178 1180 1183 1186 1189 1191 1194 1197 1199 3 1 23 08 1202 1205 1208 1211 1213 1216 1219 1222 122^ 1227 3 223 09 1230 1233 1236 1239 1242 1245 1247 1250 1253 1256 3 234 lo^ 1259 1262 1265 1268 1271 1274 1276 1279 1282 1285 3 567 11 1288 1291 1294 1297 1300 1303 1306 1309 1312 1315 3 1 1 1 12 1318 1321 1324 1327 1330 1334 1337 1340 1343 1346 3 1 1 1 13 1349 1352 1355 1358 1361 1365 1368 1371 1374 1377 3 222 14 1380 1384 1387 1390 1393 1396 1400 1403 1406 1409 4 223 15 1413 1416 1419 1422 1426 1429 1432 1435 1439 1442 3 334 16 1445 1449 1452 1455 1459 1462 1466 1469 1472 1476 3 344 17 1479 1483 1486 1489 1493 1496 1500 1503 1507 1510 4 445 18 1514 1517 1521 1524 1528 1531 1535 1538 1542 1545 4 456 19 1549 1552 1556 1560 1563 1567 1570 1574 1578 1581 4 556 20 1585 1589 1592 1596 1600 1603 1607 1611 1614 1618 4 8 9 21 1622 1626 1629 1633 1637 1641 1644 1648 1652 1656 4 1 1 22 1660 1663 1667 1671 1675 1679 1683 1687 1690 1694 4 2 2 23 1698 1702 1706 1710 1714 1718 1722 1726 1730 1734 ,4 2 3 24 1738 1742 1746*1750 1754 1758 1762 1766 1770 1774 4 3 4 25 1778 1782 1786 1791 1795 1799 1803 1807 1811 1816 4 4 5 26 1820 1824 1828 1832 1837 1841 1845 1849 1854 1858 4 5 5 27 1862 1866 1871 1875 1879 1884 1888 1892 1897 1901 4 6 6 28 1905 1910 1914 1919 1923 1928 1932 1936 1941 1945 5 6 7 29 1950 1954 1959 1963 1968 1972 1977 1982 1986 1991 4 7 8 30 1995 2000 2004 2009 2014 2018 2023 2028 2032 2037 5 1011 31 2042 2046 2051 2056 2061 2065 2070 2075 2080 2084 5 1 1 32 2089 2094 2099 2104 2109 2113 2118 2123 2128 2133 5 2 2 33 2138 2143 2148 2153 2158 2163 2168 2173 2178 2183 5 3 3 34 2188 2193 2198 2203 2208 2213 2218 2223 2228 2234 5 4 4 35 2239 2244 2249 2254 2259 2265 2270 2275 2280 2286 5 5 6 36 2291 2296 2301 2307 2312 2317 2323 2328 2333 2339 5 6 7 37 2344 2350 2355 2360 2366 2371 2377 2382 2388 2393 6 7 8 38 2399 2404 2410 2415 2421 2427 2432 2438 2443 2449 6 8 9 39 2455. 2460 2466 2472 2477 2483 2489 2495 2500 2506 6 910 4

The text on this page is estimated to be only 27.99% accurate

10 " II, ANTILOaAKITKMS, 11 0 123 4 5 6 7 8 9 Id pp. 50 3162 3170 3177 3184 3192 3199 3206 3214 3221 3228 8 1415 51 3236 3243 3251 3258 3266 3273 3281 3289 3296 3304 7 1 2 52 3311 3319 3327 3334 3342 3350 3357 3365 3373 3381 7 3 3 53 3388 3396 3404 3412 3420 3428 3436 3443 3451 3459 8 4 5 54 3467 3475 3483 3491 3499 3508 3516 3524 3532 3540 8 6 6 55 3548 3556 3565 3573 3581 3589 3597 3606 3614 3622 9 7 8 56 3631 3639 3648 3656 3664 3673 3681 3690 3698 3707 8 8 9 57 3715 3724 3733 3741 3750 3758 3767 3776 3784 3793 9 1011 58 3802 3811 3819 3828 3837 3846 3855 3864 3873 3882 8! 11 12 59 3890 3899 3908 3917 3926 3936 3945 3954 3963 3972 9 13 14 60 3981 3990 3999 4009 4018 4027 4036 4046 4055 4064 10 1617 61 4074 4083 4093 4102 4111 4121 4130 4140 4150 4159 10 2 2 62 4169 4178 4188 4198 4207 4217 4227 4236 4246 4256 10 3 3 63 4266 4276 4285 4295 4305 4315 4325 4335 4345 4355 10 5 5 64 4365 4375 4385 4395 4406 4416 4426 4436 4446 4457 10 6 7 65 4467 4477 4487 4498 4508 4519 4529 4539 4550 4560 11 8 9 66 4571 4581 4592 4603 4613 4624 4634 4645 4656 4667 10 1010 67 4677 4688 4699 4710 4721 4732 4742 4753 4764 4775 11 1112 68 4786 4797 4808 4819 4831 4842 4853 4864 4875 4887 11 1314 69 4898 4909 4920 4932 4943 4955 4966 4977 4989 5000 12 1415 W 5012 5023 5035 5047 5058 5070 5082 5093 5105 5117 T2~ 1819 71 5129 5140 5152 5164 5176 5188 5200 5212 5224 5236 12 2 2 72 5248 5260 5272 5284 5297 5309 5321 5333 5346 5358 12 4 4 73 5370 5383 5395 5408 5420 5433 5445 5458 5470 5483 12 5 6 74 5495 5508 5521 5534 5546 5559 5572 5584,5598 5610 13 7 8 75 5623 5636 5649 5662 5675 5689 5702 5715 5728 5741 13 9 10 76 5754 5768 5781 5794 5808 5821 5834 5848 5861 5875 13 1111 77 5888 5902 5916 5929 5943 5957 5970 5984 5998 6012 14 1313 78 6026 6039 6053 6067 6081 6095 6109 6124 6138 6152 14 1415 79 6166 6180 6194 6209 6223 6237 6252 6266 6281 6295 15 1617 80 6310 6324 6339 6353 6368 6383 6397 6412 6427 6442 15 2021 81 6457 647 1 6486 6501 6516 6531 6546 6561 6577 6592 15 2 2 82 6607 6622 6637 6653 6668 6683 6699 6714 6730 6745 16 4 4 83 6761 6776 6792 6808 6823 6839 6855 6871 6887 6902 16 6 6 84 6918 6934 6950 6966 6982 6998 7015 7031 7047 7063 16 8 8 85 7079 7096 7112 7129 7145 7161 7178 7194 7211 7228 16 1011 86 7244 7261 7278 7295 7311 7328 7345 7362 7379 7396 17 1213 87 7413 7430 7447 7464 7482 7499 7516 7534 7551 7568 18 1415 88 7586 7603 7621 7638 7656 7674 7691 7709 7727 7745 17 1617 89 7762 77SO 7798 7816 7834 7852 7870 7889 7907 7925 18 1819 90 7943 7962 7980 7998 8017 8035 8054 8072 8091 8110 18 2223 91 8128 8147 8166 8185 8204 8222 8241 8260 8279 8299 19 2 2 92 8318 8337 8356 8375 8395 8414 8433 8453 8472 8492 19 4 5 93 8511 8531 8551 8570 8590 8610 8630 8650 8670 8690 20 7 7 94 8710 8730 8750 8770 8790 8810 8831 8851 8872 8892 21 9 9 95 8913 8933 8954 8974 8995 9016 9036 9057 9078 9099 21 1112 96 9120 9141 9162 9183 9204 9226 9247 9268 9290 9311 22 1314 97 9333 9354 9376 9397 9419 9441 9462 9484 9506 9528 22 1516 98 9550 9572 9594 9616 9638 9661 9683 ' 9705 9727 9750 22 1818 99 9772 9795 9817 9840 9863 9886 9908 9931 9954 9977 23 2021

The text on this page is estimated to be only 28.13% accurate

Ill, ADDITION LOGARITHMS, Iog'(l4- n) lOg/7 0 1 2 3 ! 4 5 6 789 d pp. 6. 0.0000 0001 0001 0001 0001 0001 0002 0002 0003 0003 i 1 7.0 0.0004 0004 0005 0005 0005 0005 0005 0005 0005 0005 0 1 2 1 0005 0006 0006 0006 0006 0006 0006 0006 0007 0007 0 00 2 0007 0007 0007 0007 0008 0008 0008 0008 0008 0008 •i 00 3 0009 0009 0009 0009 0009 0010 0010 0010 0010 0011 0 01 4 0011 0011 0011 0012 0012 0012 0013 0013 0013 0013 1 0 1 5 0014 0014 0014 0015 0015 0015 0016 0016 0016 0017 0 1 1 6 0017 0018 0018 0018 0019 0019 0020 0020 0021 0021 1 1 1 7 0022 0022 0023 0023 0024 0024 0025 0025 0026 0027 0 1 1 8 0027 0028 0029 0029 0030 0031 0031 0032 0033 C034 0 1 2 9 0034 0035 0036 0037 0038 0039 0039 0040 0041 0042 1 1 2 8.0 0.0043 0044 0045 0046 0047 0048 0050 0051 0052 0053 1 T4 1 0054 0056 0057 0058 0060 0061 0062 0064 0065 0067 r 00 2 0068 0070 0071 0073 0075 0077 0078 0080 0082 0084 2 1 1 3 0086 0088 0090 0092 0094 0096 0098 0101 0103 0105 3 1 1 4 0108 0110 0113 0115 0118 0121 0123 0126 0129 0132 3 12 5 0135 0138 0141 0145 0148 0151 0155 0158 0162 0166 4 22 6 0170 0173 0177 0181 0186 0190 0194 0199 0203 0208 4 22 7 0212 0217 0222 0227 0232 0238 0243 0248 0254 0260 6 23 8 0266 0272 0278 0284 0291 0297 0304 0311 0318 0325 7 23 9 0332 0339 0347 0355 0363 0371 0379 0387 0396 0405 9 34 9.0 0414 0423 0432 0442 0452 0462 0472 0482 0493 0504 11 1 0515 0526 0538 0550 0562 0574 0586 0599 0612 0625 14 9.20 0.0639 0640 0642 0643 0644 0646 0647 0649 0650 0651 2 156 21 0653 0654 0656 0657 0658 0660 0661 0663 0664 0665 2 1 1 22 0667 0668 0670 0671 0673 0674 0675 0677 0678 0680 1 11 28 0681 0683 0684 0686 0687 0689 0690 0691 0693 0694 2 22 24 0696 0697 0699 0700 0702 0703 0705 0706 0708 0709 2 22 25 0711 0712 0714 0715 0717 0718 0720 0721 0723 0725 1 33 26 0726 0728 0729 0731 0732 0734 0735 0737 0738 0740 2 34 27 0742 0743 0745 0746 0748 0749 0751 0753 0754 0756 1 44 28 0757 0759 0761 0762 0764 0766 0767 0769 0770 0772 2 45 29 0774 0775 0777 0779 0780 0782 0783 0785 0787 0788 255 9.30 0.0790 0792 0793 0795 0797 0798 0800 0802 0804 0805 2 7 8 31 0807 0809 0810 0812 0814 0815 0817 0819 0821 0822 2 1 1 32 0824 0826 0827 0829 0831 0833 0834 0836 0838 0840 1 12 33 0841 0843 0845 0847 0849 0850 0852 0854 0856 0857 2 22 34 0859 0861 0863 0865 0866 0868 0870 0872 0874 0876 1 33 35 0877 0879 0881 0883 0885 0887 0888 0890 0892 0894 o 44 36 0896 0898 0900 0901 0903 0905 0907 0909 0911 0913 2 45 37 0915 0917 0918 0920 0922 0924 0926 0928 0930 0932 2 56 38 0934 0936 0938 0940 0942 0944 0945 0947 0949 0951 2 66 39 0953 0955 0957 0959 0961 0963 0965 0967 0969 0971 2 67 9.40 0.0973 0975 0977 0979 0981 0983 0985 0987 0989 0991 ~2~ 9 41 0993 0996 0998 1000 1002 1004 1006 1008 1010 1012 2 1 42 1014 1016 1018 1020 1022 1025 1027 1029 1031 1033 2 2 43 1035 1037 1039 1042 1044 1046 1048 1050 1052 1054 3 3 44 1057 1059 1061 1063 1065 1067 1070 | 1072 1074 1076 2 4 45 1078 1081 1083 1085 1087 1089 1092 1094 1096 1098 3 5 46 1101 1103 1105 1107 1110 1112 1114 1116 1119 1121 2 5 47 1123 1125 1128 1130 1132 1135 1137 1139 1141 1144 2 6 48 1146 1148 1151 1153 1155 1158 1160 1162 1165 1167 2 7 49 1169' 1172 1174 1177 1179 1181 1184 1186 1189 1191 2 8

The text on this page is estimated to be only 28.71% accurate

log (1 + ft) III ADDITION LOGARITHMS, logfl 0 123 456 7 8 9 d pp. 9.50 0.1193 1196 1198 1201 1203 1205 1208 1210 1213 1215 3 10 51 1218 1220 1222 1225 1227 1230 1232 1235 1237 1240 2 1 52 1242 1245 1247 1250 1252 1255 1257 1260 1262 1265 2 2 53 1267 1270 1272 1275 1277 1280 1283 1285 1288 1290 3 3 54 1293 1295 1298 1301 1303 1306 1308 1311 1314 1316 3 4 55 1319 1321 1324 1327 1329 1332 1335 1337 1340 1343 2 5 56 1345 1348 1351 1353 1356 1359 1361 1364 1367 1369 3 6 57 1372 1375 1377 1380 1383 1386 1388 1391 1394 1397 2 7 58 1399 1402 1405 1408 1410 1413 1416 1419 1422 1424 3 8 59 1427 1430 1433 1436 1438 1441 1444 1447 1450 1453 2 9 9.60 0.1455 1458 1461 1464 1467 1470 1473 1475 1478 1481 3 11 61 1484 1487 1490 1493 1496 1499 1502 1504 1507 1510 3 1 62 1513 1516 1519 1522 1525 1528 1531 1534 1537 1540 3 2 63 1543 1546 1549 1552 1555 1558 1561 1564 1567 1570 3 3 64 1573 1576 1579 1582 1585 1588 1591 1594 1598 1601 3 4 65 1604 1607 1610 1613 1616 1619 1622 1625 1629 1632 3 6 66 1635 1638*1641 1644 1647 1651 1654 1657 1660 1663 3 7 67 1666 1670 1673 1676 1679 1682 1686 1689 1692 1695 4 8 68 1699 1702 1705 1708 1712 1715 1718 1721 1725 1728 3 9 69 1731 1735 1738 1741 1744 1748 1751 1754 1758 1761 3 10 9.70 0.1764 1768 1771 1774 1778 1781 1784 1788 1791 1795 y 12 71 1798 1801 1805 1808 1812 1815 1818 1822 1825 1829 3 1 72 1832 1836 1839 1842 1846 1849 1853 1856 1860 1863 4 2 73 1867 1870 1874 1877 1881 1884 1888 1891 1895 1898 4 4 74 1902 1906 1909 1913 1916 1920 1923 1927 1931 1934 4 5 75 1938 1941 1945 1949 1952 1956 1959 1963 1967 1970 4 6 76 1974 1978 1981 1985 1989 1992 1996 2000 2003 2007 4 7 77 2011 2015 2018 2022 2026 2029 2033 2037 2041 2044 4 8 78 2048 2052 2056 2059 2063 2067 2071 2075 2078 2082 4 10 79 2086 2090 2094 2097 2101 2105 2109 2113 2117 2121 3 11 9.80 0.2124 2128 2132 2136 2140 2144 2148 2152 2156 2159 4 13 81 2163 2167 2171 2175 2179 2183 2187 2191 2195 2199 4 1 82 2203 2207 2211 2215 2219 2223 2227 2231 2235 2239 4 3 83 2243 2247 2251 2255 2259 2263 2267 2271 2275 2279 5 4 84 2284 2288 2292 2296 2300 2304 2308 2312 2316 2321 4 5 85 2325 2329 2333 2337 2341 2346 2350 2354 2358 2362 4 7 86 2366 2371 2373 2379 2383 2388 2392 2396 2400 2405 4 8 87 2409 2413 2417 2422 2426 2430 2434 2439 2443 2447 5 9 88 2452 2456 2460 2465 2469 2473 2478 2482 2486 2491 4 10 89 2495 2499 2504 2508 2513 2517 2521 2526 2530 2535 4 12 9.90 0.2539 2543 2548 2552 2557 2561 2566 2570 2575 2579 5 14 91 2584 2588 2593 2597 2602 2606 2611 2615 2620 2624 5 1 92 2629 2633 2638 2642 2647 2651 2656 2661 2665 2670 4 3 93 2674 2679 2684 2688 2693 2697 2702 2707 2711 2716 5 4 94 2721 2725 2730 2735 2739 2744 2749 2753 2758 2763 4 6 95 2767 2772 2777 2782 2786 2791 2796 2801 2805 2810 5 7 96 2815 2820 2824 2829 2834 2839 2844 2848 2853 2858 5 8 97 2863 2868 2873 2877 2882 2887 2892 2897 2902 2907 4 10 98 2911 2916 2921 2926 2931 2936 2941 2946 2951 2956 5 11 99 2961 2966 2970 2975 2980 2985 2990 2995 3000 3005 5 13

The text on this page is estimated to be only 28.73% accurate

10 IV. SUBTKACTION LOGAKITHMS. log! j-f n lOg/7 0 123 456 7 8 9 d pp. 6. 0.0000 0001 0001 0001 0001 0001 0002 0002 0003 0003 1 7.0 0.0004 0004 0005 0005 0005 0005 0005 0005 0005 0005 0 1 2 1 0005 0006 0006 0006 0006 0006 0006 0006 0007 0007 0 0 0 2 0007 0007 0007 0007 0008 0008 0008 0008 0008 0008 1 0 0 3 0009 0009 0009 0009 0010 0010 0010 0010 0010 0011 0 0 1 4 0011 0011 0011 0012 0012 0012 0013 0013 0013 0013 1 0 1 5 0014 0014 0014 0015 0015 0015 0016 0016 0017 0017 0 1 1 6 0017 0018 0018 0019 0019 0019 0020 0020 0021 0021 1 1 1 7 0022 0022 0023 0023 0024 0024 0025 0026 0026 0027 0 1 1 8 0027 0028 0029 0029 0030 0031 0032 0032 0033 0034 1 ] 2 9 0035 0035 0036 0037 0038 0039 0040 0041 0042 0043 1 1 2 8.0 0.0044 0045 0046 0047 0048 0049 0050 0051 0053 0054 1 3 4 1 0055 0056 0058 0059 0060 0062 0063 0065 0066 0068 1 0 0 2 0069 0071 0073 0074 0076 0078 0080 0082 0084 0086 2 1 1 3 0088 0090 0092 0094 0096 0098 0101 0103 0105 0108 2 1 1 4 0110 0113 0116 0118 0121 0124 0127 0130 0133 0136 4 1 2 5 0140 0143 0146 0150 0153 0157 0161 0164 0168 0172 4 2 2 6 0176 0181 0185 0189 0194 0198 0203 0208 0213 0218 5 2 2 7 0223 0229 0234 0240 0245 0251 0257 0264 0270 0276 7 2 3 8 0283 0290 0297 0304 0311 0319 0327 0335 0343 0351 8 2 3 9 0359 0368 0377 0386 0396 0405 0415 0425 0436 0447 11 3 4 9.0 0458 0469 0*80 0492 0504 0517 0530 0543 0556 0570 14 1 0584 0599 0614 0629 0645 0661 0678 0695 0713 0731 18 9.20 0.0749 0751 0753 0755 0757 0759 0761 0763 0765 0767 1 5 6 21 0768 0770 0772 0774 0776 0778 0780 0782 0784 0786 2 1 1 22 0788 0790 0792 0794 0796 0798 0800 0802 0804 0806 .2 1 1 23 0808 0810 0812 0814 0817 0819 0821 0823 0825 0827 2 2 2 24 0829 0831 0833 0835 0838 0840 0842 0844 0846 0848 2 2 2 25 0850 0853 0855 0857 0859 0861 0863 0866 0868 0870 2 3 3 26 0872 0875 0877 0879 0881 0884 0886 0888 0890 0893 2 3 4 27 0895 0897 0899 0902 0904 0906 0909 0911 0913 0916 2 4 4 28 0918 0920 0923 0925 0928 0930 0932 0935 0937 0940 2 4 5 29 0942 0944 0947 0949 0952 0954 0957 0959 0962 0964 3 5 5 9.30 0.0967 0969 0972 0974 0977 0979 0982 0984 0987 0989 3 TT 31 0992 0994 0997 1000 1002 1005 1007 1010 1013 1015 3 1 1 32 1018 1020 1023 1026 1028 1031 1034 1037 1039 1042 3 1 2 33 1045 1047 1050 1053 1056 1058 1061 1064 1067 1069 3 2 2 34 1072 1075 1078 1081 1084 1086 1089 1092 1095 1098 3 3 3 35 1101 1104 1106 1109 1112 1115 1118 1121 1124 1127 3 4 4 36 1130 1133 1136 1139 1142 1145 1148 1151 1154 1157 3 4 5 37 1160 1163 1166 1169 1172 1176 1179 1182 1185 1188 3 5 6 38 1191 1194 1198 1201 1204 1207 1210 1214 1217 1220 3 6 6 39 1223 1226 1230 1233 1236 1240 1243 1246 1250 1253 3 6 7 9.40 0.1256 1260 1263 1266 1270 1273 1277 1280 1283 1287 3 ~3Tl 41 1290 1294 1297 1301 1304 1308 1311 1315 1318 1322 3 i i 42 1325 1329 1333 1336 1340 1343 1347 1351 1354 1358 4 2 2 43 1362 1365 1369 1373 1377 1380 1384 1388 1392 1395 4 3 3 44 1399 1403 1407 1411 1414 1418 1422 1426 1430 1434 4 4 4 45 1438 1442 1446 1450 1454 1458 1462 1466 1470 1474 4 5 6 46 1478 1482 1486 1490 1494 1498 1502 1506 1511 1515 4 5 7 47 1519 1523 1527 1531 1536 1540 1544 1549 1553 1557 4 6 8 48 1561 1566 1570 1574 1579 1583 1588 1592 1596 1601 4 7 9 49 1605 1610 1614 1619 1623 1628 1633 1637 1642 1646 5 8 10

The text on this page is estimated to be only 28.05% accurate

IV, SUBTRACTION LOGAEITHMS, 11 IOg/7 0 1 2 34 5 6 7 8 9 (1 PP. 9.50 0.1651 1656 1660 1665 1670 1674 1679 1684 1688 1693 5 1213 51 1698 1703 1708 1712 1717 1722 1727 1732 1737 1742 5 1 1 52 1747 1752 1757 1762 1767 1772 1777 1782 1787 1792 5 2 3 53 1797 1802 1807 1812 1818 1823 1828 1833 1839 1844 5 4 4 54 1849 1854 1860 1865 1871 1876 1881 1887 1892 1898 5 5 5 55 1903 1909 1914 1920 1925 1931 1936 1942 1948 1953 6 6 7 56 1959 1965 1971 1976 1982 1988 1994 2000 2005 2011 6 7 8 57 2017 2023 2029 2035 2041 2047 2053 2059 2065 2071 6 8 9 58 2077 2084 2090 2096 2102 2108 2115 2121 2127 2134 6 1010 59 2140 2146 2153 2159 2166 2172 2179 2185 2192 2198 7 1112 9.60 0.2205 2211 2218 2225 2231 2238 2245 2252 2259 2265 7 1415 61 2272 2279 2286 2293 2300 2307 2314 2321 2328 2335 7 1 2 62 2342 2350 2357 2364 2371 2378 2386 2393 2400 2408 7 3 3 63 2415 2423 2430 2438 2445 2453 2460 2468 2476 2483 8 4 5 64 2491 2499 2507 2515 2522 2530 2538 2546 2554 2562 8 6 6 65 2570 2578 2586 2595 2603 2611 2619 2628 2636 2644 9 7 8 66 2653 2661 2^70 2678 2687 2695 2704 2713 2721 2730 9 8 9 67 2739 2748 2756 2765 2774 2783 2792 2801 2810 2819 10 1011 68 2829 2838 2847 2856 2866 2875 28S 4 2894 2903 2913 9 1112 69 2922 2932 2942 2951 2961 2971 2981 2991 3001 3011 10 1314 9.70 0.3021 3031 3041 3051 3061 3071 3082 3092 3103 3113 10 1617 71 3123 3134 3145 3155 3166 3177 3188 3198 3209 3220 11 2 2 72 3231 3242 3253 3265 3276 3287 3299 3310 3321 3333 11 3 3 73 3344 3356 3368 3380 3391 3403 3415 3427 3439 3451 12 5 5 74 3463 3476 3488 3500 3513 3525 3538 3550 3563 3576 13 6 7 75 3589 3602 3614 3627 3641 3654 3667 3680 3694 3707 14 8 9 76 3721 3734 3748 3762 3775 3789 3803 3817 3831 3846 14 1010 77 3860 3874 3889 3903 3918 3933 3947 3962 3977 3992 15 1112 78 4007 4022 4038 4053 4069 4084 4100 4116 4131 4147 16 1314 79 4163 4180 4196 4212 4229 4245 4262 4278 4295 4312 17 1415 9.80 0.4329 4346 4364 4381 4398 4416 4434 4452 4470 4488 18 1819 81 4506 4524 4542 4561 4580 4598 4617 4636 4655 4675 19 2 2 82 4694 4714 4733 4753 4773 4793 4813 4834 4854 4875 21 4 4 83 4896 4917 4938 4959 4980 5002 5024 5046 5068 5090 22 5 6 84 5112 513^ 5157 5180 5203 5227 5250 5273 5297 5321 24 7 8 85 5345 5370 5394 5419 5444 5469 5494 5520 5546 5572 26 9 10 86 5598 5624 5651 5678 5705 5732 5760 5787 5815 5844 28 1111 87 5872 5901 5930 5959 5989 6019 6049 6079 6110 6141 31 1313 88 6172 6204 6236 6268 6300 6333 6366 6400 6434 6468 34 1415 89 6502 6537 6572 6608 6644 6680 6717 6754 6792 6830 38 1617 pp. 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 £738 1 2 222 233 333 T 333 344 4 4 2 4 4 4 5 555 566 6 667 777 7 8 3 6 677 788 889 9 9 10 10 10 11 11 11 11 4 8 899 10 10 10 11 11 12 12 12 13 13 14 14 14 15 15 5 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 6 12 13 13 14 14 15 16 16 17 17 18 19 19 20 20 21 22 22 23 7 14 15 15 16 17 18 18 19 20 20 21 22 22 23 24 25 25 26 27 8 16 17 18 18 19 20 21 22 22 23 24 25 26 26 27 28 29 30 30 9 18 19 20 21 22 23 23 24 25 26 27 28 29 30 31 32 32 33 34

The text on this page is estimated to be only 28.96% accurate

12 IV, SUBTRACTION LOGARITHMS lOg/7 0 123 456 789 d PP9.900 0.6868 6872 6876 6880 6884 6888 6892 6895 6899 6903 4 4 5 901 6907 6911 6915 6919 6923 6927 6931 6935 6938 6942 4 0 1 902 6946 6950 6954 6958 6962 6966 6970 6974 6978 6982 4 1 1 903 6986 6990 6994 6998 7002 7006 7010 7014 7018 7022 4 1 2 904 7026 7030 7034 7038 7042 7047 7051 7055 7059 7063 4 2 2 905 7067 7071 7075 7079 7083 70S7 7092 7096 7100 7104 4 2 3 906 7108 7112 7116 7121 7125 7129 7133 7137 7141 7146 4 2 3 907 7150 7154 7158 7162 7167 7171 7175 7179 7183 7188 4 3 4 908 7192 7196 7200 7205 7209 7213 7217 7222 7226 7230 4 3 4 909 7234 7239 7243 7247 7252 7256 7260 7265 7269 7273 5 4 5 9.910 0.7278 7282 7286 7291 7295 7299 7304 7308 7313 7317 4 6 7 911 7321 7326 7330 7335 7339 7343 7348 7352 7357 7361 5 1 1 912 7366 7370 7375 7379 73S3 7388 7392 7397 7401 7406 4 1 1 913 7410 7415 7419 7424 7428 7433 7438 7442 7447 7451 5 2 2 914 7456 7460 7465 7469 7474 7479 7483 7488 7492 7497 5 2 3 915 7502 7506 7511 7516 7520 7525 7530 7534 7539 7544 4 3 4 916 7548 7553 7558 7562 7567 7572 7577 7581 7586 7591 4 4 4 917 7595 7600 7605 7610 7614 7619 7624 7629 7634 7638 5 4 5 918 7643 7648 7653 7658 7663 7667 7672 7677 7682 7687 5 5 6 919 7692 7697 7701 7706 7711 7716 7721 7726 7731 7736 5 5 6 9.920 0.7741 7746 7751 7756 7761 7766 7771 7776 7781 7786 5 8 9 921 7791 7796 7801 7806 7811 7816 7821 7826 7831 7836 5 1 1 922 7841 7846 7851 7856 7861 7867 7872 7877 7882 7887 5 2 2 923 7892 7897 7903 7908 7913 7918 7923 7929 7934 7,939 5 2 3 924 7944 7949 7955 7960 7965 7970 7976 7981 7986 7992 5 3 4 925 7997 8002 8007 8013 8018 8023 8029 8034 8040 8045 5 4 5 926 8050 8056 8061 8066 8072 8077 8083 8088 8094 8099 6 5 5 927 8105 8110 8115 8121 8126 8132 8137 8143 8148 8154 6 6 6 928 8160 8165 8171 8176 8182 8187 8193 8199 8204 8210 5 6 7 929 8215 8221 8227 8232 8238 8244 8249 8255 8261 8266 6 7 8 9.930 0.8272 8278 8284 8289 8295 8301 8307 8312 8318 8324 6 1011 931 8330 8336 8341 8347 8353 8359 8365 8371 8377 8382 6 1 1 932 8388 8394 8400 -8406 8412 8418 8424 8430 8436 8442 6 2 2 933 8448 8454 8460 8466 8472 8478 8484 8490 8496 8502 6 3 3 934 8508 8514 8520 8527 8533 8539 8545 8551 8557 8563 7 4 4 935 8570 8576 8582 8588 8595 8601 8607 8613 8620 8626 6 5 6 936 8632 8638 8645 8651 8657 8664 8670 8676 8683 8689 7 6 7 937 8696 8702 8708 8715 8721 8728 8734 8741 8747 8754 6 7 8 938 8760 8767 8773 8780 8786 8793 8800 8806 8813 8819 7 8 9 939 8826 8833 8839 8846 8853 8859 8866 8873 8879 8886 7 9 10 9.940 0.8893 8900 8906 8913 8920 8927 8934 8940 8947 8954 7 1213 941 8961 8968 8973 8982 8989 8996 9002 9009 9016 9023 7 1 1 942 9030 9037 9044 9051 9058 9065 9073 9080 9087 9094 7 2 3 943 9101 9108 9115 9122 9130 9137 9144 9151 9158 9166 7 4 4 944 9173 9180 9188 9195 9202 9209 9217 9224 9232 9239 7 5 5 945 9246 9254 9261 9269 9276 9284 9291 9299 9306 9314 7 6 7 946 9321 9329 9336 9344 9351 9359 9367 9374 9382 9390 7 7 8 947 9397 9405 9413 9421 9428 9436 9444 9452 9460 9467 8 8 9 948 9475 9483 9491 9499 9507 9515 9523 9531 9539 9547 8 10 10 949 9555 9563 9571 9579 9587 9595 9603 9611 96199628 8 11 12

The text on this page is estimated to be only 27.19% accurate

CONTINUED. 13 lOg/7 0 123 456 7 8 9 d pp. 9.950 0.9636 96449652 9660 9669 9677 9685 9694 9702 9710 9 1415 951 9719 97279735 9744 9752 9761 9769 9778 9786 9795 1 2 952 9803 98129820 9829 9838 9846 9855 9864 9872 9881 9 3 3 953 9890 9899 9907 9916 9925 9934 9943 9951 9960 9969 9 4 5 954 9978 9987 9996*0005 *0014*C023*0032 *0041*0050*0060 9 6 6 955 1.0069 00780087 009f 0106 0115 0124 0133 0143 0152 c 7 8 956 0161 0171 0180 0190 0199 0209 0218 0228 0237 0247 9 8 9 957 0256 02660276 0285 0295 0305 0314 0324 0334 0344 10 1011 958 0354 0364-0373 0383 0393 0403 0413 0423 0433 0443 10 1112 959 0453 0464 0474 0484 0494 0504 0514 0525 0535 0545 11 1314 9.960 1.0556 05660576 0587 0597 0608 0618 0629 0640 0650 11 1617 961 0661 0671 0682 0693 0704 0714 0725 0736 0747 0758 11 2 2 962 0769 07800791 0802 0813 0824 0835 0846 0857 0868 12 3 3 963 0880 0891 0902 0913 0925 0936 0948 0959 0971 0982 12 5 5 964 0994 1005 1017 1028 1040 1052 1064 1075 1087 1099 r 6 7 965 1111 11231133 1147 1159 1171 1183 1195 1207 1220 2 8 9 966 1232 12441257 1269 1281 1294 1306 1319 1331 1344 ± 1010 967 1357 13691382 1395 1408 1420 1433 1446 1459 1472 3 1112 968 1485 14981512 1525 1538 1551 1565 1578 1591 1605 2 1314 969 1618 16321645 1659 1673 1686 1700 1714 1728 1742 14 1415 9.970 1.1756 1770 1784 1798 1812 1826 1841 1855 1869 1884 14 1819 971 1898 1913 1927 1942 1956 1971 1986 2001 2016 2031 15 2 2 972 2046 2061 2076 2091 2106 2121 2137 2152 2167 2183 16 4 4 973 2199 2214 2230 2246 2261 2277 2293 2309 2325 2341 16 5 6 974 2357 2374 2390 2406 2423 2439 2456 2473 2489 2506 17 7 8 975 2523 25402557 2574 2591 2608 2625 2643 2660 2678 17 910 976 2695 27132731 2748 2766 2784 2802 2820 2838 2857 18 1111 977 2875 2893 2912 2931 2949 2968 2987 3006 3025 3044 19 1313 978 3063 30823102 3121 3141 3161 3180 3200 3220 3240 20 1415 979 3260 32803301 3321 3342 3362 3383 3404 3425 3446 21 1617 9.980 1.3467 34883510 3531 3553 3575, 3596 3618 3640 3663 22 2021 981 3685 3707 3730 3753 3775 3798 3821 3845 3868 3891 24 2 2 982 391^ 39393962 3986 4010 4035 4059 4084 4108 4133 25 4 4 983 4158 4183 4208 4234 4259 4285 4311 4337 4363 4390 26 6 6 984 4416 4443 4470 4497 4524 4552 4579 4607 4635 4663 29 8 8 985 4692 47204749 4778 4807 4836 4866 4896 4926 4956 30 1011 986 4986 5017 5048 5079 5110 5142 5174 5206 5238 5270 33 1213 987 5303 5336 5370 5403 5437 5471 5505 5540 5575 5610 36 1415 988 5646 5682 5718 5754 5791 5828 5866 5903 5942 5980 39 1617 989 6019 6058 6097 6137 6178 6218 6259 6301 6343 6385 43 1819 9.990 1.6428 6471 6514 6559 6603 6648 6693 6739 6786 6833 7 2223 991 6880 69286977 7026 7076 7126 7177 7228 7281 7333 S4 2 2 992 7387 7441 7496 7551 7608 7665 7722 7781 7840 7901 61 4 5 993 7962 80248087 8151 8215 8281 8348 8416 8485 8555 "1 7 7 994 8626 86998773 8848 8924 9002 9081 9162 9244 9328 55 9 9 995 9413 9500 9589 9680 9773 9868 9965 *0065*0166*0270 11 12 996 2.0377 0487 0599 0714 0833 0955 1080 1209 1342 1480 1314 997 1622 1768 1920 2078 2241 2411 2588 2772 2965 3166 1516 998 3378 36003834 4082 4345 4624 4924 5245 5592 5969 1818 999 6383 68407351 7930 8599 9391*0359 * 1608*3369*63 78 2021

The text on this page is estimated to be only 28.58% accurate

14 V. LOGARITHMIC SINES AND COSINES. log1 sin n° log cos wc n° .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 d 0 7. 2419 5429 7190 8439 9408*0200 *0870*145Q*1961 *2419 89 1 8.2419 2832 3210 3558 3880 4179 4459 4723 4971 5206 5428 88 2 5428 5640 5842 6035 6220 6397 6567 6731 6889 7041 7188 87 3 7188 7330 7468 7602 7731 7857 7979 8098 8213 8326 8436 86 4 8436 8543 8647 8749 8849 8946 9042 9135 9226 9315 9403 85 88 5 9403 9489 9573 9655 9736 9816 9894 9970*0046*0120 *0192 84 72 6 9.0192 0264 0334 0403 0472 0539 0605 0670 0734 0797 0859 83 62 7 0859 0920 0981 1040 1099 1157 1214 1271 1326-1381 1436 82 55 8 1436 1489 1542 1594 1646 1697 1747 1797 1847 1895 1943 81 48 9 1943 1991 2038 2085 2131 2176 2221 2266 2310 2353 2397 80 44 10 9.2397 2439 2482 2524 2565 2606 2647 2687 2727 2767 2806 W 39 11 2806 2845 2883 2921 2959 2997 3034 3070 3107 3143 3179 78 36 12 3179 3214 3250 3284 33193353 3387 3421 345^ 3488 3521 77 33 13 3521 3554 3586 3618 3650 3682 3713 3743 3775 3806 3837 76 31 14 3837 3867 3897 3927 3957 3986 4015 4044 4073 4102 4130 75 28 15 4130 4158 4186 4214 4242 4269 4296 4323 4350 4377 4403 74 26 16 4403 4430 4456 4482 4508 4533 4559 4584 4609 4634 4659 73 25 17 4659 4684 4709 4733 4757 4781 4805 4829 4853 4876 4900 72 24 18 4900 4923 4946 4969 4992 5015 5037 5060 5082 5104 5126 71 22 19 5126 5148 5170 5192 5213 5235 5256 5278 5299 5320 5341 70 21 20 9.5341 5361 5382 5402 5423 5443 5463 5484 5504 5523 5543 69 20 21 5543 5563 5583 5602 5621 5641 5660 5679 5698 5717 5736 68 19 22 5736 5754 5773 5792 5810 5828 5847 5865 5883 5901 5919 67 18 23 5919 5937 5954 5972 5990 6007 6024 6042 6059 6076 6093 66 17 24 6093 6110 6127 6144 6161 6177 6194 6210 6227 6243 6259 65 16 25 6259 6276 6292 6308 6324 6340 6356 6371 6387 6403 6418 64 15 26 6418 6434 6449 6465 6480 6495 6510 6526 6541 6556 6570 63 14 27 6570 6585 6600 6615 6629 6644 6659 6673 6687 6702 6716 62 14 28 6716 6730 6744 6759 6773 6787 6801 6814 6828 6842 6856 61 14 29 6856 6869 6883 6896 6910 6923 6937 6950 6963 6977 6990 60 13 lw 9.6990 7003 7016 7029 7042 7055 7068 7080 7093 7106 7118 59 12 31 7118 7131 7144 7156 7168 7181 7193 7205 7218 7230 7242 58 12 32 7242 7254 7266 7278 7290 7302 7314 7326 7338 7349 7361 57 12 33 7361 7373 7384 7396 7407 7419 7430 7442 7453 7464 7476 56 12 34 7476 7487 7498 7509 75207531 7542 7553 7564 7575 7586 55 11 35 7586 7597 7607 7618 7629 7640 7650 7661 7671 7682 7692 54 10 36 7692 7703 7713 7723 7734 7744 7754 7764 7774 7783 7793 53 10 37 7795 7805 7815 782^ 7835 7844 7854 7864 7874 7884 7893 52 9 38 7893 7903 7913 7922 7932 7941 7951 7960 7970 7979 7989 51 10 39 7989 7998 8007 8017 80268035 8044 8053 8063 8072 8081 50 9 40 9.8081 8090 8099 8108 8117 8125 8134 8143 8152 8161 8169 49 8 41 8169 8178 8187 8195 8204 8213 8221 8230 8238 8247 8255 48 8 42 .8255 8264 8272 8280 8289 8297 8305 8313 8322 8330 8338 47 8 43 8338 8346 8354 8362 8370 8378 8386 8394 8402 8410 8418 46 8 44 8418 8426 8433 8441 8449 8457 8464 8472 8480 8487 8495 45 8 45 8495 8502 8510 8517 8525 8532 8540 8547 8555 8562 8569 44 7 46 8569 8577 8584 8591 8598 8606 8613 8620 8627 8634 8641 43 7 47 8641 8648 8655 8662 8669 8676 8683 8690 8697 8704 8711 42 7 48 8711 8718 8724 8731 8738 8745 8751 8758 8765 8771 8778 41 7 49 8778 8784 8791 8797 8804 8S10 8817 8823 8830 8836 8843 40 7 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 n^ ¥

The text on this page is estimated to be only 27.37% accurate

V. LOGARITHMIC SINES AND COSINES. 15 log sinn° log cos n° n° .0 .1 .2 .3 .4 5 .6 | .7 .8 .9 1.0 d 5? 9.8843 8849 8855 8862 8868 8874 8880 8887 8893 8899 8905 39 ~6 51 8905 8911 8917 8923 8929 8935 8941 8947 8953 8959 8965 38 6 52 8965 8971 8977 8983 8989 8995 9000 9006 9012 9018 9023 37 5 53 9023 9029 9033 9041 9046 9052 9057 9063 9069 9074 9080 36 6 54 9080 9085 9091 9096 9101 9107 9112 9118 9123 9128 9134 35 6 55 9134 9139 9144 9149 915591609165 917091759181 9186 34 5 56 9186 9191 9196 9201 9206 9211 9216 9221 9226 9231 9236 33 5 57 9236 9241 9246 9251 9255 9260 9265 9270 9275 9279 9284 32 5 58 9284 9289 9294 9298 9303 9308 9312 9317 9322 9326 9331 31 5 59 9331 9335 9340 9344 9349 9353 9358 9362 9367 9371 9375 30 4 60 9.9375 9380 9384 9388 9393 9397 9401 9406 9410 9414 9418 29 4 61 9418 9422 9427 9431 9435 9439 9443 9447 9451 9455 9459 28 4 62 9459 9463 9467 9471 9475 9479 9483 9487 9491 9495 9499 27 4 63 9499 950395079510 9514 9518 9522 9525 9529 9533 9537 26 4 64 9537 9540 9544 9548 9551 9555 9558 9562 9566 9569 9573 25 4 65 9573 9576 95TO 9583 9587 9590 9594 9597 9601 9604 9607 24 3 66 9607 9611 9614 9617 9621 9624 9627 9631 9634 9637 9640 23 3 67 9640 9643 9647 9650 9653 9656 9659 9662 9666 9669 9672 22 3 63 9672 9675 9678 9681 9684 9687 9690 9693 9696 9699 9702 21 3 69 9702 9704 9707 9710 9713 9716 9719 9722 9724 9727 9730 20 3 70 9.9730 9733 9735 9738 9741 9743 9746 9749 9751 9754 9757 19 T 71 9757 9759 9762 9764 9767 9770 9772 9775 9777 9780 9782 18 2 72 9782 9785 9787 9789 9792 9794 9797 9799 9801 9804 9806 17 2 73 9806 9808 9811 9813 9815 9817 9820 9822 9824 9826 9828 16 2 74 9828 9831 9833 9835 9837 9839 9841 9843 9845 9847 9849 15 2 75 9849 9851 9853 9855 9857 9859 9861 9863 9865 9867 9869 14 2 76 9869 9871 9873 9875 9876 9878 9880 9882 9884 9885 9887 13 2 77 9887 9889 9891 9892 9894 9896 9897 9899 9901 9902 9904 12 2 78 9904 9906 9907 9909 9910 9912 9913 9915 9916 9918 9919 11 1 79 9919 9921 9922 9924 9925 9927 9928 9929 9931 9932 9934 10 2 80 9.9934 993^ 9936 9937 9939 9940 9941 9943 9944 9945 9946 9 T 81 9946 9947 9949 9950 9951 9952 9953 9954 9955 9956 9958 8 2 82 9958 9959 9960 9961 9962 9963 9964 9965 9966 9967 9968 7 1 83 9968 9968 9969 9970 9971 9972 9973 9974 9975 9975 9976 6 1 84 9976 9977 9978 9978 9979 9980 9981 9981 9982 9983 9983 5 0 85 9983 9984 9985 9985 9986 9987 9987 9988 9988 9989 9989 4 0 86 9989 9990 9990 9991 9991 9992 9992 9993 9993 9994 9994 3 0 87 9994 9994 9995 9995 9996 9996 9996 9996 9997 9997 9997 2 0 88 9997 9998 9998 9998 9998 9999 9999 9999 9999 9999 9999 1 0 89 9999 9999 0000 0000 0000 0000 0000 0000 0000 0000 0000 0 0 1.0 .9 .8 .7 .6 , 5 .4 .3 .2 .1 .0 n° d pp. 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 1 1 1 1 2 2 222 ~2 222 233 333 3 2 223 333 344 4 4 4 5 555 566 6 3 344 4 5 5 5 5 6 6 677 788 889 9 4 4 5 5 666 778 8 899 10 10 10 11 11 12 12 5 667 788 9 9 10 10 11 11 12 12 13 13 14 14 15 15 6 778 8 9 10 10 11 11 12 13 13 14 14 15 16 1617 17 18 7 889 10 11 11 12 13 13 14 15 15 16 17 18 18 19 20 20 21 8 9 10 10 11 12 13 14 14 15 16 17 18 18 19 20 21 22 22 23 24 9 10 11 12 13 14 14 15 16 17 18 19 20 21 22 23 23 24 25 26 27

The text on this page is estimated to be only 28.14% accurate

16 V. LOGARITHMIC SINES AND COSINES log- sin n° log cos n° n° 0 123 4567 8 9 10 d (M) 6. 2419 5429 7190 8439 9408*0200 *OS70*145Q*1961 *2419 89.9 0.1 7.2419 283332113558 3880 4180 4460 4723 4971 5206 5429 89.8 0.2 5429 5641 5843 6036 6221 6398 6568 6732 6890 7043 7190 89.7 0.3 7190 7332 7470 7604 7734 7859 7982 8101 8217 8329 8439 89.6 0.4 8439 8547 8651 8753 8853 8951 9046 9140 9231 9321 9408 89.5 87 0.5 9408 949495799661 9743 9822 9901 9977*0053*0127 *0200 89.4 73 0.6 8.0200 0272 0343 0412 0480 0548 0614 0679 0744 0807 0870 89.3 63 0.7 0870 0931 0992 1052 1111 1169 1227 1284 1340 1395 1450 89.2 55 0.8 1450 1503 1557 1609 1661 1713 1764 1814 1863 1912 1961 89.1 49 0.9 1961 200920562103 2150 2196 2241 2286 2331 2375 2419 89.0 44 :LO 8.2419 2462 2505 2547 2589 2630 2672 2712 2753 2793 2832 88.9 39 1.1 2832 2872 2911 2949 2988 3025 3063 3100 3137 3174 3210 88.8 36 1.2 3210 324632823317 3353 3388 3422 3456 349.1 3524 3558 88.7 34 1.3 3558 3591 3624 3657 3689 3722 3754 3786 3817 3848 3880 88.6 32 1.4 3880 3911 3941 3972 4002 4032 4062 4091 4121 4150 4179 88.5 29 1.5 4179 4208 4237 4265 4293 4322 4349 4377 4405 4432 4459 88.4 27 1.6 4459 448645134540 4567 4593 4619 4645 4671 4697 4723 88.3 26 1.7 4723 474847734799 4824 4848 4873 4898 4922 4947 4971 88.2 24 1.8 4971 4995 5019 5043 5066 5090 5113 5136 5160 5183 5206 88.1 22 1.9 5206 522852515274 5296 5318 5340 5363 5385 5406 5428 88.0 22 2.0 8.5428 5450 5471 5493 5514 5535 5557 5578 5598 5619 5640 87.9 21 2.1 5640 5661 5681 5702 5722 5742 5762 5782 5802 5822 5842 87.8 20 2.2 5842 5862 5881 5901 5920 5939 5959 5978 5997 6016 6035 87.7 19 2.3 6035 605460726091 6110 6128 6147 6165 6183 6201 6220 87.6 19 2.4 6220 6238 6256 6274 6291 6309 6327 6344 6362 6379 6397 87.5 18 2.5 6397 6414 6431 6449 6466 6483 6500 6517 6534 6550 6567 87.4 17 2.6 6567 6584 6600 6617 6633 6650 6666 6682 6699 67] 5 6731 87.3 16 2.7 6731 674767636779 6795 6810 6826 6842 6858 6873 6889 87.2 16 2.8 6889 6904 6920 6935 69506965 6981 6996 7011 7026 7041 87.1 15 2.9 7041 7056 7071 7086 7100 7115 7130 7144 7159 7174 7188 87.0 14 3.0 8.7188 7202 7217 7231 7245 7260 7274 7288 7302 7316 7330 86.9 14 3.1 7330 7344 7358 7372 7386 7400 7413 7427 7441 7454 7468 86.8 14 3.2 7468 7482 7495 7508 7522 7535 7549 7562 7575 7588 7602 86.7 14 3.3 7602 7615 7628 7641 7654 7667 7680 7693 7705 7718 7731 86.6 13 3.4 7731 7744 7756 7769 7782 7794 7807 7819 7832 7844 7857 86.5 13 3.5 7857 7869 7881 7894 7906 7918 7930 7943 7955 7967 7979 86.4 12 3.6 7979 7991 8003 8015 8027 8039 8051 8062 8074 8086 8098 86.3 12 3.7 8098 810981218133 8144 8156 8168 8179 8191 8202 8213 86.2 11 3.8 8213 8225 8236 8248 8259 8270 8281 8293 8304 8315 8326 86.1 11 3.9 8326 8337 8348 8359 S370 8381 8392 8403 8414 8425 8436 86.0 11 4.0 8.8436 8447 8457 8468 8479 8490 8500 8511 8522 8532 8543 85.9 11 4.1 8543 8553 85648575 8585 8595 8606 8616 8627 8637 8647 85.8 10 4.2 8647 8658 8668 8678 8688 8699 8709 8719 8729 8739 8749 85.7 10 4.3 8749 8759 8769 8780 8790 8799 8809 8819 8829 8839 8849 85.6 10 4.4 8849 8859 8869 8878 8888 8898 8908 8917 8927 8937 8946 85.5 9 4.5 8946 8956 8966 8975 8985 8994 9004 9013 9023 9032 9042 85.4 10 4.6 9042 905190609070 9079 9089 9098 9107 9116 9126 9135 85.3 9 4.7 9135 914491539162 9172 9181 9190 9199 9208 9217 9226 85.2 9 4.8 9226 9235 9244 9253 9262 9271 92SO 9289 9298 9307 9315 85.1 8 4.9 9315 9324 9333 9342 9351 9359 9368 9377 9386 9394 9403 85.0 9 10 987 654 321 0 n° d

The text on this page is estimated to be only 26.78% accurate

CONTINUED, log1 sin nc 17 log* cos n° n° 0 123 4 5 6789 10 (1 5.0 8.9403941294209429 9437 9446 9455 9463 9472 9480 9489 84.99 5.1 9489949795069514 9523 9531 9539 9548 9556 9565 9573 84.88 5.2 9573 9581 9589 9598 9606 9614 9623 9631 9639 9647 9655 84.78 5.3 9655 9664 9672 9680 9688 9696 9704 9712 9720 9728 9736 84.68 5.4 9736 9744 9752 9760 9768 9776 9784 9792 9800 9808 9816 84.58 5.5 9816 9824 9831 9839 9847 9855. 9863 9870 9878 9886 9894 84.48 5.6 9894 9901 9909 9917 9925. 9932 9940 9948 9955 9963 9970 84.37 5.7 9970 9978 9986 9993 *0001*OOOS*0016 *0023*0031*003S *0046 84.28 5.8 9.0046 0053 0061 0068 0075 0083 0090 0098 0105 0112 0120 84.18 5.9 0120012701340142 0149 0156 0163 0171 0178 0185 0192 84.07 6.0 9.0192 0200 0207 0214 0221 0228 0235 0243 0250 0257 0264 83.97 6.1 0264 0271 0278 0285 0292 0299 0306 0313 0320 0327 0334 83.87 6.2 0334034103480355 0362 0369 0376 0383 0390 0397 0403 83.76 6.3 0403 0410 0417 0424 0431 0438 0444 0451 0458 046^ 0472 83.6 7 6.4 0472 0478 0485 0492 0498 0505 0512 0519 0525 0532 0539 83.57 6.5 0539 0545 0552 0558 0565 0572 0578 0585 0591 0598 0605 83.47 6.6 0605 0611 0618 0624 0631 0637 0644 0650 0657 0663 0670 83.37 6.7 0670 0676 0683 0689 0695 0702 0708 0715 0721 0727 0734 83.27 6.8 0734 0740 0746 0753 0759 0765 0772 0778 0784 0790 0797 83.17 6.9 0797 0803 0809 0816 0822 0828 0834 0840 0847 0853 0859 83.06 7.0 9.0859 0865 0871 0877 0884 0890 0896 0902 0908 0914 0920 82.96 7.1 0920 0926 0932 0938 0945 0951 0957 0963 0969 0975 0981 82.86 7.2 0981 0987 0993 0999 1005 1011 1017 1022 1028 1034 1040 82.76 7.3 1040 1046 1052 1058 1064 1070 1076 1081 1087 1093 1099 82.66 7.4 1099 1105 1111 1116 1122 1128 1134 1140 1145 1151 1157 82.56 7.5 1157 1163 1168 1174 1180 1186 1191 1197 1203 1208 1214 82.46 7.6 1214 1220 1226 1231 1237 1242 1248 1254 1259 1265 1271 82.36 7.7 1271 1276 1282 1287 1293 1299 1304 1310 1315 1321 1326 82.25 7.8 1326 1332 1337 1343 1348 1354 1359 1365 1370 1376 1381 82.1 5 7.9 1381 1387 1392 1398 1403 1409 1414 1419 1425 1430 1436 82.06 8.0 9.1436 1441 1446 1452 1457 1462 1468 1473 1478 1484 1489 81.95 8.1 1489 1494 1500 1505 1510 1516 1521 1526 1532 1537 1542 81.85 8.2 1542 1547 1553 1558 1563 1568 1574 1579 1584 1589 1594 81.75 8.3 1594 1600 1605 1610 1615 1620 1625 1631 1636 1641 1646 81.65 8.4 1646 1651 1656 1661 1666 1672 1677 1682 1687 1692 1697 81.55 8.5 1697 1702 1707 1712 1717 1722 1727 1732 1737 1742 1747 81.45 8.6 1747 1752 1757 1762 1767 1772 1777 1782 1787 1792 1797 81.35 8.7 179718021807 1812 1817 1822 1827 1832 1837 1842 1847 81.25 8.8 1847 1851 1856 1861 1866 1871 1876 1881 1886 1890 1895 81.15 8.9 1895 1900 1905 1910 1915 1919 1924 1929 1934 1939 1943 81.04 10 9 8 7 6 5 4 321 0 n° o 0 123 456 789 S log sin .1 6 6.6 7.2 7.8 8.4 9 9.6 10.2 10.8 11.4 0.00 1 .7581 .2 12 12.6 13.2 13.8 ] 14.4 15 15.6 16.2 16.8 17.4 1.11 1 .7582 8.2872 .3 18 18.6 19.2 19.8S !0.4 21 21.6 22.2 22.8 23.4 2.40 1 .7583 8.6220 .4 24 24.6 25.2 25.8 J 56.4 27 27.6 28.2 28.8 29.4 3.21 1 .7584 8.7482 .5 30 30.6 31.2 31.8; 52.4 33 33.6 34.2 34.8 35.4 3.85 1 .7585 8.8270 .6 36 36.6 37.2 37.8 ; 58.4 39 39.6|40.2 40.8 41.4 4.40 8.8849 .7 42 42.6 43.2 43.8^ K.4 45 45.6 46.2 46.8 47.4 .8 48 48.6 49.2 49.850.4 51 51.6 52.2 52.8 53.4 .9 54 54.6 55.2 55.8|56.4 57 57.6 58.2 58.8 59.4

The text on this page is estimated to be only 28.32% accurate

18 VI. LOGABITEMIO TANGENTS AND COTANGENTS* log - tan n° log" cotan n° n° .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 d ~Q 7. 2419 5429 7190 8439 9409*0200 *0870*145Q*1962 *2419 89 1 8.2419 2833 3211 3559 3881 4181 4461 4725 4973 5208 5431 88 2 5431 5643 5845 6038 6223 6401 6571 6736 6894 7046 7194 87 3 7194 7337 7475 7609 7739 7865 7988 8107 8223 8336 8446 86 4 8446 8554 8659 8762 8862 8960 9056 9150 9241 9331 9420 85 89 5 9420 9506 9591 9674 9756 9836 9915 9992*0068*0143 *0216 84 73 6 9.0216 0289 0360 0430 0499 0567 0633 0699 0764 0828 0891 83 63 7 0891 0954 1015 1076 1135 1194 1252 1310 1367 1423 1478 82 55 8 1478 1533 1587 1640 1693 1745 1797 1848 1898 1948 1997 81 49 9 1997 2046 2094 2142 2189 2236 2282 2328 2374 2419 2463 80 44 10 9.2463 2507 2551 2594 2637 2680 2722 2764 2805 2846 2887 ^9 41 11 2887 2927 2967 3006 3046 3085 3123 3162 3200 3237 3275 78 38 12 3275 3312 3349 3385 3422 3458 3493 3529 3564 3599 3634 77 35 13 3634 3668 3702 3736 3770 3804 3837 3870 3903 3935 3968 76 33 14 3968 4000 4032 4064 4095 4127 4158 4189 4220 4250 4281 75 31 15 4281 4311 4341 4371 4400 4430 4459 4488 4517 4546 4575 74 29 16 4575 4603 4632 4660 4688 4716 4744 4771 4799 4826 4853 73 27 17 4853 4880 4907 4934 4961 4987 5014 5040 5066 5092 5118 72 26 18 5118 5143 5169 5195 5220 5245 5270 5295 5320 5345 5370 71 25 19 5370 5394 5419 5443 5467 5491 5516 5539 5563 5587 5611 70 24 20 9.5611 5634 5658 5681 5704 5727 5750 5773 5f96 5819 5842 69 23 21 5842 5864 5887 5909 5932 5954 5976 5998 6020 6042 6064 68 22 22 6064 6086 6108 6129 6151 6172 6194 6215 6236 6257 6279 67 22 23 6279 6300 6321 6341 6362 6383 6404 6424 6445 6465 6486 66 21 24 6486 6506 6527 6547 6567 6587 6607 6627 6647 6667 6687 65 20 25 6687 6706 6726 6746 6765 6785 6804 6824 6843 6863 6882 64 19 26 6882 6901 6920 6939 6958 6977 6996 7015 7034 7053 7072 63 19 27 7072 7090 7109 7128 7146 7165 7183 7202 7220 7238 7257 62 19 28 7257 7275 7293 7311 7330 7348 7366 7384 7402 7420 7438 61 18 29 7438 7455 7473 7491 7509 7526 7544 7562 7579 7597 7614 60 17 30 9.7614 7632 7649 7667 7684 7701 7719 7736 7753 7771 7788 59 17 31 7788 7805 7822 7839 7856 7873 7890 7907 7924 7941 7958 58 17 32 7958 7975 7992 8008 8025 8042 8059 8075 8092 8109 8125 57 16 33 8125 8142 8158 8175 8191 8208 8224 8241 8257 8274 8290 56 16 34 8290 8306 8323 8339 8355 8371 8388 8404 8420 8436 8452 55 16 35 8452 8468 8484 8501 8517 8533 8549 8565 8581 8597 8613 54 16 36 8613 8629 8644 8660 8676 8692 8708 8724 8740 8755 8771 53 16 37 8771 8787 8803 8818 8834 8850 8865 8881 8897 8912 8928 52 16 38 8928 8944 8959 8975 8990 9006 9022 9037 9053 9068 9084 51 16 39 9084 9099 9115 9130 9146 9161 9176 9192 9207 9223 9238 50 15 40 9.9238 9254 9269 9284 9300 9315 9330 9346 9361 9376 9392 49 16 41 9392 9407 9422 9438 9453 9468 9483 9499 9514 9529 9544 48 15 42 9544 9560 9575 9590 9605 9621 9636 9651 9666 9681 9697 47 16 43 9697 9712 9727 9742 9757 9772 9788 9803 9818 9833 9848 46 15 44 9848 9864 9879 9894 9909 9924 9939 9955 9970 9985 *0000 45 15 45 0.0000 0015 0030 0045 0061 0076 0091 0106 0121 0136 0152 44 16 46 0152 0167 0182 0197 0212 0228 0243 0258 0273 0288 0303 43 15 47 0303 0319 0334 0349 0364 0379 0395 0410 0425 0440 0456 42 16 48 0456 0471 0486 0501 0517 0532 0547 0562 0578 0593 0608 41 15 49 0608 0624 0639 0654 0670 0685 0700 0716 0731 0746 0762 40 16 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 n° d

The text on this page is estimated to be only 28.23% accurate

VI. LOGARITHMIC) TANGENTS AND COTANGENTS. 19 log- tan n° log- cotan n° n° .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 d 50 0.0762 0777 0793 0808 0824 0839 0854 0870 0885 0901 0916 39 15 51 0916 0932 0947 0963 0978 0994 1010 1025 1041 1056 1072 38 16 52 1072 1088 1103 1119 1135 1150 1166 1182 1197 1213 1229 37 16 53 1229 1245 1260 1276 1292 1308 1324 1340 1356 1371 1387 36 16 54 1387 1403 1419 1435 1451 1467 1483 1499 1516 1532 1548 35 16 55 1548 1564 1580 1596 1612 1629 1645 1661 1677 1694 1710 34 16 56 1710 1726 1743 1759 1776 1792 1809 1825 1842 1858 1875 33 17 57 1873 1891 1908 1925 1941 1958 1975 1992 2008 2025 2042 32 17 58 2042 2059 2076 2093 2110 2127 2144 2161 2178 2195 2212 31 17 59 2212 2229 2247 2264 2281 2299 2316 2333 2351 2368 2386 30 18 60 0.2386 2403 2421 2438 2456 2474 2491 2509 2527 2545 2562 29 17 61 2562 2580 2598 2616 2634 2652 2670 2689 2707 2725 2743 28 18 62 2743 2762 2780 2798 2817 2835 2854 2872 2891 2910 2928 27 18 63 2928 2947 2966 2985. 3004 3023 3042 3061 3080 3099 3118 26 19 64 3118 3137 3157 3176 3196 3215 3235 3254 3274 3294 3313 25 19 65 3313 3333 3353 3373 3393 3413 3433 3453 3473 3494 3514 24 20 66 3514 3535 3555 3576 3596 3617 3638 3659 3679 3700 3721 23 21 67 3721 3743 3764 3785 3806 3828 3849 3871 3892 3914 3936 22 22 68 3936 3958 3980 4002 4024 4046 4068 4091 4113 4136 4158 21 22 69 4158 4181 4204 4227 4250 4273 4296 4319 4342 4366 4389 20 23 70 0.4389 4413 4437 4461 4484 4509 4533 4557 4581 4606 4630 19 24 71 4630 465^ 4680 4705 4730 4755 4780 4805 4831 4857 4882 18 25 72 4882 4908 4934 4960 4986 5013 5039 5066 5093 5120 5147 17 27 73 5147 5174 5201 5229 5256 5284 5312 5340 5368 5397 5425 16 28 74 5425 5454 5483 5512 5541 5570 5600 5629 5659 5689 5719 15 30 75 5719 5750 5780 5811 5842 5873 5905 5936 5968 6000 6032 1432 76 6032 6065 6097 6130 6163 6196 6230 6264 6298 6332 6366 13 34 77 6366 6401 6436 6471 6507 6542 6578 6615 6651 6688 6725 12 37 78 6725 6763 6800 6838 6877 6915 6954 6994 7033 7073 7113 11 40 79 7113 7154 7195 7236 7278 7320 7363 7406 7449 7493 7537 10 44 80 0.7537 7581 7626 7672 7718 7764 7811 7858 7906 7954 8003 9 49 81 8003 8052 8102 8152 8203 8255 8307 8360 8413 8467 8522 8 55 82 8522 8577 8633 8690 8748 8806 8865 8924 8985 9046 9109 7 63 83 9109 9172 9236 9301 9367 9433 9501 9570 9640 9711 9784 6 73 84 9784 9857 9932*0008 *0085*0164*0244 *0326*0409*0494 *05SO 5 86 85 1.0580 0669 0759 0850 0944 1040 1138 1238 1341 1446 1554 4 86 1554 1664 1777 1893 2012 2135 2261 2391 2525 2663 2806 3 87 2806 2954 3106 3264 3429 3599 3777 3962 4155 4357 4569 2 88 4569 4792 5027 5275 5539 5819 6119 6441 6789 7167 7581 1 89 7581 8038 8550 9130 9800*0591*1561 *2810*4571*7581 0 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 n° d PP. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 SO 1 2 333 667 777 788 8 889 999 5 5 5 91010 5 10 3 9 10 10 10 11 11 11 11 12 12 12 13 13 13 14 14 14 14 15 15 4 12 13 13 14 14 14 15 15 16 16 16 17 17 18 18 18 19 19 20 20 5 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 6 19 19 20 20 21 22 22 23 23 24 25 25 26 26 27 28 28 29 29 30 7 22 22 23 24 25 25 26 27 27 28 29 29 30 31 32 32 33 34 34 35 8 • 25 26 26 27 28 29 30 30 31 32 33 34 34 35 36 37 38 38 39 40 9 28 29 30 31 32 32 33 34 35 36 37 38 39 40 41 41 424344 45

The text on this page is estimated to be only 27.34% accurate

20 VI, LOGABITEMIO TANGENTS AND COTANGENTS log tan n° log cotan n6 n° 0 123 456 7 8 9 10 d 0.0 6. 2419 5429 7190 84399408*0200 *OS70*1450*1961 *2419 89.9 0.1 7.2419 283332113558 38804180 4460 4723 4972 5206 5429 89.8 0.2 5429 5641 5843 6036 6221 6398 6569 6732 6890 7043 7190 89.7 0.3 7190 7332 7470 7604 7734 7860 7982 8101 8217 8329 8439 89.6 0.4 8439 854786518754 88538951 9046 9140 9231 9321 9409 89.5 88 0.5 9409 949595799662 97439823 9901 9978*0053*0127 *0200 89.4 73 0.6 8.0200 0272 0343 0412 0481 0548 0614 0680 0744 0807 0870 89.3 63 0.7 0870 093209921052 11111170 1227 1284 1340 1395 1450 89.2 55 0.8 1450 150415571610 1662 1713 1764 1814 1864 1913 1962 89.1 49 0.9 1962 201020572104 21502196 2242 2287 2331 2376 2419 89.0 43 1.0 8.2419 2462 2505 2548 25902631 2672 2713 2754 2794 2833 88.9 39 1.1 2833 2873 2912 2950 2988 3026 3064 3101 3138 3175 3211 88.8 36 1.2 3211 324732833318 3354 3389 3423 3458 3492 3525 3559 88.7 34 1.3 3559 3592 3625 3658 36913723 3755 3787 3818 3850 3881 88.6 31 1.4 3881 391239433973 40034033 4063 4093 4122 4152 4181 88.5 29 1.5 4181 421042384267 42954323 4351 4379 4406 4434 4461 88.4 27 1.6 4461 448845154542 45684595 4621 4647 4673 4699 4725 88.3 26 1.7 4725 475047754801 48264851 4875 4900 4924 4949 4973 88.2 24 1.8 4973 4997 5021 5045 50685092 5115 5139 5162 5185 5208 88.1 23 1.9 5208 5231 5253 5276 52985321 5343 5365 5387 5409 5431 88.0 22 2.0 8.5431 5453 5474 5496 55175538 5559 5580 5601 5622 5643 87^9 21 2.1 5643 5664 5684 5705 57255745 5765 5785 5805 5825 5845 87.7 20 2.2 5845 5865 5884 5904 5923 5943 5962 5981 6000 6019 6038 87.6 19 2.3 6038 605760766095 61136132 6150 6169 6187 6205 6223 87.8 18 2.4 6223 6242 6260 6277 6295 6313 6331 6348 6366 6384 6401 87.5 17 2.5 6401 641864366453 64706487 6504 6521 6538 6555 6571 87.4 16 2.6 6571 658866056621 6638 6654 6671 6687 6703 6719 6736 87.3 17 2.7 6736 6752 6768 6784 68006815 6831 6847 6863 6878 6894 87.2 16 2.8 6894 6909 6925 6940 69566971 6986 7001 7016 7031 7046 87.1 15 2.9 7046 7061 7076 7091 71067121 7136 7150 7165 7179 7194 87.0 15 3.0 8.7194 7208 7223 7237 7252 7266 7280 7294 7308 7323 7337 86^9 14 3.1 7337 7351 7365 7379 73927406 7420 7434 7448 7461 7475 86.8 14 3.2 7475 748875027515 75297542 7556 7569 7582 7596 7609 86.7 13 3.3 7609 7622 7635 7648 7661 7674 7687 7700 7713 7726 7739 86.6 13 3.4 7739 7751 7764 7777 77907802 7815 7827 7840 7852 7865 86.5 13 3.5 7865 7877 7890 7902 79147927 7939 7951 7963 7975 7988 86.4 13 3.6 7988 800080128024 8036 8048 8059 8071 8083 8095 8107 86.3 12 3.7 8107 811981308142 81548165 8177 8188 8200 8212 8223 86.2 11 3.8 8223 823482468257 8269 8280 8291 8302 8314 8325 8336 86.1 11 3.9 8336 834783588370 8381 8392 8403 8414 8425 8436 8446 86.0 10 1^0 8.8446 845784688479 84908501 8511 8522 8533 8543 8554 85^9 n 4.1 8554 8565 8575 8586 85968607 8617 8628 8638 8649 8659 85.8 10 4.2 8659 866986808690 87008711 8721 8731 8741 8751 8762 85.7 11 4.3 8762 8772 8782 8792 8802 8812 8822 8832 8842 8852 8862 85.6 10 4.4 8862 8872 8882 8891 8901 8911 8921 8931 8940 8950 8960 85.5 10 4.5 8960 8970 8979 8989 89989008 9018 9027 9037 9046 9056 85.4 10 4.6 9056 9065 9075 9084 90939103 9112 9122 9131 9140 9150 85.3 10 4.7 915Q 915991689177 91869196 9205 9214 9223 9232 9241 85.2 9 4.8 9241 925092609269 92789287 9296 9305 9313 9322 9331 85.1 9 4.9 9331 9340 9349 9358 9367 9376 9384 9393 9402 9411 9420 85.0 9 10 9 8 7 654 321 0 j.O d

The text on this page is estimated to be only 27.84% accurate

CONTINUED. log- tan n 21 log1 cotan n° n° 0 1 2 ^ J 4 5 6 7 S 9 10 d 5.0 8.9420 9428 9437 9446 9454 9463 9472 9480 9489 9497 9506 84.9 9 5.1 9506 9515 9523 9532 9540 9549 9557 9565 9574 9582 9591 84.8 9 5.2 9591 9599 9608 9616 9624 9633 9641 9649 9657 9666 9674 84.7 8 5.3 9674 9682 9690 9699 9707 9715 9723 9731 9739 9747 9756 84.6 9 5.4 9756 9764 9772 9780 9788 9796 9804 9812 9820 9828 9836 84.5 8 5.5 9836 9844 9852 9860 9867 9875 9883 989J 9S99 9907 9915 84.4 8 5.6 9915 9922 9930 9938 9946 9953 9961 9969 9977 9984 9992 84.3 8 5.7 9992 *0000*0007*0015 *0022*0030*003S *0045 "0053*0060 "0068 84.2 8 5.S 9.0068 0075 0083 0090 0098 0105 0113 0120 0128 0135 0143 84.1 8 5.9 0143 0150 0157 0165 0172 0180 0187 0194 0202 0209 0216 84.0 7 6.0 9.0216 0223 0231 0238 0245 0253 0260 0267 0274 0281 0289 83.9 8 6.1 0289 0296 0303 0310 0317 0324 0331 0338 0346 0353 0360 83.8 7 6.2 0360 0367 0374 0381 03S8 0395 0402 0409 0416 0423 0430 83.7 7 6.3 0430 0437 0444 0451 0457 0464 0471 0478 0485 0492 0499 83.6 7 6.4 0499 0506 0512 0519 0526 0533 0540 0546 0553 0560 0567 83.5 7 6.5 0567 0573 0580 0587 0593 0600 0607 0614 0620 0627 0633 83.4 6 6.6 0633 0640 06V 0653 0660 0667 0673 0680 0686 0693 0699 83.3 6 6.7 0699 0706 0712 0719 0725 0732 0738 0745 0751 0758 0764 83.2 6 6.8 0764 0771 0777 0784 0790 0796 0803 0809 0816 0822 0828 83.1 6 6.9 0828 0835 0841 0847 0854 0860 0866 0873 0879 0885 0891 83.0 6 7.0 9.0891 0898 0904 0910 0916 0923 0929 0935 0941 0947 0954 82.9 7 7.1 0954 0960 0966 0972 0978 0984 0991 0997 1003 1009 1015 82.8 6 7.2 1015 1021 1027 1033 1039 1045 1051 1058 1064 1070 1076 82.7 6 7.3 1076 1082 1088 1094 1100 1106 1112 1117 1123 1129 1135 82.6 6 7.4 1135 1141 1147 1153 1159 1165 1171 1177 1183 1188 1194 82.5 6 7.5 1194 1200 1206 1212 1218 1223 1229 1235 1241 1247 1252 82.4 5 7.6 1252 1258 1264 1270 1276 1281 1287 1293 1299 1304 1310 82.3 6 7.7 1310 1316 1321 1327 1333 1338 1344 1350 1355 1361 1367 82.2 6 7.8 1367 1372 1378 1384 1389 1395 1400 1406 1412 1417 1423!82.1 6 7.9 1423 1428 1434 1439 1445 1450 1456 1461 1467 1473 1478 82.0 5 8.0 9.1478 1484 1489 1494 1500 1505 1511 1516 1522 1527 1533181.9 ~6 8.1 1533 1538 1544 1549 1554 1560 1565 1571 1576 1581 1587 81.8 6 8.2 1587 1592 1597 1603 1608 1613 1619 1624 1629 1635 1640 81.7 5 8.3 1640 1645 1651 1656 1661 1667 1672 1677 1682 1688 1693 81.6 5 8.4 1693 1698 1703 1709 1714 1719 1724 1729 1735 1740 1745 81.5 5 8.5 1745 1750 1755 1761 1766 1771 1776 1781 1786 1791 1797 81.4 6 8.6 1797 1802 1807 1812 1817 1822 1827 1832 1837 1842 1848 81.3 6 8.7 1848 1853 1858 1863 1868 1873 1878 1883 1888 1893 189881.2 5 8.8 1898 1903 1908 1913 1918 1923 1928 1933 1938 1943 194881.1 5 8.9 1948 1953 1958 1963 1968 1973 19771 1982 1987 1992 199781.0 5 10 987 6 5 432 1 0 n° r 0 123 456 7 8 9 0 T log- tan 0 0 .016 .03 .05 .06 .083 .1 .116 .13 .15 0.00 1.7581 1.28 1.7580 8.3492 1 .16 .183 .2 .216 .23 .25 .26 .283 .3 .316 1.98 1.7579 8.5387 2 .3 .35 .36 .383 .4 .416 .43 .45 .46 .483 2.49 1.7578 8.6384 2.91 1.7577 8.7061 3 .5 .516 .53 .55 .56 .583 .6 .616 .63 .65 3.27 1.7576 8.7569 4 .6 .683 .7 .716 .73 .75 .76 .783 .8 .816 3.60 1.7575 8.7988 5 .83 .85 .86 .883 .9 .916 .93 .95 .96 .983 3.90 4-4 O 1.7574 8.8336 O Q£ "JO .18 8.8638

The text on this page is estimated to be only 27.43% accurate

22 711. LOGARITHMIC SINES AND COSINES log sin log- cos n° 0' 10' 20' 30' 40' 50' 60' (1 PP ~0 7.4637 7648 9408*0658*1627 *2419 89 45 46 47 48 49 1 8.2419 3088 3668 4179 4637 5050 5428 88 55555 2 5428 5776 6097 6397 6677 6940 7188 87 9 9 9 10 10 3 7188 7423 7645 7857 8059 8251 8436 86 14 14 14 14 15 4 8436 8613 8783 8946 9104 9256 9403 85 18 18 19 19 20 5 9403 9545 9682 9816 9945*0070 *0192 84 23 23 24 24 25 6 9.0192 0311 0426 0539 0648 0755 0859 83 27 28 28 29 29 1 0859 0961 1060 1157 1252 1345 1436 82 91 32 32 33 34 34 8 1436 1525 1612 1697 1781 1863 1943 81 80 36 37 38 38 39 9 1943 2022 2100 2176 2251 2324 2397 *o 73 41 41 42 43 44 10 9.2397 9RHA 2468 2538 2606 2674 2740 9R7O 90^4. 9QQ7 3fK& 71 1Q 2806 31 7Q 79 7ft ~66 fr\ 40 41 42 43 44 12 £>O\JO 3179 £o/\J £VJT ^W/ o\)jQ oLLy 3238 3296 3353 3410 3466 oi/y 3521 to 77 ou 55 88899 13 3521 3575 3629 3682 3734 3786 3837 76 51 12 12 13 13 13 14 3837 3887 3937 3986 4035 4083 4130 75 47 16 16 17 17 18 15 4130 4177 4223 4269 4314 4359 4403 74 44 20 21 21 22 22 16 4403 4447 4491 4533 4576 4618 4659 73 41 24 25 25 26 26 17 4659 4700 4741 4781 4821 4861 4900 72 39 28 29 29 30 31 18 4900 4939 4977 5015 5052 5090 5126 71 36 32 33 34 34 35 19 5126 5163 5199 5235 5270 5306 5341 70 35 36 37 38 39 40 20 9.5341 5375 5409 5443 5477 5510 5543 69 33 35 36 37 38 39 21 5543 5576 5609 5641 5673 5704 5736 68 32 44444 22 5736 5767 5798 5828 5859 5889 5919 67 30 77788 23 5919 5948 5978 6007 6036 6065 6093 66 28 11 11 11 11 12 24 6093 6121 6149 6177 6205 6232 6259 65 27 14 14 15' 15 16 25 6259 6286 6313 6340 6366 6392 6418 64 26 18 18 19 19 20 26 6418 6444 6470 6495 6521 6546 6570 63 24 21 22 22 23 23 27 6570 6595 6620 6644 6668 6692 6716 62 24 25 25 26 27 27 28 6716 6740 6763 6787 6810 6833 6856 61 23 28 29 30 30 31 29 6856 6878 6901 6923 6946 6968 6990 60 22 32 32 33 34 35 1*0 9.6990 7012 7033 7055 7076 7097 7118 59 Hi 30 31 32 33 34 31 7118 7139 7160 7181 7201 7222 7242 58 20 33333 32 7242 7262 7282 7302 7322 7342 7361 57 19 66677 33 7361 7380 7400 7419 7438 7457 7476 56 19 9 9 10 10 10 34 7476 7494 7513 7531 7550 7568 7586 55 18 12 12 13 13 14 35 7586 7604 7622 7640 7657 7675 7692 54 17 15 16 16 17 17 36 7692 7710 7727 7744 7761 7778 7795 53 17 18 19 19 20 20 37 7795 7811 7828 7844 7861 7877 7893 52 16 21 22 22 23 24 38 7893 7910 7926 7941 7957 7973 7989 51 16 24 25 26 26 27 39 7989 8004 8020 8035 8050 8066 8081 50 15 27 28 29 30 31 40 9.8081 8096 8111 8125 8140 8155 8169 49 14 25 26 27 28 29 41 8169 8184 8198 8213 8227 8241 8255 48 14 33333 42 8255 v8269 8283 8297 8311 8324 8338 47 14 55566 43 8338 - 8351 8365 8378 8391 8405 8418 46 13 88889 44 8418 8431 8444 8457 8469 8482 8495 45 13 10 10 11 11 12 45 8495. 8507 8520 8532 8545 8557 8569 44 12 13 13 14 14 15 46 8569 8582 8594 8606 8618 8629 8641 43 12 15 16 16 17 17 47 8641 8653 8665 8676 8688 8699 8711 42 12 18 18 19 20 20 48 8711 8722 8733 8745 8756 8767 8778 41 11 20 21 22 22 23 49 8778 8789 8800 8810 8821 8832 8843 40 11 23 23 24 25 26 60' 60' 40' 30' 20' 10' 0' n° d

The text on this page is estimated to be only 26.11% accurate

POE MINUTES, logr sin log cos n° 0' 10' 20' 30' 40' 50' 60' d PP 50 9.8843 8853 8864 8874 8884 8895. 8905 39 10 20 21 22 23 24 51 8905 8915 8925 8935 8945 8955 8965 38 10 2 2222 52 8%5 8975 S9S5 8995 9004 9014 9023 37 9 4 4455 53 9023 9033 9042 9052 9061 9070 9080 36 10 6 6777 54 9080 9089 9098 9107 9116 9125 9134 35 9 8 8 9 9 10 55 9134 9142 9151 9160 9169 9177 9186 34 9 10 11 11 12 12 56 9186 9194 9203 9211 9219 9228 9236 33 8 12 13 13 14 14 57 9236 9244 9252 9260 9268 9276 9284 32 8 14 15 15 16 17 58 9284 9292 9300 9308 9315 9323 9331 31 8 16 17 18 18 19 59 9331 9338 9346 9353 9361 9368 9375 30 7 18 19 20 21 22 60 9.9375 9383 9390 9397 9404 9411 9418 29 7 15 16 17 18 19 61 9418 9425 9432 9439 9446 9453 9459 28 6 2 2222 62 9459 9466 9473 9479 9486 9492 9499 27 7 3 3344 63 9499 9505 9512 9518 9524 9530 9537 26 7 5 5556 64 9537 9543 9549 9555 9561 9567 9573 25 6 6 6778 65 9573 9579 9584 9590 9596 9602 9607 24 5 8 8 9 9 10 66 9607 9613 ^>61S 9624 9629 9635 9640 23 5 9 10 10 11 11 67 9640 9646 9651 9656 9661 9667 9672 22 5 11 11 12 13 13 68 9672 9677 9682 9687 9692 9697 9702 21 5 12 13 14 14 15 69 9702 9706 9711 9716 9721 9725 9730 20 5 14 14 15 16 17 70 9.9730 9734 9739 9743 9748 9752 9757 19 5 10 11 12 13 14 71 9757 9761 9765 9770 9774 9778 9782 18 4 1 1111 72 9782 9786 9790 9794 9798 9802 9806 17 4 2 2233 73 9806 9810 9814 9817 9821 9825. 9828 16 3 3 3444 74 9828 9832 9836 9839 9843 9846 9849 15 3 4 4556 75 9849 9853 9856 9859 9863 9866 9869 14 3 5 6677 76 9869 9872 9875 9S78 9881 9S84 9887 13 3 6 7788 77 9887 9890 9893 9S96 9899 9901 9904 12 3 7 8 8 9 10 78 9904 9907 9909 9912 9914 9917 9919 11 2 8 9 10 10 11 79 9919 9922 9924 9927 9929 9931 9934 10 3 9 10 11 12 13 80 9.9934 9936 9938 9940 9942 9944 9946 9 2 5 6789 81 9946 9948 9950 9952 9954 9956 9958 8 2 1 1111 82 9958 9959 9961 9963 9964 9966 9968 7 2 1 1122 83 9968 9969 9971 9972 9973 9975 9976 6 1 2 2223 84 9976 9977 9979 9980 9981 9982 9983 5 1 2 2334 85 9983 9985 9986 9987 9988 9989 9989 4 0 3 3445 86 9989 9990 9991 9992 9993 9993 9994 3 1 3 4455 87 9994 9995 9995 9996 9996 9997 9997 2 0 4 4566 88 9997 9998 9998 9999 9999 9999 9999 1 0 4 5667 89 9999 *0000 *0000 *0000 *0000 *0000 *0000 0 0 5 5678 60' 50' 40' 30' 20' 10' 0' n° d 1234 0 f ' S log sin 0 f ' S log sin 0000 0011 0 00 0 3.5363 5 07 307 3.5369 8.9503 0111 1 51 111 3.5364 8.5090 5 32 332 3.5370 8.9842 0112 2 50 170 3.5365 8.6940 5 56 356 3.5371 9.0144 1122 1122 3 32 212 3.5366 8.7898 6 18 378 3.5372 9.0403 1123 4 08 248 3.5367 8.8578 6 39 399 3.5373 9.0637 1223 4 39 279 3.5368 8.9089 6 69 419 9.0849 1234

The text on this page is estimated to be only 28.04% accurate

24 VIII. LOGABITHMIO TAtfQEOTS AttD log- tan log- cotan n° 0' 10' 20' 30' 40' 50' 60' (1 PP 0 7.4637 7648 9409*0658*1627 *2419 89 95 96 97 98 99 1 8.2419 3089 3669 4181 4638 5053 5431 88 10 10 10 10 10 2 5431 5779 6101 6401 6682 6945 7194 87 19 19 19 20 20 i* 7194 7429 7652 7865. 8067 8261 8446 86 29 29 29 29 30 4 8446 8624 8795 8960 9118 9272 9420 85 38 38 39 39 40 5 9420 9563 9701 9836 9966*0093 *0216 84 48 48 49 49 50 6 9.0216 0336 0453 0567 0678 0786 0891 83 105 57 58 58 59 59 7 0891 0995. 1096 1194 1291 1385 1478 82 93 67 67 68 69 69 8 1478 1569 1658 1745 1831 191$ 1997 81 82 76 77 78 78 79 9 1997 2078 2158 2236 2313 2389 2463 80 74 86 86 87 88 89 10 9.2463 2536 2609 2680 2750 2819 2887 79 68 90 91 92 93 94 11 2887 2953 3020 3085 3149 3212 3275 78 63 99999 12 3275 3336 3397 3458 3517 3576 3634 77 58 18 18 18 19 19 13 3634 3691 3748 3804 3859 3914 3968 76 54 27 27 28 28 28 14 3968 4021 4074 4127 4178 4230 4281 75 51 36 36 37 37 38 15 4281 4331 4381 4430 4479 4527 4575 74 48 45 46 46 47 47 16 457$ 4622 4669 4716 4762 4808 4853 73 45 54 55 55 56 56 17 4853 4898 4943 4987 5031 5075 5118 72 43 63 64 64 65 66 18 5118 5161 5203 5245 5287 5329 5370 71 41 72 73 74 74 75 19 5370 5411 5451 5491 5531 5571 5611 70 40 81 82 83 84 85 ~20 9.5611 5650 5689 5727 5766 5804 5842 69 38 85 86 87 88 89 21 5842 5879 5917 5954 5991 6028 6064 68 36 99999 22 6064 6100 6136 6172 6208 6243 6279 67 36 17 17 17 18 18 23 6279 6314 6348 6383 6417 6452 6486 66 34 26 26 26 26 27 24 6486 6520 6553 6587 6620 6654 6687 65 33 34 34 35 35 36 25 6687 6720 6752 678$ 6817 6850 6882 64 32 43 43 44 44 45 26 6882 6914 6946 6977 7009 7040 7072 63 32 51 52 52 53 53 27 7072 7103 7134 716$ 7196 7226 7257 62 31 60 60 61 62 62 28 7257 7287 7317 7348 7378 7408 7438 61 30 68 69 70 70 71 29 7438 7467 7497 7526 7556 7585 7614 60 29 77 77 78 79 80 30 9.7614 7644 7673 7701 7730 7759 7788 ^9 ~29~ 80 81 82 83 84 31 7788 7816 7845 7873 7902 7930 7958 58 28 88888 32 7958 7986 8014 8042 8070 8097 8125 57 28 16 16 16 17 17 33 8125 8153 8180 8208 8235 8263 8290 56 27 24 24 25 25 25 34 8290 8317 8344 8371 8398 8425 8452 55 27 32 32 33 33 34 35 8452 8479 8506 8533 8559 8586 8613 54 27 40 41 41 42 42 36 8613 8639 8666 8692 8718 8745 8771 53 26 48 49 49 50 50 37 8771 8797 8824 8850 8876 8902 8928 52 26 56 57 57 58 59 38 8928 8954 8980 9006 9032 9058 9084 51 26 64 65 66 66 67 39 9084 9110 9135 9161 9187 9212 9238 50 26 72 73 74 75 76 40 9.9238 9264 9289 9315 9341 9366 9392 49 ~26~ 7576777879 41 9392 9417 9443 9468 9494 9519 9544 48 25 88888 42 9544 9570 9595 9621 9646 9671 9697 47 26 15 15 15 16 16 43 9697 9722 9747 9772 9798 9823 9848 46 25 23 23 23 23 24 44 9848 9874 9899 9924 9949 9975 *0000 45 25 30 30 31 31 32 45 0.0000 0025 0051 0076 0101 0126 0152 44 26 38 38 39 39 40 46 0152 0177 0202 0228 0253 0278 0303 43 25 45 46 46 47 47 47 0303 0329 0354 0379 0405 0430 0456 42 26 53 53 54 55 55 48 0456 0481 0506 0532 0557 0583 0608 41 25 60 61 62 62 63 49 0608 0634 0659 0685 0711 0736 0762 40 26 68 68 69 70 71 60' 50' 40' 30' 20' 10' 0' n° d

The text on this page is estimated to be only 27.40% accurate

log tan POB MINUTES. log1 cotan 25 n° 0' 10' 20' 30' 40' 50' 60' d PP 50 0.0762 0788 0813 0839 0865 0890 0916 39 26 70 71 72 73 74 51 0916 0942 0968 0994 1020 1046 1072 38 26 77777 52 1072 1098 1124 1150 1176 1203 1229 37 26 14 14 14 15 15 53 1229 1255 1282 1308 1334 1361 1387 36 26 21 21 22 22 22 54 1387 1414 1441 1467 1494 1521 1548 35 27 28 28 29 29 30 55 1548 1575 1602 1629 1656 1683 1710 34 27 35 36 36 37 37 56 1710 1737 1765, 1792 1820 1847 1875. 33 28 42 43 43 44 44 57 1873 1903 1930 1958 1986 2014 2042 32 28 49 50 50 51 52 58 2042 2070 2098 2127 2155 2184 2212 31 28 56 57 58 58 59 59 2212 2241 2270 2299 2327 2356 2386 30 30 63 64 65 66 67 60 s* + 0.2386 n r sr\ 2415. 2444 2474 o coo o/coo o/ico 2503 O/-Q"? 2533 rthri *) 2562 r\>j A 7 29 £)O 29 *Jf\ 65 66 67 68 69 61 62 ZioZ 2743 Z5VZ ZoZZ ZojZ 2774 2804 2835 ZOOO LiLd 2866 2897 Z/T.5 2928 28 27 30 31 13 13 13 14 14 63 2928 2960 2991 3023 3054 3086 3118 26 32 20 20 20 20 21 64 3118 3150 3183 3215 3248 3280 3313 25 33 26 26 27 27 28 65 3313 3346 3380 3413 3447 3480 3514 24 34 33 33 34 34 35 66 3514 3548 3583 3617 3652 3686 3721 23 35 39 40 40 41 41 67 3721 3757 3792 3828 3864 3900 3936 22 36 46 46 47 48 48 68 3936 3972 4009 4046 4083 4121 4158 21 37 52 53 54 54 55 69 4158 41% 4234 4273 4311 4350 4389 20 39 59 59 60 61 62 70 0.4389 4429 4469 4509 4549 4589 4630 19 41 60 61 62 63 64 71 4630 4671 4713 4755 4797 4839 4882 18 43 66666 72 4882 4925 4969 5013 5057 5102 5147 17 45 12 12 12 13 13 73 5147 5192 5238 5284 5331 5378 5425 16 47 18 18 19 19 19 74 5425 5473 5521 5570 5619 5669 5719 15 50 24 24 25 25 26 75 5719 5770 5822 5873 5926 5979 6032 14 53 30 31 31 32 32 76 6032 6086 6141 6196 6252 6309 6366 13 57 36 37 37 38 38 77 6366 6424 6483 6542 6603 6664 6725 12 61 42 43 43 44 45 78 6725 6788 6851 6915 6980 7047 7113 11 66 48 49 50 50 51 79 7113 7181 7250 7320 7391 7464 7537 10 73 54 55 56 57 58 80 0.7537 7611 7687 7764 7842 7922 8003 9 81 55 56 57 58 59 81 8003 8085 8169 8255 8342 8431 8522 8 91 66666 82 8522 8615 8709 8806 8904 9005 9109 7 104 11 11 11 12 12 83 9109 9214 9322 9433 9547 9664 9784 6 120 17 17 17 17 18 84 9784 9907*0034*0164*0299*0437 *0580 5 22 22 23 23 24 85 1.0580 0728 0882 1040 1205. 1376 1554 4 28 28 29 29 30 86 1554 1739 1933 2135 2348 2571 2806 3 33 34 34 35 35 87 2806 3055 3318 3599 3899 4221 4569 2 39 39 40 41 41 88 4569 4947 5362 5819 6331 6911 7581 1 44 45 46 46 47 89 7581 8373 9342*0591*2352* 5363 0 50 50 51 52 53 60' 60' 40' 30' 20' 10' 0' n° d 0 f ' T log tan 0 f ' T log tan 50 51 52 53 54 0 00 0 3.5363 4 19 259 3.5354 8.8778 55555 0 44 44 3.5362 8.1072 4 34 274 3.5353 8.9024 10 10 10 11 11 1 41 101 3.5361 8.4682 4 49 289 3.5352 8.9256 15 15 16 16 16 2 15 135 3.5360 8.5943 5 03 303 3.5351 8.9463 20 20 21 21 22 2 43 163 3.5359 8.6762 5 16 316 3.5350 8.9646 25 26 26 27 27 3 06 186 3.5358 8.7337 5 28 328 3.5349 8.9809 30 31 31 32 32 3 27 207 3.5357 8.7802 5 41 341 3.5348 8.9979 35 36 36 37 38 3 46 226 3.5356 8.8185 5 52 352 3.5347 9.0118 40 41 42 42 43 4 03 243 3.5355 8.8501 6 04 364 9.0265 45 46 47 48 49

The text on this page is estimated to be only 27.94% accurate

26 IX, NATURAL SINES AND COSINES. sin n° cos n° n° .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 0 (I 0' & 12' 18' 534' 30' 30' 42' 48' 54' 60' 0 0.0000 0017 0035 0052 0070 0087 0105 0122 0140 0157 0175 89 18 1 0175 0192 0209 0227 0244 0262 0279 0297 0314 0332 0349 88 17 2 0349 0366 0384 0401 0419 0436 0454 0471 0488 0506 0523 87 17 3 0523 0541 0558 0576 0593 0610 0628 0645 0663 0680 0698 86 18 4 0698 0715 0732 0750 0767 0785 0802 0819 0837 0854 0872 85 18 5 0872 0889 0906 0924 0941 0958 0976 0993 1011 1028 1045 84 17 6 1045 1063 1080 1097 1115 1132 1149 1167 1184 1201 1219 83 18 7 1219 1236 1253 1271 1288 1305 1323 1340 1357 1374 1392 82 18 8 1392 1409 1426 1444 1461 1478 1495 1513 1530 1547 1564 81 17 9 1564 1582 1599 1616 1633 1650 1668 1685 1702 1719 1736 80 17 10 0.1736 1754 1771 1788 1805 1822 1840 1857 1874 1891 1908 79 17 11 1908 1925 1942 1959 1977 1994 2011 2028 2045 2062 2079 78 17 12 2079 2096 2113 2130 2147 2164 2181 2198 2215 2233 2250 77 17 13 2250 2267 2284 2300 2317 2334 2351 2368 2385 2402 2419 76 17 14 2419 2436 2453 2470 2487 2504 2521 2538 2554 2571 2588 75 17 15 2588 2605 2622 2639 2656 2672 2689 2706 2723 2740 2756 74 16 16 2756 2773 2790 2807 2823 2840 2857 2874 2890 2907 2924 73 17 17 2924 2940 2957 2974 2990 3007 3024 3040 3057 3074 3090 72 16 18 3090 3107 3123 3140 3156 3173 3190 3206 3223 3239 3256 71 17 19 3256 3272 3289 3305 3322 3338 3355 3371 3387 3404 3420 70 16 20 0.3420 3437 3453 3469 3486 3502 3518 3535 35513567 3584 69 17 21 3584 3600 3616 3633 3649 3665 3681 3697 3714 3730 3746 68 16 22 3746 3762 3778 3795 3811 3827 3843 3859 3875 3891 3907 67 16 23 3907 3923 3939 3955 3971 3987 4003 4019 4035 4051 4067 66 16 24 4067 4083 4099 4115 4131 4147 4163 417941954210 4226 65 16 25 4226 4242 4258 4274 4289 4305 4321 4337 4352 4368 4384 64 16 26 4384 4399 4415 4431 4446 4462 4478 4493 4509 4524 4540 63 16 27 4540 4555 4571 4586 4602 4617 4633 4648 4664 4679 4695 62 16 28 469^ 471047264741 4756 4772 4787 4802 4818 4833 4848 61 15 29 4848 4863 4879 4894 4909 4924 4939 495^4970 4985 5000 60 15 30 0.5000 5015 5030 5045 5060 5075 5090 5105 5120 5135 5150 59 15 31 5150 5165 5180 5195 5210 5225 5240 5255 5270 5284 5299 58 15 32 5299 5314 5329 5344 5358 5373 5388 5402 5417 5432 5446 57 14 33 5446 5461 5476 5490 550555195534 5548 5563 5577 5592 56 15 34 5592 5606 5621 5635 5650 5664 5678 5693 5707 5721 5736 55 15 35 5736 5750 5764 5779 5793 5807 5821 5835 5850 5864 5878 54 14 36 5878 5892 5906 5920 5934 5948 5962 5976 5990 6004 6018 53 14 37 6018 6032 6046 6060 6074 6088 6] 01 611561296H3 6157 52 14 38 6157 6170 6184 6198 6211 6225 6239 6252 6266 62SO 6293 51 13 39 6293 6307 6320 6334 6347 6361 6374 6388 6401 6414 6428 50 14 40 0.6428 6441 6455 6468 6481 6494 6508 6521 6534 6547 6561 49 14 41 6561 6574 6587 6600 6613 6626 6639 6652 6665 6678 6691 48 13 42 6691 670467176730 6743 6756 6769 6782 6794 6807 6820 47 13 43 6820 6833 6845 6858 6871 6884 6896 6909 6921 6934 6947 46 13 44 6947 6959 6972 6984 6997 7009 7022 7034 7046 7059 7071 45 12 45 7071 7083 7096 7108 7120 7133 7145 7157 7169 7181 7193 44 12 46 7193 7206 7218 7230 7242 7254 7266 7278 7290 7302 7314 43 12 47 7314 7325 7337 7349 7361 7373 7385 7396 7408 7420 7431 42 11 48 7431 7443 7455 7466 7478 7490 7501 7513 7524 7536 7547 41 11 49 7547 7559 7570 7581 7593 7604 7615 7627 7638 7649 7660 40 11 60' 54' 48' 43' 36' 30' IV 18' 12' 6' 0' 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 n° d

The text on this page is estimated to be only 27.20% accurate

IX, NATURAL SINES AND COSINES, sinn° 27 cosn° n° .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 (1 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' 60' 60 0.7660 7672 7683 7694 7705 7716 7727 7738 7749 7760 7771 39 11 51 7771 7782 7793 7804 7815 7826 7837 7848 7859 7869 7880 38 11 52 7880 7891 7902 7912 7923 7934 7944 7955 7965 7976 7986 37 10 53 7986 7997 8007 8018 8028 8039 8049 8059 8070 8080 8090 36 10 54 8090 810081118121 8131 8141 8151 8161 8171 8181 8192 35 11 55 8192 820282118221 8231 8241 8251 8261 8271 8281 8290 34 9 56 8290 830083108320 8329 8339 8348 8358 8368 8377 8387 33 10 57 8387 8396 8406 8415 8425 8434 8443 8453 8462 8471 8480 32 9 58 8480 8490 8499 8508 8517 8526 8536 8545 8554 8563 8572 31 9 59 8572 858185908599 8607 8616 8625 8634 8643 8652 8660 30 8 ^0 0.8660 8669 8678 8686 8695 8704 8712 8721 8729 8738 8746 ~29 8 61 8746 8755 8763 8771 8780 8788 8796 8805 8813 8821 8829 28 8 62 8829 8838 8846 8854 8862 8870 8878 8886 8894 8902 8910 27 8 63 8910 8918 8926 8934 8942 8949 8957 896£ 8973 8980 8988 26 8 64 8988 899690039011 9018 9026 9033 9041 9048 9056 9063 25 7 65 9063 9070 9078 9085 9092 9100 9107 9114 9121 9128 9135 24 7 66 9135 914391509157 9164 9171 9178 9184 9191 9198 9205 23 7 67 9205 9212 9219 9225 9232 9239 9245 9252 9259 9265 9272 22 7 68 9272 9278 9285 9291 9298 9304 9311 9317 9323 9330 9336 21 6 69 9336 9342 9348 9354 9361 9367 9373 9379 9385 9391 9397 20 6 70 0.9397 940394099415 9421 9426 9432 9438 9444 9449 9455 19 6 71 9455 9461 9466 9472 9478 9483 9489 9494 9500 9505 9511 18 6 72 9511 951695219527 9532 9537 9542 9548 9553 9558 9563 17 5 73 9563 956895739578 9583 9588 9593 9598 9603 9608 9613 16 5 74 9613 961796229627 9632 9636 9641 9646 9650 9655 9659 15 4 75 9659 9664 9663 9673 9677 9681 9686 9690 9694 9699 9703 14 4 76 9703 970797119715 9720 9724 9728 9732 9736 9740 9744 13 4 77 9744 974897519755 9759 9763 9767 9770 9774 9778 9781 12 3 78 9781 9785 9789 9792 9796 9799 9803 9S06 9810 9813 9816 11 3 79 9816 9820 9823 9826 9829 9833 9836 9839 9842 9845 9848 10 3 80 0.9848 985198549857 9860 9863 9866 9869 9871 9874 9877 9 3 81 9877 9880 9882 9883 9888 9890 9893 9895 9898 9900 9903 8 3 82 9903 9905 9907 9910 9912 9914 9917 9919 9921 9923 9925 7 2 83 9925 9928 9930 9932 9934 9936 9938 9940 9942 9943 9945 6 2 84 9945 994799499951 9952 9954 9956 9957 9959 9960 9962 5 2 85 9962 9963 9965 9966 9968 9969 9971 9972 9973 9974 9976 4 2 86 9976 9977 9978 9979 9980 9981 9982 9983 9984 9985 9986 3 1 87 9986 9987 9988 9989 9990 9990 9991 9992 9993 9993 9994 2 1 88 9994 9995 9995 9996 9996 9997 9997 9997 9998 9998 9998 1 0 89 9998 9999 9999 9999 9999 1.000 1.000 1.000 1.000 1.000 1.000 0 0 60' 54' 48' 42' 36' 3O' 24' 18' 12' 6' 0' 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 n° d 123 456 7 8 9 10 11 12 1314 15 1617 18 19 1 001 111 1 1 2 2 222 233 333 2 Oil 122 233 3 444 555 666 3 112 233 445 5 667 788 99 10 4 112 334 556 7 7 8 9 9 10 11 11 12 13 5 123 345 678 8 9 10 11 12 13 13 14 15 16

The text on this page is estimated to be only 27.77% accurate

28 X. NATUKAL TANGENTS AND COTANGENTS. tan n° cot n° n° .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 (1 0' 6' 12' 18' 24' 30' 36' 42' 48' 54' 60' ~0 0.0000 0017 0035 0052 0070 0087 0105. 0122 0140 0157 0175 89 ~18 1 •0175 0192 0209 0227 0244 0262 0279 0297 0314 0332 0349 88 17 2 0349 0367 0384 0402 0419 0437 0454 0472 0489 0507 0524 87 17 3 0524 0542 0559 0577 0594 0612 0629 0647 0664 0682 0699 86 17 4 0699 071707340752 0769 0787 0805 0822 0840 0857 0875 85 18 5 0875 0892 0910 0928 0945 0963 0981 0998 1016 1033 1051 84 18 6 1051 1069 1086 1104 1122 1139 1157 1175 1192 1210 1228 83 18 7 1228 1246 1263 1281 1299 1317 1334 1352 1370 1388 1405 82 17 8 1405 1423 1441 1459 1477 1495 1512 1530 1548 1566 1584 81 18 9 1584 1602 1620 1638 1655 1673 1691 1709 1727 1745 1763 80 18 10 0.1763 1781 1799 1817 1835 1853 1871 1890 1908 1926 1944 79 18 11 1944 1962 1980 1998 2016 203^ 2053 2071 2089 2107 2126 78 19 12 2126 2144 2162 2180 2199 2217 2235 2254 2272 2290 2309 77 19 13 2309 2327 2345 2364 2382 2401 2419 2438 2456 2475 2493 76 18 14 2493 2512 2530 2549 2568 2586 2605 2623 2642 2661 2679 75 18 15 2679 2698 2717 2736 2754 2773 2792 28112830 2849 2867 74 18 16 2867 2886 2905 2924 2943 2962 2981 3000 3019 3038 3057 73 19 17 3057 3076 3096 3115 3134 3153 3172 3191 3211 3230 3249 72 19 18 3249 3269 3288 3307 3327 3346 3365 3385 3404 3424 3443 71 19 19 3443 3463 3482 3502 3522 3541 3561 3581 3600 3620 3640 70 20 20 0.3640 3659 3679 3699 3719 3739 3759 3779 3799 3819 3839 69 20 21 3839 3859 3879 3899 3919 3939 3959 3979 4000 4020 4040 68 20 22 4040 4061 4081 4101 4122 4142 4163 4183 4204 4224 4245 67 21 23 4245 4265 4286 4307 4327.4348-.4369 4390 4411 4431 4452 66 21 24 4452 4473 4494 4515 4536 4557 4578 45994621 4642 4663 65 21 25 4663 4684 4706 4727 4748 4770 4791 4813 4834 4856 4877 64 21 26 4877 4899 4921 4942 4964 4986 5008 5029 5051 5073 5095 63 22 27 5095 511751395161 5184 5206 5228 5250 5272 5295 5317 62 22 28 5317 5340 5362 5384 5407 5430 5452 5475 5498 5520 5543 61 23 29 5543 5566 5589 5612 5635 5658 5681 5704 5727 5750 5774 60 24 30 0.5774 5797 5820 5844 5867 5890 5914 5938 5961 5985. 6009 59 24 31 6009 6032 6056 6080 6104 6128 6152 6176 6200 6224 6249 58 25 32 6249 6273 6297 6322 6346 6371 6395 6420 6445 6469 6494 57 25 33 6494 651965446569 6594 6619 6644 6669 6694 6720 6745 56 25 34 6745 6771 6796 6822 6847 6873 6899 6924 6950 6976 7002 55 26 35 7002 7028 7054 7080 7107 7133 7159 7186 7212 7239 7265 54 26 36 7265 7292 7319 7346 7373 7400 7427 7454 7481 7508 7536 53 28 37 7536 7563 7590 7618 7646 7673 7701 7729 7757 7785 7813 52 28 38 7813 7841 7869 7898 7926 7954 7983 8012 8040 8069 8098 51 29 39 8098 8127 8156 8185 8214 8243 8273 8302 8332 8361 8391 50 30 40 0.8391 8421 8451 8481 8511 8541 8571 8601 8632 8662 8693 49 31 41 8693 8724 8754 8785 8816 8847 8878 89108941 8972 9004 48 32 42 9004 9036 9067 9099 9131 9163 9195 9228 9260 9293 9325 47 32 43 9325 9358 9391 9424 9457 9490 9523 9556 9590 9623 9657 46 34 44 9657 9691 9725 9759 9793 9827 9861 9896 9930 9965 *0000 45 35 45 1.0000 0035 0070 0105 0141 01760212 0247 0283 0319 0355 44 36 46 0355 0392 0428 0464 0501 0538 0575 06120649 0686 0724 43 38 47 0724 0761 0799 0837 0875 0913 0951 0990 1028 1067 1106 42 39 48 1106 1145 1184 1224 1263 1303 1343 1383 1423 1463 1504 41 41 49 1504 1544 1585 1626 1667 1708 1750 1792 1833 1875 1918 40 43 60' 54' 48' 42' 36' 30' 24' 18' 12' 6' 0' 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 n° (1

The text on this page is estimated to be only 27.17% accurate

X, NATUKAL TANGENTS AND COTANGENTS. 29 cotn° n° .0 .1 . 2 .3 .4 .5 .6 .7 .8 .9 1, 0 (1 0' 6' 12' 18' 34' 30' 36' 42' 48' 54' 60' 50 1.1918 1960 2002 2045 2088 2131 2174 2218 2261 2305 2349 39 44 51 2349 2393 2437 2482 2527 2572 2617 2662 2708 2753 2799 38 46 52 2799 2846 2892 2938 2985 3032 3079 3127 3175 3222 3270 37 48 53 3270 3319 3367 3416 3465 3514 3564 3613 3663 3713 3764 36 51 54 3764 3814 3865 3916 3968 4019 4071 4124 4176 4229 4281 35 52 55 4281 4335 4388 4442 4496 4550 4605 4659 4715 4770 4826 34 56 56 4826 4882 4938 4994 5051 5108 5166 5224 5282 5340 5399 33 59 57 5399 5458 5517 5577 5637 5697 5757 5818 5880 5941 6003 32 62 58 6003 6066 6128 6191 6255 6319 6383 6447 6512 6577 6643 31 66 59 6643 6709 6775 6842 6909 6977 7045 71 U 7182 7251 7321 30 70 60 1.7321 7391 7461 7532 7603 7675 7747 7820 7893 7966 8040 29 74 61 8040 8115 8190 8265 8341 8418 8495 8572 8650 8728 8807 28 79 62 8807 8887 8967 9047 9128 9210 9292 9375 9458 9542 9626 27 84 63 9626 9711 9797 9883 9970*0057*0145 *0233*0323*0413 *0503 26 90 64 2.0503 0594 0686 0778 0872 0965 1060 1155 1251 1348 1445 25 97 65 1445 1543 1642 1742 1842 1943 2045 2148 2251 2355 2460 24 105 66 2460 2566 2673 2781 1 2889 2998 3109 3220 3332 3445 3559 23 114 67 3559 3673 3789 3906 4023 4142 4262 4383 4504 4627 4751 22 124 68 4751 4876 5002 5129 5257 5386 5517 5649 5782 5916 6051 21 135 69 6051 6187 6325 6464 6605 6746 6889 7034 7179 7326 7475 20 149 70 2.7475 7625 7776 7929 8083 8239 8397 8556 8716 8878 9042 19 164 71 9042 9208 9375 9544 9714 9887*0061 *0237*0415*0595 *0777 18 182 72 3.0777 0961 1146 1334 1524 1716 1910 2106 2305 2506 2709 17 203 73 2709 2914 3122 3332 3544 3759 3977 4197 4420 4646 4874 16 228 74 4874 5105 5339 5576 5816 6059 6305 6554 6806 7062 7321 15 75 7321 7583 7848 8118 8391 8667 8947 9232 9520 9812 *0108 14 76 4.010S 0408 0713 1022 1335 1653 1976 2303 2635 2972 3315 13 77 3315 3662 4015 4373 4737 5107 5483 5864 6252 6646 7046 12 78 7046 7453 7867 8288 8716 9152 9594 *0045*0504*0970 *1446 11 79 5 1446 1929 2422 2924 3435 3955 4486 5026 5578 6140 6713 10 80 5.6713 7297 7894 8502 9124 9758*0405 *1066*J 742*2432 *3138 9 81 6.3138 3859 4596 5350 6122 6912 7720 8548 9395*0264 *1154 8 827.115-1 2066 3002 3962 4947 5958 6996 8062 9158*0285 *1443 7 83 8.1443 2636 3863 5126 6427 7769 9152 *0579*2052*3572 *5144 6 84 9.5 14 9.6779.845 10.02jlO.20 10.39 10.58 10.7810.9911.20 11 .43 0 85 11.43 11.6611.91 12.16 12.43 12.7113.00 13.30 13.62 13.95 14.30 4 86 14. 30 14.67 15.06 15.46 15.8916.3516.83 17.3417.8918.46 19.08 3 87 19.08 19.74 20.45 21.20 22.02 22.90 23.86 24.90 26.03 27.27 28.64 2 88 28.64 30.1431.8233.6935.8038.1940.92 44.0747.7452.08 57 .29 1 89 57. 29 63.66 71. 628 1. 85 95.49114.6143.2 1910286.5573.0 0 1.0 .9 , 8 .7 .6 .5 .4 .3 .2 ! .1 .0 n^ d 20 21 22 23 24 25 26J27 28 29 30 31 32 33 34 35 36 37 38 39 1 3 444 444 555 5 556 666 667 2 7 778 889 9 9 10 10 10 11 11 11 12 12 12 13 13 3 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 4 13 14 15 15 16 17 17 18 19 19 20 21 21 22 23 23 24 25 25 26 5 17 18 18 19 20 21 22 23 23 24 25 26 27 28 28 29 30 31 32 33 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1 7 111 7 8 S 888 8 999 999 10 10 10 2 13 14 14 14 15 15 15 16 16 16 17 17 17 18 18 18 19 19 19 20 3 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 4 27 27 28 29 29 30 31 31 32 33 33 34 35 35 36 37 37 38 39 39 5 33 34 35 36 37 38 38 39 40 41 42 43 43 44 45 46 47 48 48 49

The text on this page is estimated to be only 27.61% accurate

30 XI. NATUEAL SECANTS AND COSECANTS. seen0 cosecn0 n° .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 (I 0' & 12' 18' 34' 30' 36' 42' 48' 54' 60' ~¥ 1.0000 0000 0000 0000 0000 0000 0001 0001 0001 0001 0002 89 T 1 0002 0002 0002 0003 0003 0003 0004 0004 0005 0006 0006 88 0 2 0006 0007 0007 0008 0009 0010 0010 0011 0012 0013 0014 87 i 3 0014 001500160017 0018 0019 0020 0021 0022 0023 0024 86 i 4 0024 0026 0027 0028 0030 0031 0032 0034 0035 0037 0038 85 i 5 0038 0040 0041 0043 0045 0046 0048 00500051 0053 0055 84 2 6 0055 005700590061 0063 0065 0067 0069 0071 0073 0075 83 2 7 0075 0077 0079 0082 0084 0086 0089 0091 0093 0096 0098 82 2 8 0098 0101 0103 0106 0108 0111 0114 011601190122 0125 81 3 9 0125 012701300133 0136 0139 0142 0145 0148 0151 0154 80 3 10 1.0154 0157 0161 0164 0167 0170 0174 0177 0180 0184 0187 T9 3 11 0187 019101940198 0201 0205 0209 0212 0216 0220 0223 78 3 12 0223 022702310235 0239 0243 0247 0251 0255 0259 0263 77 4 13 0263 0267 0271 0276 0280 0284 0288 0293 0297 0302 0306 76 4 14 0306 0311 0315 0320 0324 0329 0334 0338 0343 0348 0353 75 5 15 0353 035803630367 0372 0377 0382 0388 0393 0398 0403 74 5 16 0403 040804130419 0424 0429 0435 0440 0446 0451 0457 73 6 17 0457 0463 0468 0474 0480 0485 0491 0497 0503 0509 0515 72 6 18 0515 0521 0527 0533 0539 0545 0551 0557 0564 0570 0576 71 6 19 0576 058305890595 0602 0608 0615 0622 0628 0635 0642 70 7 20^ 1.0642 0649 0655 0662 0669 0676 0683 0690 0697 0704 0711 69 7 21 0711 071907260733 0740 0748 0755 0763 0770 0778 0785 68 7 22 0785 0793 0801 0808 0816 0824 0832 0840 0848 0856 0864 67 8 23 0864 0872 0880 0888 0896 0904 0913 0921 0929 0938 0946 66 8 24 0946 0955 0963 0972 0981 0989 0998 1007 1016 1025 1034' 65 9 25 1034 1043 1052 1061 1070 1079 1089 10981107 1117 1126 64 9 26 1126 11361145 1155 1164 1174 1184 1194 1203 1213 1223 63 10 27 1223 1233 1243 1253 1264 1274 1284 1294 1305 1315 1326 62 11 28 1326 1336 1347 1357 1368 1379 1390 1401 1412 1423 1434 61 11 29 1434 1445 1456 1467 1478 1490 1501 1512 1524 1535 1547 60 12 30 1.1547 1559 1570 1582 1594 1606 1618 1630 1642 1654 1666 59 12 31 1666 1679 1691 1703 1716 1728 1741 1753 1766 1779 1792 58 13 32 1792 1805 1818 1831 1844 1857 1870 1883 1897 1910 1924 57 14 33 1924 1937 1951 1964 1978 1992 2006 2020 2034 2048 2062 56 14 34 2062 2076 2091 2105 2120 2134 2149 2163 2178 2193 2208 55 15 35 2208 2223 2238 2253 2268 2283 2299 2314 2329 2345 2361 54 16 36 2361 2376 2392 2408 2424 2440 2456 2472 2489 2505 2521 53 16 37 2521 253825542571 2588 2605 2622 2639 2656 2673 2690 52 17 38 2690 2708 2725 2742 2760 2778 2796 2813 2831 2849 2868 51 19 39 2868 2886 2904 2923 2941 2960 2978 2997 3016 3035 3054 50 19 40 1.3054 307330933112 3131 3151 3171 319032103230 3250 19 20 41 3250 327032913311 3331 3352 3373 3393 3414 3435 3456 48 21 42 3456 3478 3499 3520 3542 3563 3585 3607 3629 3651 3673 47 22 43 3673 369637183741 3763 3786 3809 3832 3855 3878 3902 46 24 44 3902 3925 3949 3972 3996 4020 4044 406940934118 4142 45 24 45 4142 416741924217 4242 4267 4293 4318 4344 4370 4396 44 26 46 4396 4422 4448 4474 4501 4527 4554 4581 4608 4635 4663 43 28 47 4663 4690 4718 4746 4774 4802 4830 4859 4887 4916 4945 42 29 48 4945 4974 5003 5032 5062 5092 5121 5151 5182 5212 5243 41 31 49 5243 5273 5304 5335 5366 5398 5429 5461 5493 5525. 5557 40 32 (0' 54' 48' 42' 36' 30' 24' 18' 13' 6' O' 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 n° d

The text on this page is estimated to be only 27.60% accurate

XI. NATUKAL SECANTS AND COSECANTS. 31 sec nc cosec ir n° .0 .1 , 2 .3 .4 .5 .6 .7 .8 .9 1.0 (1 0' 6' 13' 18' 24' 30' 36' 42' 48' 54' 60' 50 1.5557 5590 5622 5655 5688 5721 5755. 5788 5822 5856 5890 39 34 51 5890 5925 5959 5994 6029 6064 6099 6135 6171 6207 6243 38 36 52 6243 6279 6316 6353 6390 6427 6464 6502 6540 6578 6616 37 38 53 6616 6655 6694 6733 6772 6812 6852 6892 6932 6972 7013 36 41 54 7013 7054 7095 7137 7179 7221 7263 7305 7348 7391 7434 35 43 55 7434 7478 7522 7566 7610 7655 7700 7745 7791 7837 7883 34 46 56 7883 7929 7976 8023 8070 8118 8166 8214 8263 8312 8361 33 49 57 8361 8410 8460 8510 8561 8612 8663 8714 8766 8818 8871 32 53 58 8871 8924 8977 9031 9084 9139 9194 9249 9304 9360 9416 31 56 59 9416 9473 9530 9587 9645 9703 9762 9821 9880 9940 *0000 30 60 60 2.0000 0061 0122 0183 0245 0308 0371 0434 0498 0562 0627 29 65 61 0627 0692 0757 0824 0890 0957 1025 1093 1162 1231 1301 28 70 62 1301 1371 1441 1513 1584 1657 1730 1803 1877 1952 2027 27 75 63 2027 2103 2179 2256 2333 2412 2490 2570 2650 2730 2812 26 82 64 2812 2894 2976 3060 3144 3228 3314 3400 3486 3574 3662 25 88 65 3662 3751 3841 3931 4022 4114 4207 4300 4395 4490 4586 24 96 66 4586 4683 4780 4879 4978 5078 5180 5282 5384 5488 5593 23 105 67 5593 5699 5805 5913 6022 6131 6242 6354 6466 6580 6695 22 115 68 6695 6811 6927 7046 7165 7285 7407 7529 7653 7778 7904 21 126 69 7904 8032 8161 8291 8422 8555 8688 8824 8960 9099 9238 20 139 70 2.9238 9379 9521 9665 9811 9957*0106 *0256*0407*0561 *0716 19 155 71 3.0716 0872 1030 1190 1352 1515 1681 1848 2017 2188 2361 18 173 72 2361 2535 2712 2891 3072 3255 3440 3628 3817 4009 4203 17 194 73 4203 4399 4598 4799 5003 5209 5418 5629 5843 6060 6280 16 220 74 6280 6502 6727 6955 7186 7420 7657 7897 8140 8387 8637 15 75 8637 8890 9147 9408 9672 9939*0211 *0486*0765*1048 *1336 14 76 4.1336 1627 1923 2223 2527 2837 3150 3469 3792 4121 4454 13 77 4454 4793 5137 5486 5841 6202 6569 6942 7321 7706 8097 12 78 8097 8496 8901 9313 9732*0159*0593 *1034*1484*1942 *240811 79 5.2408 2883 3367 3860 4362 4874 5396 5928 6470 7023 7588 10 80 5.7588 8164 8751 9351 9963*0589 1227 1880 2546 3228 3925 816.3925 4637 5366 6111 6874 765^ 8454 9273*0112*0972*1853 8 827.18.53 2757 3684 4635 5611 6613 7642 8700 9787*0905 *2055 7 83 8.2055 3238 4457 5711 7004 8337 9711 * 1129*2593*4105*5668 6 84 9.567 9.7289.89510.07 10.25 10.43 10.63 10.8311.0311.25 11.47 5 85 11. 47 11.7111 .95 12.20 12.4712.7513.03 13.3413.6513.99 14.34 4 86 14.34 14.7015.0915.50 15.93 16.38 16.86 17.3717.9118.49 19.11 3 87 19. 11 19.7720.4721.23 22.04 22.93 23.88 24.92 26.05 27.29 28.65 2 88 28.65 30.1631 .8433.71 35.8138.2040.93 44.0847.7552.09 57.30 1 89 57. 30 63.6671 .628185 9549114.6143.2 191.0286.5573.0 0 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 .0 nL ~

The text on this page is estimated to be only 28.94% accurate

32 XII. RADIANS. 180 n° .0 .1 .2 .3 h m 10 0.1745 1763 1780 1798 1815 1833 1850 1868 188,5 1902 .0278 0 40 11 1920 1937 1955 1972 1990 2007 2025 2042 2059 2077 .0306 0 44 12 2094 2112 2129 2147 2164 2182 2199 2217 2234 2251 .0333 0 48 13 2269 2286 2304 2321 2339 2356 2374 2391 2409 2426 .0361 0 52 14 2443 2461 2478 2496 2513 2531 2548 2566 2583 2601 .0389 0 56 15 2618 2635 2653 2670 2688 2705 2723 2740 2758 2775 .0417 1 0 16 2793 2810 2827 2845 2862 2880 2897 2915 2932 2950 .0444 1 4 17 2967 2985 3002 3019 3037 3054 3072 3089 3107 3124 .0472 1 8 18 3142 3159 3176 3194 3211 3229 3246 3264 3281 3299 .0500 1 12 19 3316 3334 3351 3368 3386 3403 3421 3438 3456 3473 .0528 1 16 20 0.3491 3508 3526 3543 3560 3578 3595 3613 3630 3648 .0556 1 20 21 3665 3683 3700 3718 3735 3752 3770 3787 3805 3822 .0583 1 24 22 3840 3857 3875 3892 3910 3927 3944 3962 3979 3997 .0611 1 28 23 4014 4032 4049 4067 4084 4102 4119 4136 4154 4171 .0639 1 32 24 4189 4206 4224 4241 4259 4276 4294 4311 4328 4346 .0667 I 36 25 4363 4381 4398 4416 4433 4451 4468 4485 4503 4520 .0694 1 40 26 4538 4555 4573 4590 4608 4625 4643 4660 4677 4695 .0722 1 44 27 4712 4730 4747 4765. 4782 4800 4817 4835 4852 4869 .0750 1 48 28 4887 4904 4922 4939 4957 4974 4992 5009 5027 5044 .0778 1 52 29 5061 5079 5096 5114 5131 5149 5166 5184 5201 5219 .0806 1 56 30 0.5236 5253 5271 5288 5306 5323 5341 5358 5376 5393 .0833 2 0 31 5411 5428 5445 5463 5480 5498 5515 5533 5550 5568 .0861 2 4 32 5585 5603 5620 5637 5655 5672 5690 5707 5725 5742 .0889 2 8 33 5760 5777 5794 5812 5829 5847 5864 5882 5899 5917 .0917 2 12 34 5934 5952 5969 5986 6004 6021 6039 6056 6074 6091 .0944 2 16 35 6109 6126 6144 6161 6178 6196 6213 6231 6248 6266 .0972 2 20 36 6283 6301 6318 6336 6353 6370 6388 6405 6423 6440 .1000 2 24 37 6458 6475 6493 6510 6528 6545 6562 6580 6597 6615 .1028 2 28 38 6632 6650 6667 6685 6702 6720 6737 6754 6772 6789 .1056 2 32 39 6807 6824 6842 6859 6877 6894 6912 6929 6946 6964 .1083 2 36 40 0.6981 6999 7016 7034 7051 7069 7086 7103 7121 7138 .1111 2 40 41 7156 7173 7191 7208 7226 7243 7261 7278 7295 7313 .1139 2 44 42 7330 7348 7365 7383 7400 7418 7435 7453 7470 7487 .1167 2 48 43 7505 7522 7540 7557 7575 7592 7610 7627 7645 7662 .1194 2 52 44 7679 7697 7714 7732 7749 7767 7784 7802 7819 7837 .1222 2 56 45 7854 7871 7889 7906 7924 7941 7959 7976 7994 8011 .1250 3 0 46 8029 8046 8063 8081 8098 8116 8133 8151 8168 8186 .1278 3 4 47 8203 8221 8238 8255 8273 8290 8308 8325 8343 8360 .1306 3 8 48 8378 8395 8412 8430 8447 8465 8482 8500 8517 8535 .1333 3 12 49 8552 8570 8587 8604 8622 8639 8657 8674 8692 8709 .1361 3 16 50 0.8727 8744 8762 8779 8796 8814 8831 8849 8866 8884 .1389 3 20 51 8901 8919 8936 8954 8971 8988 9006 9023 9041 9058 .1417 3 24 52 9076 9093 9111 9128 9146 9163 9180 9198 9215 9233 .1444 3 28 53 9250 9268 9285 9303 9320 9338 9355 9372 9390 9407 .1472 3 32 54 9425 9442 9460 9477 9495 9512 9529 9547 9564 9582 .1500 3 36 55 9599 9617 9634 9652 9669 9687 9704 9721 9739 9756 .1528 3 40 56 9774 9791 9809 9826 9844 9861 9879 9896 9913 9931 .1556 3 44 57 9948 9966 9983*0001 *00 18*0036*0053 *007 1*0088*0105 .1583 3 48 58 1.0123 0140 0158 0175 0193 0210 0228 0245 0263 0280 .1611 3 52 59 0297 0315 0332 0350 0367 03S5 0402 0420 0437 0455 .1639 3 56

The text on this page is estimated to be only 28.67% accurate

XII, EADIANS, 33 ISO n° .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 P h m 60 1.0472 0489 0507 0524 0542 0559 0577 0594 0612 0629 .1667 4 0 61 0647 0664 0681 0699 0716 0734 0751 0769 0786 0804 .1694 4 4 62 0821 0838 0856 0873 0891 0908 0926 0943 0961 0978 .1722 4 8 63 0996 1013 1030 1048 1065 1083 1100 1118 1135 1153 .1750 4 12 64 1170 1188 1205 1222 1240 1257 1275 1292 1310 1327 .1778 4 16 65 1345 1362 1380 1397 1414 1432 1449 1467 1484 1502 .1806 4 20 66 1519 1537 1554 1572 1589 1606 1624 1641 1659 1676 .1833 4 24 67 1694 1711 1729 1746 1764 1781 1798 1816 1833 1851 .1861 4 28 68 1868 1886 1903 1921 1938 1956 1973 1990 2008 2025 .1889 4 32 69 2043 2060 2078 2095 2113 2130 2147 2165 2182 2200 .1917 4 36 70 1.2217 2235 2252 2270 2287 2305 2322 2339 2357 2374 .1944 4 40 71 2392 2409 2427 2444 2462 2479 2497 2514 2531 2549 .1972 4 44 72 2566 2584 2601 2619 2636 2654 2671 2689 2706 2723 .2000 4 48 73 2741 2758 2776 2793 2811 2828 2846 2863 2881 2898 .2028 4 52 74 2915 2933 2950 2968 2985 3003 3020 3038 3055 3073 .2056 4 56 75 3090 3107 312^ 3142 3160 3177 3195 3212 3230 3247 .2083 5 0 76 3265 3282 3299 3317 3334 3352 3369 3387 3404 3422 .2111 5 4 77 3439 3456 3474 3491 3509 3526 3544 3561 3579 3596 .2139 5 8 78 3614 3631 3648 3666 3683 3701 3718 3736 3753 3771 .2167 5 12 79 3788 3806 3823 3840 3858 3875 3893 3910 3928 3945 .2194 5 16 80 1.3963 3980 3998 4015 4032 4050 4067 4085 4102 4120 .2222 5 20 81 4137 4155 4172 4190 4207 4224 4242 4259 4277 4294 .2250 5 24 82 4312 4329 4347 4364 4382 4399 4416 4434 4451 4469 .2278 5 28 83 4486 4504 4521 4539 4556 4573 4591 4608 4626 4643 .2306 5 32 84 4661 4678 4696 4713 4731 4748 4765 4783 4800 4818 .2333 5 36 85 4835 4853 4870 4888 4905 4923 4940 4957 4975 4992 .2361 5 40 86 5010 5027 5045 5062 5080 5097 5115 5132 5149 5167 .2389 5 44 87 5184 5202 5219 5237 5254 5272 5289 5307 5324 5341 .2417 5 48 88 5359 5376 5394 5411 5429 5446 5464 5481 5499 5516 .2444 5 52 89 5533 5551 5568 5586 5603 5621 5638 5656 5673 5691 .2472 5 56 90 1.5708 5725 5743 5760 5778 5795 5813 5830 5848 5865 .2500 6 0 91 5882 5900 5917 5935 5952 5970 5987 6005 6022 6040 .2528 6 4 92 6057 6074 6092 6109 6127 6144 6162 6179 6197 6214 .2556 6 8 93 6232 6249 6266 6284 6301 6319 6336 6354 6371 6389 .2583 6 12 94 6406 6424 6441 6458 6476 6493 6511 6528 6546 6563 .2611 6 16 95 6581 6598 6616 6633 6650 6668 6685 6703 6720 6738 .2639 6 20 96 6755 6773 6790 6808 6825 6842 6860 6877 6895 6912 .2667 6 24 97 6930 6947 6965 6982 7000 7017 7034 7052 7069 7087 .2694 6 28 98 7104 7122 7139 7157 7174 7191 7209 7226 7244 7261 .2722 6 32 99 7279 7296 7314 7331 7349 7366 7383 7401 7418 7436 .2750 6 36 n' 0 123 456 7 8 9 P s T .002909 3200 3491 3782 4072 4363 4654 4945 5236 5527 0000463 4 2 .005818 6109 6400 6690 6981 7272 7563 7854 8145 8436 0926 8 3 .008727 9018 9308 9599 9890*0181*0472 *0763*1054*1345 1389 12 4 .01 1636 1926 2217 2508 2799 3090 3381 3672 3963 4254 1852 16 5 .01 4544 4835 5126 5417 5708 5999 6290 6581 6872 7162 2315 20 6 .01 7453 7744 8035 8326 8617 8908 9199 9490 9780*0071 2778 24 7 .02 0362 0653 0944 1235 1526 1817 2108 2398 2689 2980 3241 28 8 .023271 3562 3853 4144 4435 4725 5016 5307 5598 5889 3704 32 9 .02 6180 6471 6762 7053 7343 7634 7925 8216 8507 8798 4167 36

The text on this page is estimated to be only 27.29% accurate

34 XIII, KEOIPROCALS, n 0 123 456 7 8 9 a 1.0 1.0000 9901 9804 9709 9615 9524 9434 9346 9259 9174 83 1.1 0.9091 9009 8929 8850 8772 8696 8621 8547 8473 8403 70 1.2 8333 8264 8197 8130 8063 8000 7937 7874 7813 7752 60 1.8 7692 7634 7576 7519 7463 7407 7353 7299 7246 7194 51 1.4 7143 7092 7042 6993 6944 6897 6849 6803 6757 671 ?. 44 1.5 6667 6623 6579 6536 6494 6452 6410 6369 6329 6289 39 1.6 6250 6211 6173 6135 6098 6061 6024 5988 5952 5917 35 1.7 5882 5848 58.14 5780 5747 5714 5682 5650 5618 5587 31 1.8 5556 5525 5495. 5464 5435 5405 5376 5348 5319 5291 28 1.9 5263 5236 5208 5181 5155 5128 5102 5076 5051 5025 25 2.0 0.5000 4975 4950 4926 4902 4878 4854 4831 4808 4785 23 2.1 4762 4739 4717 4695 4673 4651 4630 4608 4587 4566 21 2.2 4545 4525. 450^ 4484 4464 4444 4-125 4405 4386 4367 19 2.3 4348 4329 4310 4292 4274 4255 42374219 4202. 4 184 17 2.4 4167 4149 ^132 4115 4098 4082 40654049 4032 4016 16 2.5 4000 3984 3968 3953 3937 3922 3906 3891 3S76 3861 15 2.6 3846 3831 3817 3802 3788 3774 3759 3745 3731 3717 13 2.7 3704 3690 3676 3663 3650 3636 3623 3610 3597 3584 13 2.8 3571 3559 3546 3534 3521 3509 3497 3484 3472 3460 12 2.9 3448 3436 3425 3413 3401 3390 337§ 3367 3356 3344 11 3.0 0.3333 3322 33U 3300 3289 3279 3268 3257 3247 3236 ~Tb~ 3.1 3226 3215 3205 3195 3185 3175 3165 3155 3145 3135 10 3.2 3125 3115 3106 3096 3086 3077 3067 305$ 3049 3040 10 3.3 3030 3021 3012 3003 2994 2985 2976 2967 2959 29&) 9 3.4 2941 2933 2924 2915 290*7 2899 2890 2882 2874 2865 8 3.5 2857 2849 2841 2833 2325 2817 2£09 2801 2793 2786 8 3.6 2778 2770 2762 2755 27-4.7 2740 2732 2723 2717 2710 7 3.7 2703. 2695 2688 2681 2674 2667 2660 2653 2646 2639 7 3.8 2632 2625 2618 2611 2604 2597 2591 2584 2577 2571 7 3.9 2564 2558 255.1 2545 2538 2532 2525 2519 2513 2506 6 4.0 0.2500 2494 2488 2481 2475 2469 2463 2457 2451 2443 6 4.1 2439 2433 2427 2421 2415 2410 2404 2398 2392 2387 6 4.3 2381 2375 2370 2364 2358 2353 2347 2342 2336 2331 5 4.3 2326 2320 2315 2309 2304 2299 2294 2288 2283 2278 5 4.4 2273 2268 2262 2257 2252 2247 2242 2237 2232 2227 5 4.5 2222 2217 2212 2208 22~03 2198 2193 2188 2183 2179 5 4.6 2JL74 2169 2165 2160 2155 2151 2146 2141 2137 2132 4 4.7 2128 2123 2119 2114 2110 2105 2101 2096 2092 2088 5 4.8 2083 2079 2075 2070 2066 2062 2058 2053 2049 2045 4 4.9 2041 2037 2033 2028 2024 2020 2016 201,2 2008 2004 4 5.0 0.2000 1996 1992 1988 1984 1980 1976 1972 1969 1965 4 5.1 1961 1957 1953 1949 1946 1942 1938 1934 1931 1927 4 5.2 1923 1919 1916 1912 1908 1905 1901 1898 1894 1890 3 5.3 1887 1883 1880 1876 1873 1869 1866 1862 1859 1855 3 5.4 1852 1848 1845 1842 1838 1835 1832 1828 1825 1821 3 5.5 1818 1815 1812 1808 1805 1802 1799 1295 1792 1789 3 5.6 1786 1783 1779 1776 1773 1770 1767 1764 1761 1757 3 *5.7 1754 1751 1748 1745 1742 1739 1736 1733 1730 1727 3 5.8 1724 1721 1718 1715 1712 1709 1706 1704 1701 1698 3 5.9 1695. 1692 1689 1686 1634 1681 1678 1675 1672 1669 2

The text on this page is estimated to be only 27.77% accurate

XIII. EECIPKOCALS, 35 11 0 1 2 3 4 5 6 7 8 9 a 6.0 0.1667 1664 1661 1658 1656,1653 1650 1647 1645 1642 3 6.1 1639 1637 1634 1631 1629 1626 1623 1621 1618 1616 3 6.2 1613 1610 1608 1605 1603 1600 1597 1595 1592 1590 3 6.3 1587 1585 1582 1580 1577 1575 1572 1570 1567 1565 2 6.4 1563 1560 1558 1555 1553 1550 1548 1546 1543 1541 3 6.5 1538 1536 1534 1531 1529 1527 1524 1522 1520 1517 2 6.6 1515 1513 1511 1508 1506 1504 1502 1499 1497 1495 2 6.7 1493 1490 1488 1486 1484 1481 1479 1477 1475 1473 2 6.8 1471 * 1468 1466 1464 1462 1460 1458 1456 1453 1451 2 6.9 1449 1447 1445 1443 1441 1439 1437 1435 1433 1431 2 7.0 0.1429 1427 1425 1422 1420 1418 1416 1414 1412 1410 2 7.1 1408 1406 1404 1403 1401 1399 1397 1395 1393 1391 2 7.2 138? 1387 1385 1383 1381 1379 1377 1376 1374 1372 2 7.3 1370 1368 1366 1364 1362 1361 1359 1357 1355 1353 2 7.4 1351 1350 1348 1346 1344 1342 1340 1339 1337 1335 2 7.5 1333 1332 1330 1328 1326 1325 1323 1321 1319 1318 2 7.6 1316 1314 1312 1311 1309 1307 1305 1304 1302 1300 1 7.7 1299 1297 1295 1294 1292 1290 1289 1287 1285 1284 2 7.8 1282 1280 1279 1277 1276 1274 1272 1271 1269 1267 1 7.9 1266 1264 1263 1261 1259 1258 1256 1255 1253 1252 2 8.0 0.1250 1248 1247 1245 1244 1242 1241 1239 1238 1236 1 8.1 1235 1233 1232 1230 1229 1227 1225 1224 1222 1221 1 8.2 1220 1218 1217 1215 1214 1212 1211 1209 1208 1206 1 8.3 1205 1203 1202 1200 1199 1198 1196 1195 1193 1192 2 8.4 1190 1189 1188 1186 1185 1183 1182 1181 1179 1178 2 8.5 1176 1175 1174 1172 1171 1170 1168 1167 1166 1164 1 8.6 1163 1161 1160 1159* 1157 1156 1155 1153 1152 1151 2 8.7 1149 1148 1147 1145 1144 1143 1142 1140 1139 1138 2 8.8 1136 1135 1134 1133 1131 1130 1129 1127 1126 1125 1 8.9 1124 1122 1121 1120 1119 1117 1116 1114 1114 1112 1 9.0 0.1111 1110 1109 1107 1106 1105 1104 1103 1101 1100 1 9.1 1099 1098 1096 1095 1094 1093 1092 1091 1089 1088 1 9.2 1087 1086 1085 1083 1082 1081 1080 1079 1078 1076 1 9.3 1075 1074 1073 1072 1071 1070 1068 1067 1066 1065 1 9.4 1064 1063 1062 1060 1059 1058 1057 1056 1055 1054 1 9.5 1053 105*2 1050 1049 1048 1047 1046 1045 1044 1043 1 9.6 1042 1041 1040 1038 1037 1036 1035 1034 1033 1032 1 9.7 1031 1030 1029 1028 1027 1026 1025 1024 1022 1021 1 9.8 1020 1019 1018 1017 1016 1015 1014 1013 1012 1011 1 9.9 1010 1009 1008 1007 1006 1005 1004 1003 1002 1001 1 * 3 456 789 11 12 13 14 15 16 1 .5 .(3) .25 .2 .1(6) .1429.125 .(1) .(09) .08(3) .0769 .0714 .0(6) .0625 2 ,6) .5 .4 .(3) .75 .6 .5 .2857.25 .(2) .4286 .375 .(3) .(18) .1(6) .1538 .(27) .25 " .2308 .1429.1(3) .125 .2143 .2 .1875 4 .8 .(6) .5714 .5 .(4) .(36) .(3) .3077 .2857 .2(6) .25 5 .8(3) .7143 .625 .(5) .(45) .41 (6) .3846 .3571 .(3) .3125 6 .8571 .75 .(6) .(54) .5 .4615 .4286 .4 .375 7 .875 .(7) .(63) .58(3) .5385 .5 .4(6) .4375 8 .(8) .(72) .(6) .61541 .5714.5(3) .5 9 .(81) .75 .6923 .6429.6 .5625

The text on this page is estimated to be only 28.25% accurate

3(5 XIV. SQUAKES. n 0 123 456 7 8 9 (1 1.0 1.000 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 22 1.1 1.210 1.232 1.254 1.277 1.300 1.323 1.346 1.369 1.392 1.416 24 .2 1.440 1.464 1.488 1.513 1.538 1.563 1.588 1.613 1.638 1.664 26 .3 1.690 1.716 1.742 1.769 1.796 1.823 1.850 1.877 1.904 1.932 28 A 1.960 1.9S8 2.016 2.045 2.074 2.103 2.132 2.161 2.190 2.220 30 .5 2.250 2.280 2.310 2.341 2.372 2.403 2.434 2.465 2.496 2.528 32 .6 2.560 2.592 2.624 2.657 2.690 2.723 2.756 2.789 2.822 2.856 34 1.7% 2.890 2.924 2.958 2.993 3.028 3.063 3.098 3.133 3.168 3.204 36 1.8 3.240 3.276 3.312 3.349 3.386 3.423 3.460 3.-I97 3.534 3.572 3S 1.9 3.610 3.648 3.686 3.725 3.764 3.803 3.842 3.SS1 3.920 3.960 40 2.0 4.000 4.040 4.080 4.121 4.162 4.203 4.244 4.285 4.326 4.368 42 2.1 4.410 4.452 4.494 4.537 4.580 4.623 4.666 4.709 4.752 4.796 44 2.2 4.840 4.884 4.928 4.973 5.018 5.063 5.108 5.153 5.198 5.244 46 2.3 5.290 5.336 5.382 5.429 5.476 5.523 5.570 5.617 5.664 5.712 48 2.4 5.760 5.808 5.856 5.905 5.954 6.003 6.052 6.101 6 150 6.200 50 2.5 6.250 6.300 6 350 6.401 6.452 6.503 6.554 6.605 6.656 6.708 52 2.6 6.760 6.812 6.864 6.917 6.970 7.023 7.076 7.129 7.182 7.236 54 2.7 7.290 7.344 7.398 7.453 7.508 7.563 7.618 7.673 7.728 7.784 56 2.8 7.840 7.896 7.952 8.009 8.066 8.123 8. ISO 8.237 8.294 8.352 58 2.9 8.410 8.468 8.526 8.585 8.644 8.703 8.762 8.821 8.880 8.940 60 3.0 9.000 9.060 9.120 9.181 9.242 9.303 9.364 9.425 9.486 9.548 62 3.1 9.610 9.672 9.734 9.797 9.860 9.923 9.986 10.05 10.11 10.18 6 3.2 10.24 10.30 10.37 10.43 10.50 10.56 10.63 10.69 10.76 10.82 7 3.3 10.89 10.96 11.02 11.09 11.16 11.22 11.29 11.36 11.42 11,49 7 3.4 11.56 11.63 11.70 11.76 11.83 11.90 11.97 12.04 12.11 12.18 7 3.5 12.25 12.32 12.39 12.46 12.53 12.60 12.67 12.74 12.82 12.89 7 3.6 12.96 13.03 13.10 13.18 13.25 13.32 13.40 13.47 13.54 13.62 7 3.7 13.69 13.76 13.84 13.91 13.99 14.06 14.14 14.21 14.29 14.36 8 3.8 14.44 14.52 14.59 14.67 14.75 14.82 14.90 14.98 15.05 15.13 8 3.9 15.21 15.29 15.37 15.44 15.52 15.60 15.68 15.76 15.84 15.92 8 4.0 16.00 16.08 16.16 16.24 16.32 16.40 16.48 16.56 16.65 16.73 T 4.1 16.81 16.89 16.97 17.06 17.14 17.22 17.31 17.39 17.47 17.56 8 4.2 17.64 17.72 17.81 17.89 17.98 18.06 18.15 18.23 18.32 18.40 9 4.3 18.49 18.58 18.66 18.75 18.84 18.92 19.01 19.10 19.18 19.27 9 4.4 19.36 19.45 19.54 19.62 19.71 19.80 19.89 19.98 20.07 20.16 9 4.5 20.25 20.34 20.43 20.52 20.61 20.70 20.79 20.88 20.98 21.07 9 4.6 21.16 21.25 21.34 21.44 21.53 21.62 21.72 21.81 21.90 22.00 9 4.7 22.09 22.18 22.28 22.37 22.47 22.56 22.66 22.75 22.85 22.94 10 4.8 23.04 23.14 23.23 23.33 23.43 23.52 23.62 23.72 23.81 23.91 10 4.9 24.01 24.11 24.21 24.30 24.40 24.50 24.60 24.70 24.80 24.90 10 5.0 25.00 25.10 25.20 25.30 25.40 25.50 25.60 25.70 25.81 25.91 To~ 5.1 26.01 26.11 26.21 26.32 26.42 26.52 26.63 26.73 26.83 26.94 10 5.2 27.04 27.14 27.25 27.35 27.46 27.56 27.67 27.77 27.88 27.98 11 5.3 28.09 28.20 28.30 28.41 28.52 28.62 28.73 28.84 28.94 29.05 11 5.4 29.16 29.27 29.38 29.48 29.59 29.70 29.81 29.92 30.03 30.14 11 5.5 30.25 30.36 30.47 30.58 30.69 30.80 30.91 31.02 31.14 31.25 11 5.6 31.36 31.47 31.58 31.70 31.81 31.92 32.04 32.15 32.26 32.38 11 5.7 32.49. 32.60 32.72 32.83 32.95 33.06 33.18 33.29 33.41 33.52 12 5.8 33.64 33.76 33.87 33.99 34.11 34.22 34.34 34.46 34.57 34.69 12 5.9 34.81 34.93 35.03 35.16 35.28 35.40 35.52 35.64 35.76 35.88 12

The text on this page is estimated to be only 28.55% accurate

XIV. SQUARES. 37 11 0 123 456 7 8 9 (1 6.0 36.00 36.12 36.24 36.36 36.48 36.60 36.72 36.84 36.97 37.09 12 G.I 37.21 37.33 37.45 37.58 37.70 37.82 37.95 38.07 38.19 38.32 12 6.2 33.44 38.56 38.69 38.81 38.94 39.06 39.19 39.31 39.44 39.56 13 6.3 39.69 39.82 39.94 40.07 40.20 40.32 40.45 40.58 40.70 40.83 13 6.4 40.96 41.09 41.22 41.34 41.47 41.60 41.73 4186 41.99 42.12 13 6.5 42.25 42.38 42.51 42.64 42.77 42.90 43.03 43.16 43.30 43.43 13 6.6 43.56 43.69 43.82 43.96 44.09 44.22 44.36 44.49 44.62 44.76 13 6.7 44.89 45.02 45.16 45.29 45.43 45.56 45.70 45.83 45.97 46.10 14 6.8 46.24 46.38 46.51 46.65 46.79 46.92 47.06 47.20 47.33 47.47 14 6.9 47.61 47.75 47.89 48.02 48.16 48.30 48.44 48.58 48.72 48.86 14 7.0 49.00 49.14 49.28 49.42 49.56 49.70 49.84 49.98 50.13 50.27 T4~ 7.1 50.41 50.55 50.69 50.84 50.98 51.12-51.27 51.41 51.55 51.70 14 7.2 51.84 51.98 52.13 52.27 52.42 52.56 52.71 52.85 53.00 53.14 15 7.3 53.29 53.44 53.58 53.73 53.88 54.02 54.17 54.32 54.46 54.61 15 7.4 54.76 54.91 55.06 55.20 55.35 55.50 55.65 55.80 55.95 56.10 15 7.5 56.25 56.40 56.55 56.70 56.85 57.00 57.15 57.30 57.46 57.61 15 7.6 57.76 57.9* 58.06 58.22 58.37 58.52 58.68 58.83 58.98 59.14 15 7.7 59.29 59.44 59.60 59.75 59.91 60.06 60.22 60.37 60.53 60.68 16 7.8 60.84 61.00 61.15 61.31 61.47 61.62 61.78 61.94 62.09 62.25 16 7.9 62.41 62.57 62.73 62.88 63.04 63.20 63.36 63.52 63.68 63.84 16 8.0 64.00 64.16 64.32 64.48 64.64 64.80 64.96 65.12 65.29 65.45 16 8.1 65.61 65.77 65.93 66.10 66.26 66.42 66.59 66.75 66.91 67.08 16 8.2 67.24 67.40 67.57 67.73 67.90 68.06 68.23 68.39 68.56 68.72 17 8.3 68.89 69.06 69.22 69.39 69.56 69.72 69.89 70.06 70.22 70.39 17 8.4 70.56 70.73 70.90 71.06 71.23 71.40 71.57 71.74 71.91 72.08 17 8.5 72.25 72.42 72.59 72.76 72.93 73.10 73.27 73.44 73.62 73.79 17 8.6 73.96 74.13 74.30 74.48 74.65 74.82 75.00 75.17 75.34 75.52 17 8.7 75.69 75.86 76.04 76.21 76.39 76.56 76.74 76.91 77.09 77.26 18 8.8 77.44 77.62 77.79 77.97 78.15 78.32 78.50 78.68 78.85 79.03 18 8.9 79.21 79.39 79.57 79.74 79.92 80.10 80.28 80.46 80.64 80.82 18 9.0 81.00 81.18 81.36 81.54 81.72 81.90 82.08 82.26 82.45 82.63 18 9.1 82.81 82.99 83.17 83.36 83.54 83.72 83.91 84.09 84.27 84.46 18 9.2 84.64 84.82 85.01 85.19 85.38 85.56 85.75 85.93 86.12 86.30 19 9.3 86.49 86.68 86.86 87.05 87.24 87.42 87.61 87.80 87.98 88.17 19 9.4 88.36 88.55 88.74 88.92 89.11 89.30 89.49 89.68 89.87 90.06 19 9.5 90.25 90.44 90.63 90.82 91.01 91.20 91.39 91.58 91.78 91.97 19 9.6 92.16 92.35 92.54 92.74 92.93 93.12 93.32 93.51 93.70 93.90 19 9.7 94.09 94.28 94.48 94.67 94.87 95.06 95.26 95.45 95.65 95.84 20 9.8 96.04 96.24 96.43 96.63 96.83 97.02 97.22 97.42 97.61 97.81 20 9.9 98.01 98.21 98.41 98.60 98.80 99.00 99.20 99.40 99.60 99.80 20 n .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 (1 1 1.000 *826 *694 *592 *510 *444 *391 *346 *309 *277 27 2 0.250 227 207 189 174 160 148 137 128 119 8 3 0.111 104 *977 *918 *865 *S16 *772 *730 *693 *657 32 4 0.0 625 595 567 541 517 494 473 453 434 416 16 5 0.0 400 384 370 356 343 331 319 308 297 287 9 6 0.0 278 269 260 252 244 237 230 223 216 210 6 7 0.0 204 198 193 188 183 178 173 169 164 160 4 8 0.0 156 152 149 145 142 138 135 132 129 126 3 9 0.0 123 121 118 116 113 111 109 106 104 102 2

The text on this page is estimated to be only 28.98% accurate

XV. CUBES. n3 n 0 123 456 7 8 9 (1 1.0 1.000 1.030 1.061 1.093 1.123 1.158 1.191 1.225 1.260 1.295 36 1.1 1.331 1.368 1.405 1.443 1.482 1.521 1.561 1.602 1.643 1.685 43 .2 1.728 1.772 1.816 1.861 1.907 1.953 2.000 2.048 2.097 2.147 50 .3 2.197 2.248 2.300 2.353 2.406 2.460 2.515 2.571 2.628 2.686 58 A 2.744 2.803 2.863 2.924 2.986 3.049 3.112 3.177 3.242 3.308 67 .5 3.375 3.443 3.512 3.582 3.652 3.724 3.796 3.870 3.944 4.020 76 .6 4.096 4.173 4.252 4.331 4.411 4.492 4.574 4.657 4.742 4.827 86 1.7 4.913 5.000 5.088 5.178 5.268 5.359 5.452 5.545 5.640 5.735 97 1.8 5.832 5.930 6.029 6.128 6.230 6.332 6.435 6.539 6.645 6.751 108 1.9 6.859 6.968 7.078 7.189 7.301 7.413 7.530 7.645 7.762 7.881 119 2.0 8.000 8.121 8.242 8.365 8.490 8.615 8.742 8.870 8.999 9.129 132 2.1 9.261 9.394 9.528 9.664 9.800 9:938 10.08 10.22 10.36 10.50 15 2.2 10.648 10.79 10.94 11.09 11.24 11.39 11.54 11.70 11.85 12.01 16 2.3 12.167 12.33 12.49 12.63 12.81 12.98 13.14 13.31 13.48 13.65 17 2.4 13.824 14.00 14.17 14.33 14.53 14.71 14.89 15.07 15.25 15.44 19 2.5 15.625 15.81 16.00 16.19 16.39 16.58 16.78 16.97 17.17 17.37 21 2.6 17.576 17.78 17.98 18.19 18.40 18.61 18.82 19.03 19.23 19.47 21 2.7 19.683 19.90 20.12 20.35 20.57 20.80 21.02 21.25 21.48 21.72 23 2.8 21.952 22.19 22.43 22.67 22.91 23.15 23.39 23.64 23.89 24.14 25 2.9 24.389 24.64 24.90 25.15 25.41 25.67 25.93 26.20 26.46 26.73 27 3.0 27.000 27.27 27.54 27.82 28.09 28.37 28.65 28.93 29.22 29.50 29 3.1 29.791 30.08 30.37 30.66 30.96 31.26 31.55 31.86 32.16 32.46 31 3.2 32.768 33.08 33.39 33.70 34.01 34.33 34.65 34.97 35.29 35.61 33 3.3 35.937 36.26 36.59 36.93 37.26 37.60 37.93 38.27 38.61 38.9,6 34 3.4 39.304 39.65 40.00 40.35 40.71 41.06 41.42 41.78 42.14 42.51 37 3.5 42.875 43.24 43.61 43.99 44.36 44.74 45.12 45.50 45.88 46.27 39 3.6 46.656 47.0^ 47.44 47.83 48.23 48.63 49.03 49.43 49.84 50.24 41 3.7 50.653 51.06 51.48 51.90 52.31 52.73 53.16 53.58 54.01 54.44 43 3.8 54.872 55.31 55.74 56.18 56.62 57.07 57.51 57.96 58.41 58.86 46 3.9 59.319 59.78 60.24 60.70 61.16 61.63 62.10 62.57 63.04 63.52 48 4^0 64.000 64.48 64.96 65.45 65.94 66.43 66.92 67.42 67.92 68.42 ^50 4.1 68.921 69.43 69.93 70.44 70.96 71.47 71.99 72.51 73.03 73.56 53 4.2 74.088 74.62 75.15 75.69 76.23 76.77 77.31 77.85 78.40 78.95 56 4.3 79.507 80.06 80.62 81.18 81.73 82.31 82.88 83.45 84.03 84.60 58 4.4 85.184 85.77 86.35 86.94 87.53 88.12 88.72 89.31 89.92 90.52 61 4.5 91.125 91.73 92.33 92.96 93.58 94.20 94.82 95.44 96.07 96.70 64 4.6 97.336 97.97 98.61 99.25 99.90 100.5 101.2 101.8 102.5 103.2 6 4.7 103.823 104.3 105.2 105.8 106.3 107.2 107.9 108.5 109.2 109.9 7 4.8 110.592 111.3 112.0 112.7 113.4 114.1 114.8 115.5 116.2 116.9 7 4.9 117.649 118.4 119.1 119.8 120.6 121.3 122.0 122.8 123.5 124.3 7 5.0 125.000 125.8 126.5 127.3 128.0 128.8 129.6 130.3 131.1 131.9 8 5.1 132.651 133.4 134.2 135.0 135.8 136.6 137.4 138.2 139.0 139.8 8 5.2 140.608 141.4 142.2 143.1 143.9 144.7 145.5 146.4 147.2 148.0 9 5.3 148.877 149.7 150.6 151.4 152.3 153.1 154.0 154.9 155.7 156.6 9 5.4 157.464 158.3 159.2 160.1 161.0 161.9 162.8 163.7 164.6 165.5 9 5.5 166.375 167.3 168.2 169.1 170.0 171.0 171.9 172.8 173.7 174.7 9 5.6 175.616 176.6 177.5 178.5 179.4 180.4 181.3 182.3 183.3 184.2 10 5.7 185.193 186.2 187.1 188.1 189.1 190.1 191.1 192.1 193.1 194.1 10 5.8 195.112 196.1 197.1 198.2 199.2 200.2 201.2 202.3 203.3 204.3 11 5.9 205.379 206.4 207.3 208.5 209.6 210.6 211.7 212.8 213.8 214.9 11

The text on this page is estimated to be only 28.43% accurate

XV. CUBES. n 0 123 456 7 8 9 d 6.0 216.000 217.1 218.2 219.3 220.3 221.4 222.5 223.6 224.8 225.9 11 6.1 226.981 228.1 229.2 230.3 231.5 232.6 233.7 234.9 236.0 237.2 11 6.2 238.328 239.5. 240.6 241.8 243.0 244.1 245.3 246.5 247.7 248.9 11 6.3 250.047 251.2 252.4 253.6 254.8 256.0 257.3 258.5 259.7 260.9 12 6.4 262.144 263.4 264.6 265.8 267.1 268.3 269.6 270.8 272.1 273.4 12 6.5 274.625 275.9 277.2 278.4 279.7 281.0 282.3 283.6 284.9 286.2 13 6.6 287.496 288.8 290.1 291.4 292.8 294.1 295.4 296.7 298.1 299.4 14 6.7 300.763 302.1 303. 5. 304.8 306.2 307.5 308.9 310.3 311.7 313.0 14 6.8 314.432 315.8 317.2 318.6 320.0 321.4 322.8 324.2 325.7 327.1 14 6.9 328.509 329.9 331.4 332.8 334.3 335.7 337.2 338.6 340.1 341.5 15 7.0 343.000 344.5 345.9 347.4 348.9 350.4 351.9 353.4 354.9 356.4 15 7.1 357.911 359.4 360.9 362.5. 364.0 365.5 367.1 368.6 370.1 371.7 15 7.2 373.248 374.8 376.4 377.9 379.5 381.1 382.7 384.2 385.8 387.4 16 7.3 389.017 390.6 392.2 393.8 395.4 397.1 398.7 400.3 401.9 403.6 16 7.4 405.224 406.9 408.5 410.2 411.8 413.5 415.2 416.8 418.5 420.2 17 7.5 421.875 423.6 425.3 427.0 428.7 430.4 432.1 433.8 435.5 437.2 18 7.6 -138976 4-10.7 442.5 444.2 445.9 447.7 449.5 451.2 453.0 454.8 17 7.7 456533 458.3 460.1 461.9 463.7 465.5 467.3 469.1 470'9 472.7 19 7.S 474.552 476.4 478.2 480.0 481.9 483.7 485.6 487.4 489.3 491.2 18 7.9 493.039 494.9 496.8 498.7 500.6 502.5 504.4 506.3 508.2 510.1 19 8.0 512.000 513.9 515.8 517.8 519.7 521.7 523.6 525.6 527.5 529.5 19 8.1 531 441 533.4 535.4 537.4 539.4 541.3 543.3 545.3 547.3 549.4 20 8.2 551.368 553.4 555.4 557.4 559.5 561.5 563.6 565.6 567.7 569.7 21 8.3 571.787 573.9 575.9 578.0 580.1 582.2 584.3 586.4 588.5 590.6 21 8.4|592.704 594.8 596.9 599.1 601.2 603.4 605.5 607.6 609.8 612.0 21 8.5 614.125 616.3 618.5 620.7 622.8 625.0 627.2 629.4 631.6 633.8 23 8.6 636.056 638.3 640.5 642.7 645.0 647.2 649.5 651.7 654.0 656.2 23 8.7 658.503 660.8 663.1 665.3 667.6 669.9 672.2 674.5 676.8 679.2 23 8.8 681.472 683.8 686.1 688.5 690.8 693.2 695.5 697.9 700.2 702.6 24 8.9 704.969 707.3 709.7 712.1 714.5 716.9 719.3 721.7 724.2 726.6 24 9.0 729.000 731.4 733.9 736.3 738.8 741.2 743.7 746.1 748.6 751.1 25 9.1 753.571 756.1 758.6 761.0 763.6 766.1 768.6 771.1 773.6 776.2 25 9.2 778.688 781.2 783.8 786.3 788.9 791.5 794.0 796.6 799.2 801.8 26 9.3804.357 807.0 809.6 812.2 814.8 817.4 820.0 822.7 825.3 827.9 27 9.4 830.584 833.2 835.9 838.6 841.2 843.9 846.6 849.3 852.0 854.7 27 9.5 857.375 860.1 862.8 865.5 868.3 871.0 873.7 876.5 879.2 882.0 27 9.6 884.736 887.5 890.3 893.1 895.8 898.6 901.4 904.2 907.0 909.9 28 9.7 912.673 915.5 918.3 921.2 924.0 926.9 929.7 932.6 935.4 938.3 29 9.8 941.192 944.1 947.0 949.9 952.8 955.7 958.6 961.5 964.4 967.4 29 9.9970.299 973.2 976.2 979.1 982.1 985.1 988.0 991.0 994.0 997.0 30 n .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 d 1 1.000 *757 *579 *455 *364 *296 *244 *204 *171 *146 21 2 0.125 108 *939 *822 *723 *640 *569 *508 *456 *410 40 3 0.0 370 336 305 278 254 233 214 197 182 169 13 4 0.0 156 145 135 126 117 110 103 *963 *904 +850 50 5 0.00 800 754 711 672 635 601 569 540 513 487 24 6 0.00 463 441 420 400 381 364 348 332 318 304 12 7 0.00 292 279 268 257 247 237 228 219 211 203 8 8 0.00 195 188 181 17^ 169 163 157 152 147 142 5 9 0.00 137 133 129 124 120 117 113 110 106 103 3

The text on this page is estimated to be only 28.78% accurate

40 XVI. SQUARE EOOTS: n 0 123 456 7 8 9 (1 1.0 1.0000 0050 0100 0149 0198 0247 0296 0344 0392 0440 48 1.1 0488 0536 0583 0630 0677 0724 0770 0817 0863 0909 45 1.2 0954 1000 1045 1091 1136 1180 1225 1269 1314 1358 44 1.3 1402 1446 1489 1533 1576 1619 1662 1705 1747 1790 42 1.4 1832 1874 1916 1958 2000 2042 2083 2124 2166 2207 40 1.5 2247 2288 2329 2369 2410 2450 2490 2530 2570 2610 39 1.6 2649 2689 2728 2767 2806 2845 2884 2923 2961 3000 38 1.7 3038 3077 3115 3153 3191 3229 3266 3304 3342 3379 37 1.8 3416 3454 3491 3528 3565 3601 3638 3675 3711 3748 36 1.9 3784 3820 3856 3892 3928 3964 4000 4036 4071 4107 35 2.0 1.4142 4177 4213 4248 4283 4318 4353 4387 4422 4457 ^54~ 2.1 4491 4526 4560 4595 4629 4663 4697 4731 4765 4799 33 2.2 4832 4866 4900 4933 4967 5000 5033 5067 5100 5133 33 2.8 5166 5199 5232 5264 5297 5330 5362 5395 5427 5460 32 2.4 5492 5524 5556 5588 5620 5652 5684 5716 5748 5780 31 2.5 5811 5843 5875 5906 5937 5969 6000 6031 6062 6093 32 2.6 6125 6155 6186 6217 6248 6279 6310 6340 6371 6401 31 2.7 6432 6462 6492 6523 6553 6583 6613 6643 6673 6703 30 2.8 6733 6763 6793 6823 6852 6882 6912 6941 6971 7000 29 2.9 7029 7059 7088 7117 7146 7176 7205 7234 7263 7292 29 3.0 1.7321 7349 7378 7407 7436 7464 7493 7521 7550 7578 29 3.1 7607 7635 7664 7692 7720 7748 7776 7804 7833 7861 28 3.2 7889 7916 7944 7972 8000 8028 8055 8083 8111 8138 28 3.3 8166 8193 8221 8248 8276 8303 8330 8358 8385 8412. 27 3.4 8439 8466 8493 8520 8547 8574 8601 8628 8655 8682 26 3.5 8708 8735 8762 8788 8815 8841 8868 8894 8921 8947 27 3.6 8974 9000 9026 9053 9079 9105 9131 9157 9183 9209 26 3.7 9235 9261 9287 9313 9339 9365 9391 9416 9442 9468 26 3.8 9494 9519 9545 9570 9596 9621 9647 9672 9698 9723 25 3.9 9748 9774 9799 9824 9849 9875 9900 9925 9950 9975 25 4.0 2.0000 0025 0050 0075 0100 0125 0149 0174 0199 0224 24 4.1 0248 0273 0298 0322 0347 0372 0396 0421 0445 0469 25 4.2 0494 0518 0543 0567 0591 0616 0640 0664 0688 0712 24 4.3 0736 0761 0785 0809 0833 0857 0881 0905 0928 0952 24 4.4 0976 1000 1024 1048 1071 1095 1119 1142 1166 1190 23 4.5 1213 1237 1260 1284 1307 1331 1354 1378 1401 1424 24 4.6 1448 1471 1494 1517 1541 1564 1587 1610 1633 1656 23 4.7 1679 1703 1726 1749 1772 1794 1817 1840 1863 1886 23 4.8 1909 1932 1954 1977 2000 2023 2045 2068 2091 2113 23 4.9 2136 2159 2181 2204 2226 2249 2271 2293 2316 2338 23 5.0 2.2361 2383 2405 2428 2450 2472 2494 2517 2539 2561 22 5.1 2583 2605 2627 2650 2672 2694 2716 2738 2760 2782 22 5.2 2804 2825 2847 2869 2891 2913 2935 2956 2978 3000 22 5.3 3022 3043 3065 3087 3108 3130 3152 3173 3195 3216 22 5.4 3238 3259 3281 3302 3324 3345 3367 3388 3409 3431 21 5.5 3452 3473 3495 3516 3537 3558 3580 3601 3622 3643 21 5.6 3664 3685 3707 3728 3749 3770 3791 3812 3833 3854 21 5.7 3875. 3896 3917 3937 3958 3979 4000 4021 4042 4062 21 5.8 4083 4104 4125 4145 4166 4187 4207 4228 4249 4269 21 5.9 4290 4310 4331 4352 4372 4393 4413 4434 4454 4474 21

The text on this page is estimated to be only 28.48% accurate

FIRST PART. 41 n 0 123 456 789 d 6.0 2.4495 4515 4536 4556 4576 4597 4617 4637 4658 4678 20 6.1 4698 4718 4739 4759 4779 4799 4819 4839 4860 4880 20 6.2 4900 4920 4940 4960 4980 5000 5020 5040 5060 5080 20 6.S t 5100 5120 5140 5159 5179 5199 5219 5239 5259 5278 20 6.4 5298 5318 5338 5357 5377 5397 5417 5436 5456 5475 20 6.5 5495 5515 5534 5554 5573 5593 5612 5632 5652 5671 19 6.6 ; 5690 5710 5729 5749 5768 5788 5807 5826 5846 5865 19 6.7 5884 5904 5923 5942 5962 5981 6000 6019 6038 6058 19 6.8 6077 6096 6115 6134 6153 6173 6192 6211 6230 6249 19 6.S > 6268 6287 6306 6325 6344 6363 6382 6401 6420 6439 19 7.0 2.6458 6476 6495 6514 6533 6552 6571 6589 6608 6627 19 7.1 6646 6665 6683 6702 6721 6739 6758 6777 6796 6814 19 7.2 6833 6851 6870 6889 6907 6926 6944 6963 6981 7000 19 7.3 7019 7037 7055 7074 7092 7111 7129 7148 7166 7185 18 7.4 7203 7221 7240 7258 7276 7295 7313 7331 7350 7368 18 7.5 7386 7404 7423 7441 7459 7477 7495 7514 7532 7550 18 7.6 7568 7586 7604 7622 7641 7659 7677 7695 7713 7731 18 7.7 7749 7767 7785 7803 7821 7839 7857 7875 7893 7911 17 7.8 7928 7946 7964 7982 8000 8018 8036 8054 8071 8089 18 7.9 8107 8125 8142 8160 8178 8196 8213 8231 8249 8267 17 8.0 2.8284 8302 8320 8337 8355 8373 8390 8408 8425 8443 17 8.1 8460 8478 8496 8513 8531 8548 8566 8583 8601 8618 18 8.2 8636 8653 8671 8688 8705 8723 8740 8758 8775 8792 18 8.3 8810 8827 8844 8862 8879 8896 8914 8931 8948 8965 18 8.4 8983 9000 9017 9034 9052 9069 9086 9103 9120 9138 17 8.5 9155 9172 9189 9206 9223 9240 9257 9275 9292 9309 17 8.6 9326 9343 9360 9377 9394 9411 9428 9443 9462 9479 17 8.7 9496 9513 9530 9547 9563 9580 9597 9614 9631 9648 17 8.8 9665 9682 9698 9715 9732 9749 9766 9783 9799 9816 17 8.9 9833 9850 9866 9883 9900 9917 9933 9950 9967 9983 17 9.0 3.0000 0017 0033 0050 0067 0083 0100 0116 0133 0150 ~16~ 9.1 0166 0183 0199 0216 0232 0249 0265 0282 0299 0315 17 9.2 0332 0348 0364 0381 0397 0414 0430 0447 0463 0480 16 9.3 > 0496 0512 0529 0545 0561 0578 0594 0610 0627 0643 16 9.4 0659 0676 0692 0708 0725 0741 0757 0773 0790 0806 16 9.5 0822 0838 0854 0871 0887 0903 0919 0935 0952 0968 16 9.C 0984 1000 1016 1032 1048 1064 1081 1097 1113 1129 16 9.7 1145 1161 1177 1193 1209 1225 1241 1257 1273 1289 16 9.8 1305 1321 1337 1353 1369 1385 1401 1417 1432 1448 16 9.9 1464 1480 1496 1512 1528 1544 1559 1575 1591 1607 16 n .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 d 1 1.000 *953 *913 *877 *845 *816 *791 *767 *745 *725 18 2 0.707 690 674 659 645 632 620 609 598 587 10 3 0.577 568 559 550 542 535 527 520 513 506 6 4 0.500 494 488 482 477 471 466 461 456 452 5 5 0.447 443 439 434 430 426 423 419 415 412 4 6 0.408 405 402 398 395 392 389 386 383 381 3 7 0.378 375 373 370 368 365 363 360 358 356 2 8 0.354 351 349 347 345 343 341 339 337 335 2 9 0.333 331 330 328 326 324 323 321 319 318 2

The text on this page is estimated to be only 28.99% accurate

XVI. SQUARE BOOTS; 11 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 (1 10 3.1623 1780 1937 2094 2249 2404 2558 2711 2863 3015 151 11 3166 3317 3466 3615 3764 3912 4059 4205 4351 4496 145 12 4641 4785 4928 5071 5214 5355 5496 5637 5777 5917 139 13 6056 6194 6332 6469 6606 6742 6878 7014 7148 7283 134 14 7417 7550 7683 7815 7947 8079 8210 8341 8471 8601 129 15 8730 8859 8987 9115 9243 9370 9497 9623 9749 9875 125 16 4.0000 0125 0249 0373 0497 0620 0743 0866 0988 1110 121 17 1231 1352 1473 1593 1713 1833 1952 2071 2190 2308 118 18 2426 2544 2661 2778 2895 3012 3128 3243 3359 3474 115 19 3589 3704 3818 3932 4045 4159 4272 4385 4497 4609 112 20 4.4721 4833 4944 5056 5166 5277 5387 5497 5607 5717 109 21 5826 5935 6043 6152 6260 6368 6476 6583 6690 6797 107 22 6904 7011 7117 7223 7329 7434 7539 7645 7749 7854 104 23 7958 8062 8166 8270 8374 8477 8580 8683 8785 8888 102 24 8990 9092 9193 9295 9396 9497 9598 9699 9800 9900 100 25 5.0000 0100 0200 0299 0398 0498 0596 0695 0794 0892 98 26 0990 1088 1186 1284 1381 1478 1575 1672 1769 1865 97 27 1962 2058 2154 2249 2345 2440 2536 2631 2726 2820 95 28 2915 3009 3104 3198 3292 3385 3479 3572 3666 3759 93 29 3852 3944 4037 4129 4222 4314 4406 4498 4589 4681 91 30 5.4772 4863 4955 5045 5136 5227 5317 5408 5498 5588 90 31 5678 5767 5857 5946 6036 6125 6214 6303 6391 6480 89 32 6569 6657 6745 6833 6921 7009 7096 7184 7271 7359 87 33 7446 7533 7619 7706 7793 7879 7966 8052 8138 8224* 86 34 8310 8395 8481 8566 8652 8737 8822 8907 8992 9076 85 35 9161 9245 9330 9414 9498 9582 9666 9749 9833 9917 83 36 6.0000 0083 0166 0249 0332 0415 0498 0581 0663 0745 83 37 0828 0910 0992 1074 1156 1237 1319 1400 1482 1563 81 38 1644 1725 1806 1887 1968 2048 2129 2209 2290 2370 80 39 2450 2530 2610 2690 2769 2849 2929 3008 3087 3166 80 40 6.3246 3325 3403 3482 3561 3640 3718 3797 3875 3953 78 41 4031 4109 4187 4265 4343 4420 4498 4576 4653 4730 77 42 4807 4885 4962 5038 5115 5192 5269 5345 5422 5498 76 43 5574 5651 5727 5803 5879 5955 6030 6106 6182 6257 75 44 6332 6408 6483 6558 6633 6708 6783 6858 6933 7007 75 45 7082 7157 7231 7305 7380 7454 7528 7602 7676 7750 73 46 7823 7897 7971 8044 8118 8191 8264 8337 8411 8484 73 47 8557 8629 8702 8775 8848 8920 8993 9065 9138 9210 72 48 9282 9354 9426 9498 9570 9642 9714 9785 9857 9929 71 49 7.0000 0071 0143 0214 0285 0356 0427 0498 0569 0640 71 50 7.0711 0781 0852 0922 0993 1063 1134 1204 1274 1344 70 51 1414 1484 1554 1624 1694 1764 ]833 1903 1972 2042 69 52 2111 2180 2250 2319 2388 2457 2526 2595 2664 2732 69 53 2801 2870 2938 3007 3075 3144 3212 3280 3348 3417 68 54 3485 3553 3621 3689 3756 3824 3892 3959 4027 4095 67 55 4162 4229 4297 4364 4431 4498 4565 4632 4699 4766 67 56 4833 4900 4967 5033 5100 5166 5233 5299 5366 5432 66 57 5498 5565 5631 5697 5763 5829 5895 5961 6026 6092 66 58 6158 6223 6289 6354 6420 6485 6551 6616 6681 6746 65 59 6811 6877 6942 7006 7071 7136 7201 7266 7330 7395 65

The text on this page is estimated to be only 28.77% accurate

SECOND PAET. 43 • .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 <1 60 7.7460 7524 7589 7653 7717 7782 7846 7910 7974 8038 64 61 8102 8166 8230 8294 8358 8422 8486 8549 8613 8677 63 62 8740 8804 8867 8930 8994 9057 9120 9183 9246 9310 63 63 9373 9436 9498 9561 9624 9687 9750 9812 9875 9937 63 64 8.0000 0062 0125 0187 0250 0312 0374 0436 0498 0561 62 65 0623 0685 0747 0808 0870 0932 0994 1056 1117 1179 61 66 1240 1302 1363 1425 1486 1548 1609 1670 1731 1792 62 67 1854 1915 1976 2037 2098 2158 2219 2280 2341 2401 61 68 2462 2523 2583 2644 2704 2765 2825 2885 2946 3006 60 69 3066 3126 3187 3247 3307 3367 3427 3487 3546 3606 60 70 8.3666 3726 3785 3845 3905 3964 4024 4083 4143 4202 59 71 4261 4321 4380 4439 4499 4558 4617 4676 4735 4794 59 72 4853 4912 4971 5029 5088 5147 5206 5264 5323 5381 59 73 5440 5499 5557 5615 5674 5732 5790 5849 5907 5965 58 74 6023 6081 6139 6197 6255 6313 6371 6429 6487 6545 58 75 6603 6660 6718 6776 6833 6891 6948 7006 7063 7121 57 76 7178 7235 7293 7350 7407 7464 7521 7579 7636 7693 57 77 7750 7807 7864 7920 7977 8034 8091 8148 8204 8261 57 78 8318 8374 8431 8487 8544 8600 8657 8713 8769 8826 56 79 8882 8938 8994 9051 9107 9163 9219 9275 9331 9387 56 80 8.9443 9499 9554 9610 9666 9722 9778 9833 9889 9944 56 81 9.0000 0056 0111 0167 0222 0277 0333 0388 0443 0499 55 82 0554 0609 0664 0719 0774 0830 0885 0940 0995 1049 55 83 1104 1159 1214 1269 1324 1378 1433 1488 1542 1597 55 84 1652 1706 1761 1815 1869 1924 1978 2033 2087 2141 54 85 2195 2250 2304 2358 2412 2466 2520 2574 2628 2682 54 86 2736 2790 2844 2898 2952 3005 3059 3113 3167 3220 54 87 3274 3327 3381 3434 3488 3541 3595 3648 3702 3755 53 88 3808 3862 3915 3968 4021 4074 4128 4181 4234 4287 53 89 4340 4393 4446 4499 4552 4604 4657 4710 4763 4816 52 90 9.4S68 4921 4974 5026 5079 5131 5184 5237 5289 5341 53 91 5394 5446 5499 5551 5603 5656 5708 5760 5812 5864 53 92 5917 5969 6021 6073 6125 6177 6229 6281 6333 6385 52 93 6437 6488 6540 6592 6644 6695 6747 6799 6850 6902 52 94 6954 7005 7057 7108 7160 7211 7263 7314 7365 7417 51 95 7468 7519 7570 7622 7673 7724 7775 7826 7877 7929 51 96 7980 8031 8082 8133 8184 8234 8285 8336 8387 8438 51 97 8489 8539 8590 8641 8691 8742 8793 8843 8894 8944 51 98 8995 9045 9096 9146 9197 9247 9298 9348 9398 9448 51 99 9499 9549 9599 9649 9700 9750 9800 9850 9900 9950 50 n 0 123 456 789 d 1 0.316 302 289 277 267 258 250 243 236 229 5 2 0.224 219 213 209 204 200 196 192 189 186 3 3 0.183 180 177 174 171 169 167 164 162 160 2 4 0.158 156 154 152 151 149 147 146 144 143 2 5 0.141 140 139 137 136 135 134 132 131 130 1 6 0.129 128 127 126 125 124 123 122 121 120 0 7 0.120 119 118 117 116 115 115 114 113 113 1 8 0.112 111 110 110 109 108 108 107 107 106 1 9 0.105 105 104 104 103 103 102 102 101 101 1

The text on this page is estimated to be only 28.83% accurate

XVII. CUBE ROOTS: • 0 123 456 7 8 9 i 1.0 1.0000 0033 0066 0099 0132 0164 0196 0228 0260 0291 32 1.1 0323 0354 0385 0416 0446 0477 0507 0537 0567 0597 30 1.2 0627 0656 0685 0714 0743 0772 0801 0829 0858 0886 28 1.3 0914 0942 0970 0997 1025 1052 1079 1106 1133 1160 27 1.4 1187 1213 1240 1266 1292 1319 1344 1370 1396 1422 25 1.5 1447 1473 1498 1523 1548 1573 1598 1623 1647 1672 24 1.6 1696 1720 1745 1769 1793 1817 1840 1864 1888 1911 24 1.7 1935 1958 1981 2005 2028 2051 2074 2096 2119 2142 22 1.8 2164 2187 2209 2232 2254 2276 2298 2320 2342 2364 22 1.9 . 2386 2407 2429 2450 2472 2493 2515 2536 2557 2578 21 2.0 1.2599 2620 2641 2662 2683 2703 2724 2745 2765 2785 21 2.1 2806 2826 2846 2866 2887 2907 2927 2947 2966 2986 20 2.2 3006 3026 3045 3065 3084 3104 3123 3142 3162 3181 19 2.3 3200 3219 3238 3257 3276 3295 3314 3333 3351 3370 19 2.4 3389 3407 3426 3444 3463 3481 3499 3518 3536 3554 18 2.5 3572 3590 3608 3626 3644 3662 3680 3698 3715 3733 18 2.6 3751 3768 3786 3803 3821 3838 3856 3873 3890 3908 17 2.7 3925 3942 3959 3976 3993 4010 4027 4044 4061 4078 17 2.8 4093 4111 4128 4145 4161 4178 419^ 4211 4228 4244 16 2.9 4260 4277 4293 4309 4326 4342 4358 4374 4390 4406 16 3.0 1.4422 4439 4454 4470 4486 4502 4518 4534 4550 4565 16 3.1 4581 4597 4612 4628 4643 4659 4674 4690 4705 4721 15 3.2 4736 4751 4767 4782 4797 4812 4828 4843 4858 4873 15 3.3 4888 4903 4918 4933 4948 4963 4978 4993 5007 5022 15 3.4 5037 5052 5066 5081 5096 5110 5125 5139 5154 5168 15 3.5 5183 5197 5212 5226 5241 5255 5269 5283 5298 5312 14 3.6 5326 5340 535£ 5369 5383 5397 5411 5425 5439 5453 14 3.7 5467 5481 5495 5508 5522 5536 5550 5564 5577 5591 14 3.8 5605 5619 5632 5646 5659 5673 5687 5700 5714 5727 14 3.9 5741 5754 5767 5781 5794 5808 5821 5834 5848 5861 13 4.0 1.5874 5887 5900 5914 5927 5940 5953 5966 5979 5992 13 4.1 6005 6018 6031 6044 6057 6070 6083 6096 6109 6121 13 4.2 6134 6147 6160 6173 6185 6198 6211 6223 6236 6249 12 4.3 6261 6274 6287 6299 6312 6324 6337 6349 6362 6374 12 4.4 6386 6399 6411 6424 6436 6448 6461 6473 6485 6497 13 4.5 6510 6522 6534 6546 6558 6571 6583 6595 6607 6619 12 4.6 6631 6643 6655 6667 6679 6691 6703 6715 6727 6739 12 4.7 6751 6763 6774 6786 6798 6810 6822 6833 6845 6857 12 4.8 6869 6880 6892 6904 6915 6927 6939 6950 6962 6973 12 4.9 6985 6997 7008 7020 7031 7043 7054 7065 7077 7088 12 5.0 1.7100 7111 7123 7134 7145 7157 7168 7179 7190 7202 11 5.1 7213 7224 7235 7247 7258 7269 7280 7291 7303 7314 11 5.2 7325 7336 7347 7358 7369 7380 7391 7402 7413 7424 11 5.3 7435 7446 7457 7468 7479 7490 7501 7512 7522 7533 11 5.4 7544 7555 7566 7577 7587 7598 7609 7620 7630 7641 11 5.5 7652 7662 7673 7684 7694 7705 7716 7726 7737 7748 10 5.6 7758 7769 7779 7790 7800 7811 7821 7832 7842 7853 10 5.7 7863 7874 7884 7894 7905 7915 7926 7936 7946 7957 10 5.8 7967 7977 7988 7998 8008 8018 8029 8039 8049 8059 11 5.9 8070 8080 8090 8100 8110 8121 8131 8141 8151 8161 10

The text on this page is estimated to be only 27.78% accurate

FIEST PAET. 45 • 0 123 456 789 d 6.0 1.8171 8181 8191 8201 8211 8222 8232 8242 8252 8262 10 6.1 S272 8282 8292 8302 8311 8321 8331 8341 8351 8361 10 6.2 8371 8381 8391 8400 8410 8420 8430 8440 8450 8459 10 6.3 8469 8479 8489 8498 8508 8518 8528 8537 8547 8557 9 6.4 8566 8576 8586 8595 8605 8615 8624 8634 8643 8653 10 6.5 8663 8672 8682 8691 8701 8710 8720 8729 8739 8748 10 6.6 ; 8758 8767 8777 8786 8796 8805 8814 8824 8833 8843 9 6.7 8852 8861 8871 8880 8889 8899 8908 8917 8927 8936 9 6.8 8945 8955 8964 8973 8982 8992 9001 9010 9019 9029 9 6.9 9038 9047 9056 9065 9074 9084 9093 9102 9111 9120 9 7.0 1.9129 9138 9148 9157 9166 9175 9184 9193 9202 9211 9 7.1 9220 9229 9238 9247 9256 9265 9274 9283 9292 9301 9 7.2 9310 9319 9328 9337 9345 9354 9363 9372 9381 9390 9 7.3 9399 9408 9416 9425 9434 9443 9452 9461 9469 9478 9 7.4 9487 9496 9504 9513 9522 9531 9539 9548 9557 9566 8 7.5 9574 9583 9592 9600 9609 9618 9626 9635 9644 9652 9 7.6 9661 9670 9678 9687 9695 9704 9713 9721 9730 9738 9 7.7 9747 9755 9764 9772 9781 9789 9798 9806 9815 9823 9 7.8 9832 9840 9S49 9857 9866 9874 9883 9891 9899 9908 8 7.9 9916 9925 9933 9941 9950 9958 9967 9975 9983 9992 8 8.0 2.0000 0008 0017 0025 0033 0042 0050 0058 0066 0075 8 8.1 0083 0091 0100 0108 0116 0124 0132 0141 0149 0157 8 8.2 0165 0173 0182 0190 0198 0206 0214 0223 0231 0239 8 8.3 0247 0255 0263 0271 0279 0288 0296 0304 0312 0320 8 8.4 0328 0336 0344 0352 0360 0368 0376 0384 0392 0400 8 8.5 0408 0416 0424 0432 0440 0448 0456 0464 0472 0-180 8 8.1 » > 0488 0496 0504 0512 0520 0528 0536 0543 0551 0559 8 8.7 0567 0575 0583 0591 0599 0606 0614 0622 0630 0638 8 8.8 0646 0653 0661 0669 0677 0685 0692 0700 0708 0716 8 8.9 0724 0731 0739 0747 0755 0762 0770 0778 0785 0793 8 9.0 2.0S01 0809 0816 0824 0832 OS39 0847 0855 0862 0870 8 9.1 OS7S 0885 0893 0901 0908 0916 0923 0931 0939 0946 8 9.2 0954 0961 0969 0977 09S4 0992 0999 1007 1014 1022 7 9.3 1029 1037 1045 1052 1060 1067 1075 1082 1090 1097 8 9.4 1105 1112 1120 1127 1134 1142 1149 1157 1164 1172 7 9.5 1179 1187 1194 1201 1209 1216 1224 1231 1238 1246 7 9.6 1253 1261 1268 1275 1283 1290 1297 1305 1312 1319 8 9.7 1327 1334 1341 1349 1356 1363 1371 1378 1385 1392 8 9.8 1400 1407 1414 1422 1429 1436 1443 1451 1458 1465 7 9.9 1472 1480 1487 1494 1501 1508 1516 1523 1530 1537 7 n .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 d IT 1.000 *969 *941 *916 *894 *874 *855 *838 *822 *807 13 2 0.794 781 769 758 747 737 727 718 709 701 8 3 0.693 686 679 672 665 659 652 647 641 635 5 4 0.630 625 620 615 610 606 601 597 593 589 4 5 0.585 581 577 574 570 567 563 560 557 553 3 6 0.550 547 544 541 539 536 533 530 528 525 2 7 0.523 520 518 516 513 511 509 506 504 502 2 8 0.500 498 496 494 492 490 488 486 484 483 2 9 0.481 479 477 476 474 472 471 469 467 466 2

The text on this page is estimated to be only 28.87% accurate

XVII. CUBE KOOTS: n .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 d 10 2.1544 1616 1687 1757 1828 1898 1967 2036 2104 2172 68 11 2240 2307 2374 2440 2506 2572 2637 2702 2766 2831 63 12 2894 2957 3021 3084 3146 3208 3270 3331 3392 3453 60 13 3513 3573 3633 3693 3752 3811 3870 3928 3986 4044 57 14 4101 4159 4216 4272 4329 4385 4441 4497 4552 4607 55 15 4662 4717 4771 4825 4879 4933 4987 5040 5093 5146 52 16 5198 5251 5303 5355 5407 5458 5509 5561 5612 5662 51 17 5713 5763 5813 5863 5913 5962 6012 6061 6110 6159 48 18 6207 6256 6304 6352 6400 6448 6495 6543 6590 6637 47 19 6684 6731 6777 6824 6870 6916 6962 7008 7053 7099 45 20 2.7144 7189 7234 7279 7324 7369 7413 7457 7501 7545 44 21 '7589 7633 7677 7720 7763 7806 7850 7892 7935 7978 42 22 8020 8063 8105 8147 8189 8231 8273 8314 8356 8397 42 28 8439 8480 8521 8562 8603 8643 8684 8724 8765 880i 40 24 8843 8885 8925 8965 9004 9044 9083 9123 9162 9201 39 25 9240 9279 9318 9357 9395 9434 9472 9511 9549 9587 38 26 9625 9663 9701 9738 9776 9814 9851 9888 9926 9963 37 27 3.0000 0037 0074 0111 0147 0184 0221 0257 0293 0330 36 28 0366 0402 0438 0474 0510 0546 0581 0617 0652 0688 35 29 0723 0758 0794 0829 0864 0899 0934 0968 1003 1038 34 30 3.1072 1107 1141 1176 1210 1244 1278 1312 1346 1380 34 31 1414 1448 1481 1515 1548 1582 1615 1648 1682 1715 33 32 1748 1781 1814 1847 1880 1913 1945 1978 2010 2043 32 33 2075 2108 2140 2172 2204 2237 2269 2301 2332 2364 32 34 2396 2428 2460 2491 2523 2554 2586 2617 2648 2679 32 35 2711 2742 2773 2804 2835 2866 2897 2927 2958 2989 30 36 3019 3050 3080 3111 3141 3171 3202 3232 3262 3292 30 37 3322 3352 3382 3412 3442 3472 3501 3531 3561 3590 30 38 3620 3649 3679 3708 3737 3767 3796 3825 3854 3883 29 39 3912 3941 3970 3999 4028 4056 4085 4114 4142 4171 29 40 3.4200 4228 4256 4285 4313 4341 4370 4398 4426 4454 28 41 4482 4510 4538 4566 4594 4622 4650 4677 4705 4733 27 42 4760 4788 4815 4843 4870 4898 4925 4952 4980 5007 27 43 5034 5061 5088 5115 5142 5169 5196 5223 5250 5277 26 44 5303 5330 5357 5384 5410 5437 5463 5490 5516 5543 26 45 5569 5595 5622 5648 5674 5700 5726 5752 5778 5805 25 46 5830 5856 5882 5908 5934 5960 5986 6011 6037 6063 25 47 6088 6114 6139 6165 6190 6216 6241 6267 6292 6317 25 48 6342 6368 6393 6418 6443 6468 6493 6518 6543 6568 25 49 6593 6618 6643 6668 6692 6717 6742 6766 6791 6816 24 50 3.6840 6865 6889 6914 6938 6963 6987 7011 7036 7060 24 51 7084 7109 7133 7157 7181 7205 7229 7253 7277 7301 24 52 7325 7349 7373 7397 7421 7444 7468 7492 7516 7539 24 53 7563 7586 7610 7634 7657 7681 7704 7728 7751 7774 24 54 7798 7821 7844 7868 7891 7914 7937 7960 7983 8006 24 55 8030 8053 8076 8099 8121 8144 8167 8190 8213 8236 23 56 8259 8281 8304 8327 8349 8372 8395 8417 8440 8462 23 57 8485 8508 8530 8552 8575 8597 8620 8642 8664 8687 22 58 8709 8731 8753 8775 8798 8820 8842 8864 8886 8908 22 59 8930 8952 8974 8996 9018 9040 9061 9083 9105 9127 22

The text on this page is estimated to be only 28.60% accurate

SECOND PAET. 47 n .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 d 60 3.9149 9170 9192 9214 9235 9257 9279 9300 9322 9343 22 61 9365 9386 9408 9429 9451 9472 9494 9515 9536 9558 21 62 9579 9600 9621 9643 9664 9685 9706 9727 9748 9770 21 63 9791 9812 9833 9854 9875 9896 9916 9937 9958 9979 21 64 4.0000 0021 0042 0062 0083 0104 0125 0145 0166 0187 20 65 0207 0228 0248 0269 0290 0310 0331 0351 0372 0392 20 66 0412 0433 0453 0474 0494 0514 0534 0555 0575 0595 20 67 0615 0636 0656 0676 0696 0716 0736 0756 0776 0797 20 68 0817 0837 0857 0877 0896 0916 0936 0956 0976 0996 20 69 1016 1035 1055 1075 1095 1114 1134 1154 1174 1193 20 70 4.1213 1232 1252 1272 1291 1311 1330 1350 1369 1389 19 71 1408 1428 1447 1466 1486 1505 1524 1544 1563 1582 20 72 1602 1621 1640 1659 1679 1698 1717 1736 1755 1774 19 73 1793 1812 1832 1851 1870 1889 1908 1927 1946 1964 19 74 1983 2002 2021 2040 2059 2078 2097 2115 2134 2153 19 75 2172 2190.2209 2228 2246 2265 2284 2302 2321 2340 18 76 2358 2377 2395 2414 2432 2451 2469 2488 2506 2525 18 77 2543 2562 2580 2598 2617 2635 2653 2672 2690 2708 19 78 2727 2745 2763 2781 2799 2818 2836 2854 2872 2890 18 79 2908 2927 2945 2963 2981 2999 3017 3035 3053 3071 18 80 4.30S9 3107 3125 3143 3160 3178 3196 3214 3232 3250 17 81 3267 3285 3303 3321 3339 3356 3374 3392 3409 3427 18 82 3445 3463 3480 3498 3515 3533 3551 3568 3586 3603 18 83 3621 3638 3656 3673 3691 3708 3726 3743 3760 3778 17 84 3795 3813 3830 3847 3865 3882 3899 3917 3934 3951 17 85 3968 3986 4003 4020 4037 4054 4072 4089 4106 4123 17 86 4140 4157 4174 4191 4208 4225 4242 4259 4276 4293 17 87 4310 4327 4344 4361 4378 4395 4412 4429 4446 4463 17 88 4480 4496 4513 4530 4547 4564 4580 4597 4614 4630 17 89 4647 4664 4681 4698 4714 4731 4748 4764 4781 4797 17 90 4.4814 4831 4847 4864 4880 4897 4913 4930 4946 4963 16 91 4979 4996 5012 5029 5045 5062 5078 5094 5111 5127 17 92 5144 5160 5176 5193 5209 5225 5241 5258 5274 5290 17 93 5307 5323 5339 5355 5371 5388 5404 5420 5436 5452 16 94 5468 5485 5501 5517 5533 5549 5565 5581 5597 5613 16 95 5629 5645 5661 5677 5693 5709 5725 5741 5757 5773 16 96 5789 5804 5820 5836 5852 5868 5884 5900 5915 5931 16 97 5947 5963 5979 5994 6010 6026 6042 6057 6073 6089 15 98 6104 6120 6136 6151 6167 6183 6198 6214 6229 6245 16 99 6261 6276 6292 6307 6323 6338 6354 6369 6385 6400 16 n 0 123 456 7 8 9 d 1 0.464 450 437 425 415 405 397 389 382 375 7 2 0.368 362 357 352 347 342 338 333 329 325 3 3 0.322 318 315 312 . 309 306 303 300 297 295 3 4 0.292 290 288 285 283 281 279 277 275 273 2 5 0.271 270 268 266 265 263 261 260 258 257 2 6 0.255 254 253 251 250 249 247 246 245 244 1 7 0.243 241 240 239 238 237 236 235 234 233 1 8 0.232 231 230 229 228 227 227 226 225 224 1 9 0.223 222 222 221 220 219 218 218 217 216 1

The text on this page is estimated to be only 28.64% accurate

48 XVII. CUBE KOOTSi n 0 123 456 7 8 9 (1 10 4.6416 6570 6723 6875 7027 7177 7326 7475 7622 7769 145 11 7914 8059 8203 8346 8488 8629 8770 8910 9049 9187 137 12 9324 9461 9597 9732 9866*0000*0133 *0265*0397*0528 130 13 5.0658 0788 0916 1045 1172 1299 1426 1551 1676 1801 124 14 1925 2048 2171 2293 2415 2536 2656 2776 2896 3015 118 15 3133 3251 3368 3485 3601 3717 3832 3947 4061 4175 113 16 4288 4401 4514 4626 4737 4848 4959 5069 5178 5288 109 17 5397 5505 5613 5721 5828 5934 6041 6147 6252 6357 105 18 6462 6567 6671 6774 6877 6980 7083 7185 7287 7388 101 19 7489 7590 7690 7790 7890 7989 8088 8186 8285 8383 97 20 5.8480 8578 867^ 8771 8868 8964 9059 9155 9250 9345 94 21 9439 9533 9627 9721 9814 9907*0000 *0092*01S5*0277 91 22 6.0368 0459 0550 0641 0732 0822 0912 1002 1091 1180 89 23 1269 1358 1446 1534 1622 1710 1797 1885 1972 2058 87 24 2145. 2231 2317 2403 2488 2573 2658 2743 2828 2912 84 25 2996 3080 3164 3247 3330 3413 3496 3579 3661 3743 82 26 3825 3907 3988 4070 4151 4232 4312 4393 4473 4553 80 27 4633 4713 4792 4872 4951 5030 5108 5187 5265 5343 78 28 5421 5499 5577 5654 5731 5808 5885 5962 6039 6115 76 29 6191 6267 6343 6419 6494 6569 6644 6719 6794 6869 74 30 6.6943 7018 7092 7166 7240 7313 7387 7460 7533 7606 73 31 7679 7752 7824 7897 7969 8041 8113 8185 8256 8328 71 32 8399 8470 8541 8612 8683 8753 8824 8894 8964 9034 70 33 9104 9174 9244 9313 9382 9451 9521 9589 9658 9727 68 34 9795 9864 9932*0000 *0068*0136*0203 *0271*0338*0406 67 35 7.0473 0540 0607 0674 0740 0807 0873 0940 1006 1072 66 36 1138 1204 1269 1335 1400 1466 1531 1596 1661 1726 65 37 1791 1855 1920 1984 2048 2112 2177 2240 2304 2368 64 38 2432 2495 2558 2622 2685 2748 2811 2874 2936 2999 62 39 3061 3124 3186 3248 3310 3372 3434 3496 3558 3619 62 40 7.3681 3742 3803 3864 3925 3986 4047 4108 4169 4229 61 41 4290 4350 4410 4470 4530 4590 4650 4710 4770 4829 60 42 4889 4948 5007 5067 5126 5185 5244 5302 5361 5420 58 43 5478 5537 5595 5654 5712 5770 5828 5886 5944 6001 58 44 6059 6117 6174 6232 6289 6346 6403 6460 6517 6574 57 45 6631 6688 6744 6801 6857 6914 6970 7026 7082 7138 56 46 7194 7250 7306 7362 7418 7473 7529 7584 7639 7695 55 47 7750 7805 7860 7915 7970 8025 8079 8134 8188 8243 54 48 8297 8352 8406 8460 8514 8568 8622 8676 8730 8784 53 49 8837 8891 8944 8998 9051 9105 9158 9211 9264 9317 53 50 7.9370 9423 9476 9528 9581 9634 9686 9739 9791 9843 53 51 9896 9948*0000*0052 *01 04*01 56*0208 *0260*03 11*0363 52 52 8.0415 0466 0517 0569 0620 0671 0723 0774 0825 0876 51 53 0927 0978 1028 1079 1130 1180 1231 1281 1332 1382 51 54 1433 1483 1533 1583 1633 1683 1733 1783 1833 1882 50 55 1932 1982 2031 2081 2130 2180 2229 2278 2327 2377 49 56 2426 2475 2524 2573 2621 2670 2719 2768 2816 2865 48 57 2913 2962 3010 3059 3107 3155 3203 3251 3300 3348 48 58 3396 3443 3491 3539 3587 3634 3682 3730 3777 3825 47 59 3872 3919 3967 4014 4061 4108 4155 4202 4249 4296 47

The text on this page is estimated to be only 28.49% accurate

•Vn THIED PART. 49 n 0 123 456 7 8 9 (1 60 8.4343 4390 4437 44S4 4530 4577 4623 4670 4716 4763 46 61 4809 4856 4902 4948 4994 5040 5086 5132 5178 5224 46 62 5270 5316 5362 5408 5453 5499 5544 5590 5635 5681 45 63 5726 5772 5817 5862 5907 5952 5997 6043 6088 6132 45 64 6177 6222 6267 6312 6357 6401 6446 6490 6535 6579 45 65 6624 6668 6713 6757 6801 6845 6890 6934 6978 7022 44 66 7066 7110 7154 7198 7241 7285 7329 7373 7416 7460 43 67 7503 7547 7590 7634 7677 7721 7764 7807 7850 7893 44 68 7937 7980 8023 8066 8109 8152 8194 8237 8280 8323 43 69 8366 8408 8451 8493 8536 8578 8621 8663 8706 8748 42 70 8.8790 8833 8875. 8917 8959 9001 9043 9085 9127 9169 42 71 9211 9253 9295 9337 9378 9420 9462 9503 9545 9587 41 72 9628 9670 9711 9752 9794 9835 9876 9918 9959*0000 41 73 9.0041 0082 0123 0164 0205 0246 0287 0328 0369 0410 40 74 0450 0491 0532 0572 0613 0654 0694 0735 0775 0816 40 75 0856 0896 0937 0977 1017 1057 1098 1138 1178 1218 40 76 1258 1298 1338 1378 1418 1458 1498 1537 1577 1617 40 77 1657 1696 1736 1775 1815 1855 1894 1933 1973 2012 40 78 2052 2091 2130 2170 2209 2248 2287 2326 2365 2404 39 79 2443 2482 2521 2560 2599 2638 2677 2716 2754 2793 39 80 9.2832 2870 2909 2948 2986 3025. 3063 3102 3140 3179 38 81 3217 3255 3294 3332 3370 3408 3447 3485 3523 3561 38 82 3599 3637 3675 3713 3751 3789 3827 3865 3902 3940 38 83 3978 4016 4053 4091 4129 4166 4204 4241 4279 4316 38 84 4354 4391 4429 4466 4503 4541 4578 4615 4652 4690 37 85 4727 4764 4801 4838 4875 4912 4949 4986 5023 5060 37 86 5097 5134 5171 5207 5244 5281 5317 5354 5391 5427 37 87 5464 5501 5537 5574 5610 5647 5683 5719 5756 5792 36 88 5828 5865 5901 5937 5973 6010 6046 6082 6118 6154 36 89 6190 6226 6262 6298 6334 6370 6406 6442 6477 6513 36 90 9.6549 6585. 6620 6656 6692 6727 6763 6799 6834 6870 35 91 6905 6941 6976 7012 7047 7082 7118 7153 7188 7224 35 92 7259 7294 7329 7364 7400 7435 7470 7505 7540 7575 35 93 7610 7645. 7680 77 15. 7750 7785 7819 7854 7889 7924 35 94 7959 7993 8028 8063 8097 8132 8167 8201 8236 8270 35 95 8305 8339 8374 8408 8443 8477 8511 8546 8580 8614 34 96 8648 8683 8717 8751 8785 8819 8854 8888 8922 8956 34 97 8990 9024 9058 9092 9126 9160 9194 9227 9261 9295 34 98 9329 9363 9396 9430 9464 9497 9531 9565 9598 9632 34 99 9666 9699 9733 9766 9800 9833 9866 9900 9933 9967 33 n 0 123 456 7 8 9 d .1 2.154 087 027 *974 *926 *882 *842 *805 *771 *739 29 .2 1.710 682 657 632 609 587 567 547 529 511 17 .3 1.494 478 462 447 433 419 406 393 381 369 12 .4 1357 346 335 325 315 305 295 286 277 268 8 .5 1.260 252 244 236 228 221 213 206 199 192 6 .6 1.186 179 173 167 160 154 149 143 137 132 6 .7 1.126 121 116 111 106 101 096 091 086 082 5 .8 1.077 073 068 064 060 056 052 048 044 040 4 .9 1.036 032 028 025 021 017 014 010 007 003 3

The text on this page is estimated to be only 28.51% accurate

50 XVHI. MULTIPLES. 100 101 102 103 104 105 106 107 108 109 1 2 3 4 5 6 7 8 9 100 200 300 400 500 600 700 800 900 101 102 103 202 204 206 303 306 309 404 408 412 505 510 515 606 612 618 707 714 721 808 816 824 909 918 927 104 105 106 208 210 212 312 315 318 416 420 424 520 525 530 624 630 636 728 735 742 832 840 848 936 945 954 107 108 109 214 216 218 321 324 327 428 432 436 535 540 545 642 648 654 749 756 763 856 864 872 963 972 981 110 111 112 113 114 115 116 117 118 119 1 2 3 4 5 6 7 8 9 110 220 330 440 550 660 770 880 990 111 112 113 222 224 226 333 336 339 444 448 452 555 560 565 666 672 678 777 784 791 888 896 904 999 1008 1017 114 115 116 228 230 232 342 345 348 456 460 464 570 575 580 684 690 696 798 805 812 912 920 928 1026 1035 1044 117 118 119 234 236 238 351 354 357 468 472 476 585 590 595 702 708 714 819 826 833 936 944 952 1053 1062 1071 120 121 122 123 124 125 126 127 128 129 1 2 3 4 5 6 7 8 9 120 240 360 480 600 720 840 960 1080 121 122 123 242 244 246 363 366 369 484 488 492 605 610 615 726 732 738 847 854 861 968 976 984 1089 1098 1107 124 125 126 248 250 252 372 375 378 496 500 504 620 625 630 744 750 756 868 875 882 992 1000 1008 1116 1125 1134 127 128 129 254 256 258 381 384 387 508 512 516 635 640 645 762 768 774 889 896 903 1016 1024 1032 1143 1152 1161 130 131 132 133 134 135 136 137 138 139 1 2 3 4 5 G 7 8 9 130 260 390 520 650 780 910 1040 1170 131 132 133 262 264 266 393 396 399 524 528 532 655 660 665 786 792 798 917 924 931 1048 1056 1064 1179 1188 1197 134 135 136 268 270 272 402 405 408 536 540 544 670 675 680 804 810 816 938 945 952 1072 1080 1088 1206 1215 1224 137 138 139 274 276 278 411 414 417 548 552 556 685 690 695 822 828 834 959 966 973 1096 1104 1112 1233 1242 1251 140 141 142 143 144 145 146 147 148 149 1 2 3 4 5 6 7 8 9 140 280 420 560 700 840 980 1120 1260 141 142 143 282 284 286 423 426 429 564 568 572 705 710 715 846 852 858 987 994 1001 1128 1136 1144 1269 1278 1287 144 145 146 288 290 292 432 435 438 576 580 584 720 725 730 864 870 876 1008 1015 1022 1152 1160 1168 1296 1305 1314 147 148 149 294 296 298 441 444 447 588 592 596 735 740 745 882 888 894 1029 1036 1043 1176 1184 1192 1323 1332 1341

The text on this page is estimated to be only 29.20% accurate

XVIII. MULTIPLES. 51 1 2 3 4 5 6 7 8 9 150 151 152 153 154 155 156 157 158 159 150 300 450 600 750 900 1050 1200 1350 151 152 153 302 304 306 453 456 459 604 608 612 755 760 765 906 912 918 1057 1064 1071 1208 1216 1224 1359 1368 1377 154 155 156 308 310 312 462 465 468 616 620 624 770 775 780 924 930 936 1078 1085 1092 1232 1240 1248 1386 1395 1404 157 158 159 314 316 318 471 474 477 628 632 636 785 790 795 942 948 954 1099 1106 1113 1256 1264 1272 1413 1422 1431 160 161 162 163 164 165 166 167 168 169 1 2 3 4 5 6 7 8 9 160 320 480 640 800 960 1120 1280 1440 161 162 163 322 324 326 483 486 489 644 648 652 805 810 815 966* 972 978 1127 1134 1141 1288 1296 1304 1449 1458 1467 164 165 166 328 330 332 492 495 498 656 660 664 820 825 830 984 990 996 1148 1155 1162 1312 1320 1328 1476 1485 1494 167 168 169 334 336 338 501 504 507 668 672 676 835 840 845 1002 1008 1014 1169 1176 1183 1336 1344 1352 1503 1512 1521 170 171 172 173 174 175 176 177 178 179 1 2 3 4 6 7 8 9 170 340 510 680 850 1020 1190 1360 1530 171 172 173 342 344 346 513 516 519 684 688 692 855 860 865 1026 1032 1038 1197 1204 1211 1368 1376 1384 1539 1548 1557 174 175 176 348 350 352 522 525 528 696 700 704 870 875 880 1044 1050 1056 1218 1225 1232 1392 1400 1408 1566 1575 1584 177 178 179 354 356 358 531 534 537 708 712 716 885 890 895 1062 1068 1074 1239 1246 1253 1416 1424 1432 1593 1602 1611 180 181 182 183 184 185 186 187 188 189 1 2 3 4 5 6 7 8 9 180 360 540 720 900 1080 1260 1440 1620 181 182 183 362 364 366 543 546 549 724 728 732 905 910 915 1086 1092 1098 1267 1274 1281 1448 1456 1464 1629 1638 1647 184 185 186 368 370 372 552 555 558 736 740 744 920 925 930 1104 1110 1116 1288 1295 1302 1472 1480 1488 1656 1665 1674 187 188 189 374 376 378 561 564 567 748 752 756 935 940 945 1122 1128 1134 1309 1316 1323 1496 1504 1512 1683 1692 1701 190 191 192 193 194 195 196 197 198 199 1 2 3 4 5 6 7 8 9 190 380 570 760 950 1140 1330 1520 1710 191 192 193 382 384 386 573 576 579 764 768 772 955 960 965 1146 1152 1158 1337 1344 1351 1528 1536 1544 1719 1728 1737 194 195 196 388 390 392 582 585 588 776 780 784 970 975 980 1164 1170 1176 1358 1365 1372 1552 1560 1568 1746 1755 1764 197 198 199 394 396 398 591 594 597 788 792 796 985 990 995 1182 1188 1194 1379 1386 1393 1576 1584 1592 1773 1782 1791

The text on this page is estimated to be only 28.37% accurate

52 XVIII, MULTIPLES. 200 201 202 203 204 205 206 207 208 209 1 2 3 200 400 600 201 202 203 402 404 406 603 606 609 204 205 206 408 410 412 612 615 618 207 208 209 414 416 418 621 624 627 4 5 6 800 1000 1200 804 808 812 1005 1010 1015 1206 1212 1218 816 820 824 1020 1025 1030 1224 1230 1236 828 832 836 1035 1040 1045 1242 1248 1254 7 8 9 1400 1600 1800 1407 1414 1421 1608 1616 1624 1809 1818 1827 1428 1435 1442 1632 1640 1648 1836 1845 1854 1449 1456 1463 1656 1664 1672 1863 1872 1881 210 211 212 213 214 215 216 217 218 219 1 2 3 210 420 630 211 212 213 422 424 426 633 636 639 214 215 216 428 430 432 642 645 648 217 218 219 434 436 438 651 654 657 4 5 6 840 1050 1260 844 848 852 1055 1060 1065 1266 1272 1278 856 860 864 1070 1075 1080 1284 1290 1296 868 872 876 1085 1090 1095 1302 1308 1314 7 8 9 1470 1680 1890 1477 1484 1491 1688 1696 1704 1899 1908 1917 1498 1505 1512 1712 1720 1728 1926 1935 1944 1519 1526 1533 1736 1744 1752 1953 1962 1971 220 221 222 223 224 225 226 227 228 229 1 2 3 220 440 660 221 222 223 442 444 446 663 666 669 224 225 226 448 450 452 672 675 678 227 228 229 454 456 458 681 684 687 4 5 6 880 1100 1320 884 888 892 1105 1110 1115 1326 1332 1338 896 900 904 1120 1125 1130 1344 1350 1356 908 912 916 1135 1140 1145 1362 1368 1374 7 8 9 1540 1760 1980 1547 1554 1561 1768 1776 1784 1989 1998 2007 1568 1575 1582 1792 1800 1808 2016 2025 2034 1589 1596 1603 1816 1824 1832 2043 2052 2061 230 231 232 233 234 235 236 237 238 239 1 2 3 230 460 690 231 232 233 462 464 466 693 696 699 234 235 236 468 470 472 702 705 708 237 238 239 474 476 478 711 714 717 4 5 6 920 1150 1380 924 928 932 1155 1160 1165 1386 1392 1398 936 940 944 1170 1175 1180 1404 1410 1416 948 952 956 1185 1190 1195 1422 1428 1434 7 8 9 1610 1840 2070 1617 1624 1631 1848 1856 1864 2079 2088 2097 1638 1645 1652 1872 1880 1888 2106 2115 2124 1659 1666 1673 1896 1904 1912 2133 2142 2151 240 241 242 243 244 245 246 247 248 249 1 2 3 240 480 720 241 242 243 482 484 486 723 726 729 244 245 246 488 490 492 732 735 738 247 248 249 494 496 498 741 744 747 4 5 6 960 1200 1440 964 968 972 1205 1210 1215 1446 1452 1458 976 980 984 1220 1225 1230 1464 1470 1476 988 992 996 1235 1240 1245 1482 1488 1494 7 8 9 1680 1920 2160 1687 1694 1701 1928 1936 1944 2169 2178 2187 1708 1715 1722 1952 1960 1968 2196 2205 2214 1729 1736 1743 1976 1984 1992 2223 2232 2241

The text on this page is estimated to be only 28.90% accurate

XVIII. MULTIPLES. 53 250 251 252 253 254 255 256 257 258 259 1 2 3 4 5 6 7 8 9 250 500 750 1000 1250 1500 1750 2000 2250 251 252 253 502 504 506 753 756 759 1004 1008 1012 1255 1260 1265 1506 1512 1518 1757 1764 1771 2008 2016 2024 2259 2268 2277 254 255 256 508 510 512 762 765 768 1016 1020 1024 1270 1275 1280 1524 1530 1536 1778 1785 1792 2032 2040 2048 2286 2295 2304 257 258 259 514 516 518 771 774 777 1028 1032 1036 1285 1290 1295 1542 1548 1554 1799 1806 1813 2056 2064 2072 2313 2322 2331 260 261 262 263 264 265 266 267 268 269 1 2 3 4 5 6 7 8 9 260 520 780 1040 1300 1560 1820 2080 2340 261 262 263 522 524 526 783 786 789 1044 1048 1052 1305 1310 1315 1566 1572 1578 1827 1834 1841 2088 2096 2104 2349 2358 2367 264 265 266 528 530 532 792 795 798 1056 1060 1064 1320 1325 1330 1584 1590 1596 1848 1855 1862 2112 2120 2128 2376 2385 2394 267 268 269 534 536 538 801 804 807 1068 1072 1076 1335 1340 1345 1602 1608 1614 1869 1876 1883 2136 2144 2152 2403 2412 2421 270 271 272 273 274 275 276 277 278 279 1 2 3 4 5 6 7 8 9 270540 810 1080 1350 1620 1890 2160 2430 271 272 273 542 544 546 813 816 819 1084 1088 1092 1355 1360 1365 1626 1632 1638 1897 1904 1911 2168 2176 2184 2439 2448 2457 274 275 276 548 550 552 822 825 828 1096 1100 1104 1370 1375 1380 1644 1650 1656 1918 1925 1932 2192 2200 2208 2466 2475 2484 277 278 279 554 556 558 831 834 837 1108 1112 1116 1385 1390 1395 1662 1668 1674 1939 1946 1953 2216 2224 2232 2493 2502 2511 280 281 282 283 284 285 286 287 288 289 1 2 3 4 5 6 7 8 9 280 560 840 1120 1400 1680 1960 2240 2520 281 282 283 562 564 566 843 846 849 1124 1128 1132 1405 1410 1415 1686 1692 1698 1967 1974 1981 2248 2256 2264 2529 2538 2547 284 285 286 568 570 572 852 855 858 1136 1140 1144 1420 1425 1430 1704 1710 1716 1988 1995 2002 2272 2280 2288 2556 2565 2574 287 288 289 574 576 578 861 864 867 1148 1152 1156 1435 1440 1445 1722 1728 1734 2009 2016 2023 2296 2304 2312 2583 2592 2601 290 291 292 293 294 295 296 297 298 299 1 2 3 4 5 6 7 8 9 290 580 870 1160 1450 1740 2030 2320 2610 291 292 293 582 584 586 873 876 879 1164 1168 1172 1455 1460 1465 1746 1752 1758 2037 2044 2051 2328 2336 2344 2619 2628 2637 294 295 296 588 590 592 882 885 888 1176 1180 1184 1470 1475 1480 1764 1770 1776 2058 2065 2072 2352 2360 2368 2646 2655 2664 297 298 299 594 596 598 891 894 897 1188 1192 1196 1485 1490 1495 1782 1788 1794 2079 2086 2093 2376 2384 2392 2673 2682 2691

The text on this page is estimated to be only 29.05% accurate

54 XVIII. MULTIPLES. 300 301 302 303 304 305 306 307 308 309 1 2 3 300 600 900 301 302 303 602 604 606 903 906 909 304 305 306 608 610 612 912 915 918 307 308 309 614 616 618 921 924 927 4 5 6 1200 1500 1800 1204 1208 1212 1505 1510 1515 1806 1812 1818 1216 1220 1224 1520 1525 1530 1824 1830 1836 1228 1232 1236 1535 1540 1545 1842 1848 1854 7 8 9 2100 2400 2700 2107 2114 2121 2408 2416 2424 2709 2718 2727 2128 2135 2142 2432 2440 2448 2736 2745 2754 2149 2156 2163 2456 2464 2472 2763 2772 2781 310 311 312 313 314 315 316 317 318 319 1 2 3 310 620 930 311 312 313 622 624 626 933 936 939 314 315 316 628 630 632 942 945 948 317 318 319 634 636 638 951 954 957 4 5 6 1240 1550 1860 1244 1248 1252 1555 1560 1565 1866 1872 1878 1256 1260 1264 1570 1575 1580 1884 1890 1896 1268 1272 1276 1585 1590 1595 1902 1908 1914 7 8 9 2170 2480 2790 2177 2184 2191 2488 2496 2504 2799 2808 2817 2198 2205 2212 2512 2520 2528 2826 2835 2844 2219 2226 2233 2536 2544 2552 2853 2862 2871 320 321 322 323 324 325 326 327 328 329 1 2 3 320 640 960 321 322 323 642 644 646 963 966 969 324 325 326 648 650 652 972 975 978 327 328 329 654 656 658 981 984 987 4 5 6 1280 1600 1920 1284 1288 1292 1605 1610 1615 1926 1932 1938 1296 1300 1304 1620 1625 1630 1944 1950 1956 1308 1312 '1316 1635 1640 1645 1962 1968 1974 7 8 9 2240 2560 2880 2247 2254 2261 2568 2576 2584 2889 2898 2907 2268 2275 2282 2592 2600 2608 2916 2925 2934 2289 2296 2303 2616 2624 2632 2943 2952 2961 330 331 332 333 334 335 336 337 338 339 1 2 3 330 660 990 331 332 333 662 664 666 993 996 999 334 335 336 668 670 672 1002 1005 1008 337 338 339 674 676 678 1011 1014 1017 4 5 6 1320 1650 1980 1324 1328 1332 1655 1660 1665 1986 1992 1998 1336 1340 1344 1670 1675 1680 2004 2010 2016 1348 1352 1356 1685 1690 1695 2022 2028 2034 7 8 9 2310 2640 2970 2317 2324 2331 2648 2656 2664 2979 2988 2997 2338 2345 2352 2672 2680 2688 3006 3015 3024 2359 2366 2373 2696 2704 2712 3033 3042 3051 340 341 342 343 344 345 346 347 348 349 1 2 3 340 680 1020 341 342 343 682 684 686 1023 1026 1029 344 345 346 688 690 692 1032 1035 1038 347 348 349 694 696 698 1041 1044 1047 4 5 6 1360 1700 2040 1364 1368 1372 1705 1710 1715 2046 2052 2058 1376 1380 1384 1720 1725 1730 2064 2070 2076 1388 1392 1396 1735 1740 1745 2082 2088 2094 7 8 9 2380 2720 3060 2387 2394 2401 2728 2736 2744 3069 3078 3087 2408 2415 2422 2752 2760 2768 3096 3105 3114 2429 2436 2443 2776 2784 2792 3123 3132 3141

The text on this page is estimated to be only 28.97% accurate

XVIII. MULTIPLES. 350 351 352 353 354 355 356 357 358 359 1 2 3 4 5 6 7 8 9 350 700 1050 1400 1750 2100 2450 2800 3150 351 352 353 702 704 706 1053 1056 1059 1404 1408 1412 1755 1760 1765 2106 2112 2118 2457 2464 2471 2808 2816 2824 3159 3168 3177 354 355 356 708 710 712 1062 1065 1068 1416 1420 1424 1770 1775 1780 2124 2130 2136 2478 2485 2492 2832 2840 2848 3186 3195 3204 357 358 359 714 716 718 1071 1074 1077 1428 1432 1436 1785 1790 1795 2142 2148 2154 2499 2506 2513 2856 2864 2872 3213 3222 3231 360 361 362 363 364 365 366 367 368 369 1 2 3 4 5 6 7 8 9 360 720 1080 1440 1800 2160 2520 2880 3240 361 362 363 722 724 726 1083 1086 1089 1444 1448 1452 1805 1810 1815 2166 2172 2178 2527 2534 2541 2888 2896 2904 3249 3258 3267 364 365 366 728 730 732 1092 1095 1098 1456 1460 1464 1820 1825 1830 2184 2190 2196 2548 2555 2562 2912 2920 2928 3276 3285 3294 367 368 369 734 736 738 1101 1104 1107 1468 1472 1476 1835 1840 1845 2202 2208 2214 2569 2576 2583 2936 2944 2952 3303 3312 3321 370 371 372 373 374 375 376 377 378 379 1 2 3 4 5 6 7 8 9 370 740 1110 1480 1850 2220 2590 2960 3330 371 372 373 742 744 746 1113 1116 1119 1484 1488 1492 1855 1860 1865 2226 2232 2238 2597 2604 2611 2968 2976 2984 3339 3348 3357 374 375 376 748 750 752 1122 1125 1128 1496 1500 1504 1870 1875 1880 2244 2250 2256 2618 2625 2632 2992 3000 3008 3366 3375 3384 377 378 379 754 756 758 1131 1134 1137 1508 1512 1516 1885 1890 1895 2262 2268 2274 2639 2646 2653 3016 3024 3032 3393 3402 3411 380 381 382 383 384 385 386 387 388 389 1 2 3 4 6 7 8 9 380 760 1140 1520 1900 2280 2660 3040 3420 381 382 383 762 764 766 1143 1146 1149 1524 1528 1532 1905 1910 1915 2286 2292 2298 2667 2674 2681 3048 3056 3064 3429 3438 3447 384 385 386 768 770 772 1152 1155 1158 1536 1540 1544 1920 1925 1930 2304 2310 2316 2688 2695 2702 3072 3080 3088 3456 3465 3474 387 388 389 774 776 778 1161 1164 1167 1548 1552 1556 1935 1940 1945 2322 2328 2334 2709 2716 2723 3096 3104 3112 3483 3492 3501 390 391 392 393 394 395 396 397 398 399 1 2 3 4 5 6 7 8 9 390 780 1170 1560 1950 2340 2730 3120 3510 391 392 393 782 784 786 1173 1176 1179 1564 1568 1572 1955 1960 1965 2346 2352 2358 2737 2744 2751 3128 3136 3144 3519 3528 3537 394 395 396 788 790 792 1182 1185 1188 1576 1580 1584 1970 1975 1980 2364 2370 2376 2758 2765 2772 3152 3160 3168 3546 3555 3564 397 398 399 794 796 798 1191 1194 1197 1588 1592 1596 1985 1990 1995 2382 2388 2394 2779 2786 2793 3176 3184 3192 3573 3582 3591

The text on this page is estimated to be only 28.99% accurate

56 XVIII. MULTIPLES. 400 401 402 403 404 405 406 407 408 409 1 2 3 400 800 1200 401 402 403 802 804 806 1203 1206 1209 404 405 406 808 810 812 1212 1215 1218 407 408 409 814 816 818 1221 1224 1227 4 5 6 1600 2000 2400 1604 1608 1612 2005 2010 2015 2406 2412 2418 1616 1620 1624 2020 2025 2030 2424 2430 2436 1628 1632 1636 2035 2040 2045 2442 2448 2454 7 8 9 2800 3200 3600 2807 2814 2821 3208 3216 3224 3609 3618 3627 2828 2835 2842 3232 3240 3248 3636 3645 3654 2849 2856 2863 3256 3264 3272 3663 3672 3681 410 411 412 413 414 415 416 417 418 419 1 2 3 410 820 1230 411 412 413 822 824 826 1233 1236 1239 414 415 416 828 830 832 1242 1245 1248 417 418 419 834 836 838 1251 1254 1257 4 5 6 1640 2050 2460 1644 1648 1652 2055 2060 2065 2466 2472 2478 1656 1660 1664 2070 2075 2080 2484 2490 2496 1668 1672 1676 2085 2090 2095 2502 2508 2514 7 8 9 2870 3280 3690 2877 2884 2891 3288 3296 3304 3699 3708 3717 2898 2905 2912 3312 3320 3328 3726 3735 3744 2919 2926 2933 3336 3344 3352 3753 3762 3771 420 421 422 423 424 425 426 427 428 429 1 2 3 420 840 1260 421 422 423 842 844 846 1263 1266 1269 424 425 426 848 850 852 1272 1275 1278 427 428 429 854 856 858 1281 1284 1287 4 5 6 1680 2100 2520 1684 1688 1692 2105 2110 2115 2526 2532 2538 1696 1700 1704 2120 2125 2130 2544 2550 2556 1708 1712 1716 2135 2140 2145 2562 2568 2574 7 8 9 2940 3360 3780 2947 2954 2961 3368 3376 3384 3789 3798 3807 2968 2975 2982 3392 3400 3408 3816 3825 3834 2989 2996 3003 3416 3424 3432 3843 3852 3861 430 431 432 433 434 435 436 437 438 439 1 2 3 430 860 1290 431 432 433 862 864 866 1293 1296 1299 434 435 436 868 870 872 1302 1305 1308 437 438 439 874 876 878 1311 1314 1317 4 6 1720 2150 2580 1724 1728 1732 2155 2160 2165 2586 2592 2598 1736 1740 1744 2170 2175 2180 2604 2610 2616 1748 1752 1756 2185 2190 2195 2622 2628 2634 7 8 9 3010 3440 3870 3017 3024 3031 3448 3456 3464 3879 3888 3897 3038 3045 3052 3472 3480 3488 3906 3915 3924 3059 3066 3073 3496 3504 3512 3933 3942 3951 440 441 442 443 444 445 446 447 448 449 1 2 3 440 880 1320 441 442 443 882 884 886 1323 1326 1329 444 445 446 888 890 892 1332 1335 1338 447 448 449 894 896 898 1341 1344 1347 4 5 6 1760 2200 2640 1764 1768 1772 2205 2210 2215 2646 2652 2658 1776 1780 1784 2220 2225 2230 2664 2670 2676 1788 1792 1796 2235 2240 2245 2682 2688 2694 7 8 9 3080 3520 3960 3087 3094 3101 3528 3536 3544 3969 3978 3987 3108 3115 3122 3552 3560 3568 3996 4005 4014 3129 3136 3143 3576 3584 3592 4023 4032 4041

The text on this page is estimated to be only 29.21% accurate

XVIII. MULTIPLES. 57 450 451 452 453 454 455 456 457 458 459 1 2 3 4 5 6 7 8 9 450 900 1350 1800 2250 2700 3150 3600 4050 451 452 453 902 904 906 1353 1356 1359 1804 1808 1812 2255 2260 2265 2706 2712 2718 3157 3164 3171 3608 3616 3624 4059 4068 4077 454 455 456 908 910 912 1362 1365 1368 1816 1820 1824 2270 2275 2280 2724 2730 2736 3178 3185 3192 3632 3640 3648 4086 4095 4104 457 458 459 914 916 918 1371 1374 1377 1828 1832 1836 2285 2290 2295 2742 2748 2754 3199 3206 3213 3656 3664 3672 4113 4122 4131 460 461 462 463 464 465 466 467 468 469 1 2 4 5 6 7 8 9 460 920 1380 1840 2300 2760 3220 3680 4140 461 462 463 922 924 926 1383 1386 1389 1844 1848 1852 2305 2310 2315 2766 2772 2778 3227 3234 3241 3688 3696 3704 4149 4158 4167 464 465 466 928 930 932 1392 1395 1398 1856 1860 1864 2320 2325 2330 2784 2790 2796 3248 3255 3262 3712 3720 3728 4176 4185 4194 467 468 469 934 936 938 1401 1404 1407 1868 1872 1876 2335 2340 2345 2802 2808 2814 3269 3276 3283 3736 3744 3752 4203 4212 4221 470 471 472 473 474 475 476 477 478 479 1 2 3 4 5 6 7 8 9 470 940 1410 1880 2350 2820 3290 3760 4230 471 472 473 942 944 946 1413 1416 1419 1884 1888 1892 2355 2360 2365 2826 2832 2838 3297 3304 3311 3768 3776 3784 4239 4248 4257 474 475 476 948 950 952 1422 1425 1428 1896 1900 1904 2370 2375 2380 2844 2850 2856 3318 3325 3332 3792 3800 3808 4266 4275 4284 477 478 479 954 956 958 1431 1434 1437 1908 1912 1916 2385 2390 2395 2862 2868 2874 3339 3346 3353 3816 3824 3832 4293 4302 4311 480 481 482 483 484 485 486 487 488 489 1 2 3 4 5 6 7 8 9 480 960 1440 1920 2400 2880 3360 3840 4320 481 482 483 962 964 966 1443 1446 1449 1924 1928 1932 2405 2410 2415 2886 2892 2898 3367 3374 3381 3848 3856 3864 4329 4338 4347 484 485 486 968 970 972 1452 1455 1458 1936 1940 1944 2420 2425 2430 2904 2910 2916 3388 3395 3402 3872 3880 3888 4356 4365 4374 487 488 489 974 976 978 1461 1464 1467 1948 1952 1956 2435 2440 2445 2922 2928 2934 3409 3416 3423 3896 3904 3912 4383 4392 4401 490 491 492 493 494 495 496 497 498 499 1 2 3 4 5 6 7 8 9 490 980 1470 1960 2450 2940 3430 3920 4410 491 492 493 982 984 986 1473 1476 1479 1964 1968 1972 2455 2460 2465 2946 2952 2958 3437 3444 3451 3928 3936 3944 4419 4428 4437 494 495 496 988 990 992 1482 1485 1488 1976 1980 1984 2470 2475 2480 2964 2970 2976 3458 3465 3472 3952 3960 3968 4446 4455 4464 497 498 499 994 996 998 1491 1494 1497 1988 1992 1996 2485 2490 2495 2982 2988 2994 3479 3486 3493 3976 3984 3992 4473 4482 4491

The text on this page is estimated to be only 28.88% accurate

58 XVIII, MULTIPLES. 500 501 502 503 504 505 506 507 508 509 1 2 3 500 1000 1500 501 502 503 1002 1004 1006 1503 1506 1509 504 505 506 1008 1010 1012 1512 1515 1518 507 508 509 1014 1016 1018 1521 1524 1527 4 5 6 2000 2500 3000 2004 2008 2012 2505 2510 2515 3006 3012 3018 2016 2020 2024 2520 2525 2530 3024 3030 3036 2028 2032 2036 2535 2540 2545 3042 3048 3054 7 8 9 3500 4000 4500 3507 3514 3521 4008 4016 4024 4509 4518 4527 3528 3535 3542 4032 4040 4048 4536 4545 4554 3549 3556 3563 4056 4064 4072 4563 4572 4581 510 511 512 513 514 515 516 517 518 519 1 2 3 510 1020 1530 511 512 513 1022 1024 1026 1533 1536 1539 514 515 516 1028 1030 1032 1542 1545 1548 517 518 519 1034 1036 1038 1551 1554 1557 4 5 6 2040 2550 3060 2044 2048 2052 2555 2560 2565 3066 3072 3078 2056 2060 2064 2570 2575 2580 3084 3090 3096 2068 2072 2076 2585 2590 2595 3102 3108 3114 7 8 9 3570 4080 4590 3577 3584 3591 4088 4096 4104 4599 4608 4617 3598 3605 3612 4112 4120 4128 4626 4635 4644 3619 3626 3633 4136 4144 4152 4653 4662 4671 520 521 522 523 524 525 526 527 528 529 1 2 3 520 1040 1560 521 522 523 1042 1044 1046 1563 1566 1569 524 525 526 1048 1050 1052 1572 1575 1578 527 528 529 1054 1056 1058 1581 1584 1587 4 5 6 2080 2600 3120 2084 2088 2092 2605 2610 2615 3126 3132 3138 2096 2100 2104 2620 2625 2630 3144 3150 3156 2108 2112' 2116 2635 2640 2645 3162 3168 3174 7 8 9 3640 4160 4680 3647 3654 3661 4168 4176 4184 46S9 4698 4707 3668 3675 3682 4192 4200 4208 4716 4725 4734 3689 3696 3703 4216 4224 4232 4743 4752 4761 530 531 532 533 534 535 536 537 538 539 1 2 3 530 1060 1590 531 532 533 1062 1064 1066 1593 1596 1599 534 535 536 1068 1070 1072 1602 1605 1608 537 538 539 1074 1076 1078 1611 1614 1617 4 5 6 2120 2650 3180 2124 2128 2132 2655 2660 2665 3186 3192 3198 2136 2140 2144 2670 2675 2680 3204 3210 3216 2148 2152 2156 2685 2690 2695 3222 3228 3234 7 8 9 3710 4240 4770 3717 3724 3731 4248 4256 4264 4779 4788 4797 3738 3745 3752 4272 4280 4288 4806 4815 4824 3759 3766 3773 4296 4304 4312 4833 4842 4851 540 541 542 543 544 545 546 547 548 549 1 2 3 540 1080 1620 541 542 543 1082 1084 1086 1623 1626 1629 544 545 546 1088 1090 1092 1632 1635 1638 547 548 549 1094 1096 1098 1641 1644 1647 4 5 6 2160 2700 3240 2164 2168 2172 2705 2710 2715 3246 3252 3258 2176 2180 2184 2720 2725 2730 3264 3270 3276 2188 2192 2196 2735 2740 2745 3282 3288 3294 7 8 9 3780 4320 4860 3787 3794 3801 4328 4336 4344 4869 4878 4887 3808 3815 3822 4352 4360 4368 4896 4905 4914 3829 3836 3843 4376 4384 4392 4923 4932 4941

The text on this page is estimated to be only 28.99% accurate

XVIII. MULTIPLES. 59 550 551 552 553 554 555 556 557 558 559 1 2 3 4 5 6 7 8 9 550 1100 1650 2200 2750 3300 3850 4400 4950 551 552 553 1102 1104 1106 1653 1656 1659 2204 2208 2212 2755 2760 2765 3306 3312 3318 3857 3864 3871 4408 4416 4424 4959 4968 4977 554 555 556 1108 1110 1112 1662 1665 1668 2216 2220 2224 2770 2775 2780 3324 3330 3336 3878 3885 3892 4432 4440 4448 4986 4995 5004 557 558 559 1114 1116 1118 1671 1674 1677 2228 2232 2236 2785 2790 2795 3342 3348 3354 3899 3906 3913 4456 4464 4472 5013 5022 5031 560 561 562 563 564 565 566 567 568 569 1 2 3 4 5 6 7 8 9 560 1120 1680 2240 2800 3360 3920 4480 5040 561 562 563 1122 1124 1126 1683 1686 1689 2244 2248 2252 2805 2810 2815 3566 3372 3378 3927 3934 3941 4488 4496 4504 5049 5058 5067 564 565 566 1128 1130 1132 1692 1695 1698 2256 2260 2264 2820 2825 2830 3384 3390 3396 3948 3955 3962 4512 4520 4528 5076 5085 5094 567 568 569 1134 1136 1138 1701 1704 1707 2268 2272 2276 2835 2840 2845 3402 3408 3414 3969 3976 3983 4536 4544 4552 5103 5112 5121 570 571 572 573 574 575 576 577 578 579 2 3 4 5 6 7 8 9 570 1140 1710 2280 2850 3420 3990 4560 5130 571 572 573 1142 1144 1146 1713 1716 1719 2284 2288 2292 2855 2860 2865 3426 3432 3438 3997 4004 4011 4568 4576 4584 5139 5148 5157 574 575 576 1148 1150 1152 1722 1725 1728 2296 2300 2304 2870 2875 2880 3444 3450 3456 4018 4025 4032 4592 4600 4608 5166 5175 5184 577 578 579 1154 1156 1158 1731 1734 1737 2308 2312 2316 2885 2890 2895 3462 3468 3474 4039 4046 4053 4616 4624 4632 5193 5202 5211 580 581 582 583 584 585 586 587 588 589 1 2 3 4 5 6 7 8 9 580 1160 1740 2320 2900 3480 4060 4640 5220 581 582 583 1162 1164 1166 1743 1746 1749 2324 2328 2332 2905 2910 2915 3486 3492 3498 4067 4074 4081 4648 4656 4664 5229 5238 5247 584 585 586 1168 1170 1172 1752 1755 1758 2336 2340 2344 2920 2925 2930 3504 3510 3516 4088 4095 4102 4672 4680 4688 5256 5265 5274 587 588 589 1174 1176 1178 1761 1764 1767 2348 2352 2356 2935 2940 2945 3522 3528 3534 4109 4116 4123 4696 4704 4712 5283 5292 5301 590 591 592 593 594 595 596 597 598 599 1 2 3 4 5 6 7 8 9 590 1180 1770 2360 2950 3540 4130 4720 5310 591 592 593 1182 1184 1186 1773 1776 1779 2364 2368 2372 2955 2960 2965 3546 3552 3558 4137 4144 4151 4728 4736 4744 5319 5328 5337 594 595 596 1188 1190 1192 1782 1785 1788 2376 2380 2384 2970 2975 2980 3564 3570 3576 4158 4165 4172 4752 4760 4768 5346 5355 5364 597 598 599 1194 1196 1198 1791 1794 1797 2388 2392 2396 2985 2990 2995 3582 3588 3594 4179 4186 4193 4776 4784 4792 5373 5382 5391

The text on this page is estimated to be only 28.82% accurate

60 XVIII. MULTIPLES. 600 601 602 603 604 605 606 607 608 609 1 2 3 4 5 6 7 8 9 600 1200 1800 2400 3000 3600 4200 4800 5400 601 602 603 1202 1204 1206 1803 1806 1809 2404 2408 2412 3005 3010 3015 3606 3612 3618 4207 4214 4221 4808 4816 4824 5409 5418 5427 604 605 606 1208 1210 1212 1812 1815 1818 2416 2420 2424 3020 3025 3030 3624 3630 3636 4228 4235 4242 4832 4840 4848 5436 5445 5454 607 608 609 1214 1216 1218 1821 1824 1827 2428 2432 2436 3035 3040 3045 3642 3648 3654 4249 4256 4263 4856 4864 4872 5463 5472 5481 610 611 612 613 614 615 616 617 618 619 1 2 3 4 5 6 7 8 9 610 1220 1830 2440 3050 3660 4270 4880 5490 611 612 613 1222 1224 1226 1833 1836 1839 2444 2448 2452 3055 3060 3065 3666 3672 3678 4277 4284 4291 4888 4896 4904 5499 5508 5517 614 615 616 1228 1230 1232 1842 1845 1848 2456 2460 2464 3070 3075 3080 3684 3690 3696 4298 4305 4312 4912 4920 4928 5526 5535 5544 617 618 619 1234 1236 1238 1851 1854 1857 2468 2472 2476 3085 3090 3095 3702 3708 3714 4319 4326 "4333 4936 4944 4952 5553 5562 5571 620 621 622 623 624 625 626 627 628 629 1 2 3 4 5 6 7 8 9 620 1240 ]860 2480 3100 3720 4340 4960 5580 621 622 623 1242 1244 1246 1863 1866 1869 2484 2488 2492 3105 3110 3115 3726 3732 3738 4347 4354 4361 4968 4976 4984 5589 5598 5607 624 625 626 1248 1250 1252 1872 1875 1878 2496 2500 2504 3120 3125 3130 3744 3750 3756 4368 4375 4382 4992 5000 5008 5616 5625 5634 627 628 629 1254 1256 1258 1881 1884 1887 2508 2512 2516 3135 3140 3145 3762 3768 3774 4389 4396 4403 5016 5024 5032 5643 5652 5661 630 631 632 633 634 635 636 637 638 639 1 2 3 4 5 6 7 8 9 630 1260 1890 2520 3150 3780 4410 5040 5670 631 632 633 1262 1264 1266 1893 1896 1899 2524 2528 2532 3155 3160 3165 3786 3792 3798 4417 4424 4431 5048 5056 5064 5679 5688 5697 634 635 636 1268 1270 1272 1902 1905 1908 2536 2540 2544 3170 3175 3180 3804 3810 3816 4438 4445 4452 5072 5080 5088 5706 5715 5724 637 638 639 1274 1276 1278 1911 1914 1917 2548 2552 2556 3185 3190 3195 3822 3828 3834 4459 4466 4473 5096 5104 5112 5733 5742 5751 640 641 642 643 644 645 646 647 648 649 1 2 3 4 5 6 7 8 9 640 1280 1920 2560 3200 3840 4480 5120 5760 641 642 643 1282 1284 1286 1923 1926 1929 2564 2568 2572 3205 3210 3215 3846 3852 3858 4487 4494 4501 5128 5136 5144 5769 5778 5787 644 645 646 1288 1290 1292 1932 1935 1938 2576 2580 2584 3220 3225 3230 3864 3870 3876 4508 4515 4522 5152 5160 5168 5796 5805 5814 647 648 649 1294 1296 1298 1941 1944 1947 2588 2592 2596 3235 3240 3245 3882 3888 3894 4529 4536 4543 5176 5184 5192 5823 5832 5841

The text on this page is estimated to be only 28.50% accurate

XVIII. MULTIPLES. 61 650 651 652 653 654 655 656 657 658 659 1 2 3 4 5 6 7 8 9 650 1300 1950 2600 3250 3900 4550 5200 5850 651 652 653 1302 1304 1306 1953 1956 1959 2604 260S 2612 3255 3260 3265 3906 3912 3918 4557 4564 4571 5208 5216 5224 5859 5868 5877 654 655 656 1308 1310 1312 1962 1965 1968 2616 2620 2624 3270 3275 3280 3924 3930 3936 4578 4585 4592 5232 5240 5248 5886 5895 5904 657 658 659 1314 1316 1318 1971 1974 1977 2628 2632 2636 3285 3290 3295 3942 3948 3954 4599 4606 4613 5256 5264 5272 5913 5922 5931 660 661 662 663 664 665 666 667 668 669 1 2 3 4 5 6 7 8 9 660 1320 1980 2640 3300 3960 4620 5280 5940 661 662 663 1322 1324 1326 1983 1986 1989 2644 2648 2652 3305 3310 3315 396$ 3972 3978 4627 4634 4641 5288 5296 5304 5949 5958 5967 664 665 666 1328 1330 1332 1992 1995 1998 2656 2660 2664 3320 3325 3330 3984 3990 3996 4648 4655 4662 5312 5320 5328 5976 5985 5994 667 668 669 1334 1336 1338 2001 2004 2007 2668 2672 2676 3335 33-40 3345 4002 4008 4014 4669 4676 4683 5336 5344 5352 6003 6012 6021 670 671 672 673 674 675 676 677 678 679 1 2 3 4 5 6 7 8 9 670 1340 2010 2680 3350 4020 4690 5360 6030 671 672 673 1342 1344 1346 2013 2016 2019 2684 2688 2692 3355 3360 3365 4026 4032 4038 4697 4704 4711 5368 5376 5384 6039 6048 6057 674 675 676 1348 1350 1352 2022 2025 2028 2696 2700 2704 3370 3375 3380 4044 4050 4056 4718 4725 4732 5392 5400 5408 6066 6075 60S4 677 678 679 1354 1356 1358 2031 2034 2037 2708 2712 2716 3385 3390 3395 4062 4068 4074 4739 4746 4753 5416 5424 5432 6093 6102 6111 680 681 682 683 684 685 686 687 688 689 1 2 3 4 5 6 7 8 9 680 1360 20-10 2720 3400 4080 4760 5440 6120 681 682 683 1362 1364 1366 2043 2046 2049 2724 2728 2732 3405 3410 3415 4086 4092 4098 4767 4774 4781 5448 5456 5464 6129 6138 6147 684 685 686 1368 1370 1372 2052 2055 2058 2736 2740 2744 3420 3425 3430 4104 4110 4116 4788 4795 4802 5472 5480 5488 6156 6165 6174 687 688 689 1374 1376 1378 2061 2064 2067 2748 2752 2756 3435 3440 3445 4122 4128 4134 4809 4816 4823 5496 5504 5512 6183 6192 6201 690 691 692 693 694 695 696 697 698 699 1 2 3 4 5 6 7 8 9 690 1380 2070 2760 3450 4140 4830 5520 6210 691 692 693 1382 1384 1386 2073 2076 2079 2764 2768 2772 3455 3460 3465 4146 4152 4158 4837 4844 4851 5528 5536 5544 6219 6228 6237 694 695 696 1388 1390 1392 2082 2085 2088 2776 2780 2784 3470 3475 3480 4164 4170 4176 4858 4865 4872 5552 5560 5568 6246 6255 6264 697 698 699 1394 1396 1398 2091 2094 2097 2788 2792 2796 3485 3490 3495 4182 4188 4194 4879 4886 4893 5576 5584 5592 6273 6282 6291

The text on this page is estimated to be only 29.10% accurate

62 XVIII. MULTIPLES. 700 701 702 703 704 705 706 707 708 709 1 2 3 4 5 6 7 8 9 700 1400 2100 2800 3500 4200 4900 5600 6300 701 702 703 1402 1404 1406 2103 2106 2109 2804 2808 2812 3505 3510 3515 4206 4212 4218 4907 4914 4921 5608 5616 5624 6309 6318 6327 704 705 706 1408 1410 1412 2112 2115 2118 2816 2820 2824 3520 3525 3530 4224 4230 4236 4928 4935 4942 5632 5640 5648 6336 6345 6354 707 708 709 1414 1416 1418 2121 2124 2127 2828 2832 2836 3535 3540 3545 4242 4248 4254 4949 4956 4963 5656 5664 5672 6363 6372 6381 710 711 712 713 714 715 716 717 718 719 1 2 3 4 5 6 7 8 9 710 1420 2130 2840 3550 4260 4970 5680 6390 *711 712 713 1422 1424 1426 2133 2136 2139 2844 2848 2852 3555 3560 3565 4266 4272 4278 4977 4984 4991 5688 5696 5704 6399 6408 6417 714 715 716 1428 1430 1432 2142 2145 2148 2856 2860 2864 3570 3575 3580 4284 4290 4296 4998 5005 5012 5712 5720 5728 6426 6435 6444 717 718 719 1434 1436 1438 2151 2154 2157 2868 2872 2876 3585 3590 3595 4302 4308 4314 5019 5026 5033 5736 5744 5752 6453 6462 6471 720 721 722 723 724 725 726 727 728 729 1 2 3 4 5 6 7 8 9 720 1440 2160 2880 3600 4320 5040 5760 6480 721 722 723 1442 1444 1446 2163 2166 2169 2884 2888 2892 3605 3610 3615 4326 4332 4338 5047 5054 5061 5768 5776 5784 6489 6498 6507 724 725 726 1448 1450 1452 2172 2175 2178 2896 2900 2904 3620 3625 3630 4344 4350 4356 5068 5075 5082 5792 5800 5808 6516 6525 6534 727 728 729 1454 1456 1458 2181 2184 2187 2908 2912 2916 3635 3640 3645 4362 4368 4374 5089 5096 5103 5816 5824 5832 6543 6552 6561 730 731 732 733 734 735 736 737 738 739 1 2 3 4 5 6 7 8 9 730 1460 2190 2920 3650 4380 5110 5840 6570 731 732 733 1462 1464 1466 2193 2196 2199 2924 2928 2932 3655 3660 3665 4386 4392 4398 5117 5124 5131 5848 5856 5864 6579 6588 6597 734 735 736 1468 1470 1472 2202 2205 2208 2936 2940 2944 3670 3675 3680 4404 4410 4416 5138 5145 5152 5872 5880 5888 6606 6615 6624 737 738 739 1474 1476 1478 2211 2214 2217 2948 2952 2956 3685 3690 3695 4422 4428 4434 5159 5166 5173 5896 5904 5912 6633 6642 6651 740 741 742 743 744 745 746 747 748 749 1 2 3 4 5 6 7 8 9 740 1480 2220 2960 3700 4440 5180 5920 6660 741 742 743 1482 1484 1486 2223 2226 2229 2964 2968 2972 3705 3710 3715 4446 4452 4458 5187 5194 5201 5928 5936 5944 6669 6678 6687 744 745 746 1488 1490 1492 2232 2235 2238 2976 2980 2984 3720 3725 3730 4464 4470 4476 5208 5215 5222 5952 5960 5968 6696 6705 6714 747 748 749 1494 1496 1498 2241 2244 2247 2988 2992 2996 3735 3740 3745 4482 4488 4494 5229 5236 5243 5976 5984 5992 6723 6732 6741

The text on this page is estimated to be only 28.78% accurate

XVIII. MULTIPLES. 63 750 751 752 753 754 755 756 757 758 759 1 2 3 4 5 6 7 8 9 750 1500 2250 3000 3750 4500 5250 6000 6750 751 752 753 1502 1504 1506 2253 2256 2259 3004 3008 3012 3755 3760 3765 4506 4512 4518 5257 5264 5271 6008 6016 6024 6759 6768 6777 754 755 756 1508 1510 1512 2262 2265 2268 3016 3020 3024 3770 3775 3780 4524 4530 4536 5278 5285 5292 6032 6040 6048 6786 6795 6804 757 758 759 1514 1516 1518 2271 2274 2277 3028 3032 3036 3785 3790 3795 4542 4548 4554 5299 5306 5313 6056 6064 6072 6813 6822 6831 760 761 762 763 764 765 766 767 768 769 1 2 3 4 5 6 7 8 9 760 1520 2280 3040 3800 4560 5320 6080 6840 761 762 763 1522 1524 1526 2283 2286 2289 3044 3048 3052 3805 3810 3815 456(5 4572 4578 5327 5334 5341 6088 6096 6104 6849 6858 6867 764 765 766 1528 1530 1532 2292 2295 2298 3056 3060 3064 3820 3825 3830 4584 4590 4596 5348 5355 5362 6112 6120 6128 6876 6885 6894 767 768 769 1534 1536 1538 2301 2304 2307 3068 3072 3076 3835 3840 3845 4602 4608 4614 5369 5376 5383 6136 6144 6152 6903 6912 6921 770 771 772 773 774 775 776 777 778 779 1 2 3 4 5 6 7 8 9 770 1540 2310 3080 3850 4620 5390 6160 6930 771 772 773 1542 1544 1546 2313 2316 2319 3084 3088 3092 3855 3860 3865 4626 4632 4638 5397 5404 5411 6168 6176 6184 6939 6948 6957 774 775 776 1548 1550 1552 2322 2325 2328 3096 3100 3104 3870 3875 3880 4644 4650 4656 5418 5425 5432 6192 6200 6208 6966 6975 6984 777 778 779 1554 1556 1558 2331 2334 2337 3108 3112 3116 3885 3890 3895 4662 4668 4674 5439 5446 5453 6216 6224 6232 6993 7002 7011 780 781 782 783 784 785 786 787 788 789 1 2 3 4 5 6 7 8 9 780 1560 2340 3120 3900 4680 5460 6240 7020 781 782 783 1562 1564 1566 2343 2346 2349 3124 3128 3132 3905 3910 3915 4686 4692 4698 5467 5474 5481 6248 6256 6264 7029 7038 7047 784 785 786 1568 1570 1572 2352 2355 2358 3136 3140 3144 3920 3925 3930 4704 4710 4716 5488 5495 5502 6272 6280 6288 7056 7065 7074 787 788 789 1574 1576 1578 2361 2364 2367 3148 3152 3156 3935 3940 3945 4722 4728 4734 5509 5516 5523 6296 6304 6312 7083 7092 7101 790 791 792 793 794 795 796 797 798 799 1 2 3 4 5 6 7 8 9 790 1580 2370 3160 3950 4740 5530 6320 7110 791 792 793 1582 1584 1586 2373 2376 2379 3164 3168 3172 3955 3960 3965 4746 4752 4758 5537 5544 5551 6328 6336 6344 7119 7128 7137 794 795 796 1588 1590 1592 2382 2385 2388 3176 3180 3184 3970 3975 3980 4764 4770 4776 5558 5565 5572 6352 6360 6368 7146 7155 7164 797 798 799 1594 1596 1598 2391 2394 2397 3188 3192 3196 3985 3990 3995 4782 4788 4794 5579 5586 5593 6376 6384 6392 7173 7182 7191

The text on this page is estimated to be only 29.19% accurate

64 XVIII. MULTIPLES. 800 801 802 803 804 805 806 807 808 809 1 2 3 4 5 6 7 8 9 800 1600 2400 3200 4000 4800 5600 6400 7200 801 802 803 1602 1604 1606 2403 2406 2409 3204 3208 3212 4005 4010 4015 4806 4812 4818 5607 5614 5621 6408 6416 6424 7209 7218 7227 804 805 806 1608 1610 1612 2412 2415 2418 3216 3220 3224 4020 4025 4030 4824 4830 4836 5628 5635 5642 6432 6440 6448 7236 7245 7254 807 808 809 1614 1616 1618 2421 2424 2427 3228 3232 3236 4035 4040 4045 4842 4848 4854 5649 5656 5663 6456 6464 6472 7263 7272 72S1 810 811 812 813 814 815 816 817 818 819 1 2 3 4 5 6 7 8 9 810 1620 2430 3240 4050 4860 5670 6480 7290 811 812 813 1622 1624 1626 2433 2436 2439 3244 3248 3252 4055 4060 4065 4866 4872 4878 5677 5684 5691 6488 6496 6504 7299 7308 7317 814 815 816 1628 1630 1632 2442 2445 2448 3256 3260 3264 4070 4075 4080 4884 4890 4896 5698 5705 5712 6512 6520 6528 7326 7335 7344 817 818 819 1634 1636 1638 2451 2454 2457 3268 3272 3276 4085 4090 4095 4902 4908 4914 5719 5726 5733 6536 6544 6552 7353 7362 7371 820 | 821 822 823 824 825 826 827 828 829 1 2 3 4 5 6 7 8 9 820 1640 2460 3280 4100 4920 5740 6560 7380 821 822 823 1642 1644 1646 2463 2466 2469 3284 3288 3292 4105 4110 4115 4926 4932 4938 5747 5754 5761 6568 6576 6584 7389 7398 7407 824 825 826 1648 1650 1652 2472 2475 2478 3296 3300 3304 4120 4125 4130 4944 4950 4956 5768 5775 5782 6592 6600 6608 7416 7425 7434 827 828 829 1654 1656 1658 2481 2484 2487 3308 3312 3316 4135 4140 4145 4962 4968 4974 5789 5796 5803 6616 6624 6632 7443 7452 7461 830 831 832 833 834 835 836 837 838 839 1 2 3 4 5 6 7 8 9 830 1660 2490 3320 4150 4980 5810 6640 7470 831 832 833 1662 1664 1666 2493 2496 2499 3324 3328 3332 4155 4160 4165 4986 4992 4998 5817 5824 5831 6648 6656 6664 7479 7488 7497 834 835 836 1668 1670 1672 2502 2505 2508 3336 3340 3344 4170 4175 4180 5004 5010 5016 5838 5845 5852 6672 6680 6688 7506 7515 7524 837 838 839 1674 1676 1678 2511 2514 2517 3348 3352 3356 4185 4190 4195 5022 5028 5034 5859 5866 5873 6696 6704 6712 7533 7542 7551 840 841 842 843 844 845 846 847 848 849 1 2 3 4 5 6 7 8 9 840 1680 2520 3360 4200 5040 5880 6720 7560 841 842 843 1682 1684 1686 2523 2526 2529 3364 3368 3372 4205 4210 4215 5046 5052 5058 5887 5894 5901 6728 6736 6744 7569 7578 7587 844 845 846 1688 1690 1692 2532 2535 2538 3376 3380 3384 4220 4225 4230 5064 5070 5076 5908 5915 5922 6752 6760 6768 7596 7605 7614 847 848 849 1694 1696 1698 2541 2544 2547 3388 3392 3396 4235 4240 4245 5082 5088 5094 5929 5936 5943 6776 6784 6792 7623 7632 7641

The text on this page is estimated to be only 29.19% accurate

XVIII. MULTIPLES. 65 850 851 852 853 854 855 856 857 858 859 1 2 3 4 5 6 7 • 8 9 850 1700 2550 3400 4250 5100 5950 6800 7650 851 852 853 1702 1704 1706 2553 2556 2559 3404 3408 3412 4255 4260 4265 5106 5112 5118 5957 5964 5971 6808 6816 6824 7659 7668 7677 854 855 856 1708 1710 1712 2562 2565 2568 3416 3420 3424 4270 4275 4280 5124 5130 5136 5978 5985 5992 6832 6840 6848 7686 7695 7704 857 858 859 1714 1716 1718 2571 2574 2577 3428 3432 3436 4285 4290 4295 5142 5148 5154 5999 6006 6013 6856 6864 6872 7713 7722 7731 860 861 862 863 864 865 866 867 868 869 1 2 3 4 5 6 7 8 9 860 1720 2580 3440 4300 5160 6020 6880 7740 861 862 863 1722 1724 1726 2583 2586 2589 3444 3448 3452 4305 4310 4315 516£ 5172 5178 6027 6034 6041 6888 6896 6904 7749 7758 7767 864 865 866 1728 1730 1732 2592 2595 2598 3456 3460 3464 4320 4325 4330 5184 5190 5196 6048 6055 6062 6912 6920 6928 7776 7785 7794 867 868 869 1734 1736 1738 2601 2604 2607 3468 3472 3476 4335 4340 4345 5202 5208 5214 6069 6076 6083 6936 6944 6952 7803 7812 7821 870 871 872 873 874 875 876 877 878 879 1 2 3 4 5 6 7 8 9 870 1740 2610 3480 4350 5220 6090 6960 7830 871 872 873 1742 1744 1746 2613 2616 2619 3484 3488 3492 4355 4360 4365 5226 5232 5238 6097 6104 6111 6968 6976 6984 7839 7848 7857 874 875 876 1748 1750 1752 2622 2625 2628 3496 3500 3504 4370 4375 4380 5244 5250 5256 6118 6125 6132 6992 7000 7008 7866 7875 7884 877 878 879 1754 1756 1758 2631 2634 2637 3508 3512 3516 4385 4390 4395 5262 5268 5274 6139 6146 6153 7016 7024 7032 7893 7902 7911 880 881 882 883 884 885 886 887 888 889 1 2 3 4 5 6 7 8 9 880 1760 2640 3520 4400 5280 6160 7040 7920 881 882 883 1762 1764 1766 2643 2646 2649 3524 3528 3532 4405 4410 4415 5286 5292 5298 6167 6174 6181 7048 7056 7064 7929 7938 7947 884 885 886 1768 1770 1772 2652 2655 2658 3536 3540 3544 4420 4425 4430 5304 5310 5316 6188 6195 6202 7072 7080 7088 7956 7965 7974 887 888 889 1774 1776 1778 2661 2664 2667 3548 3552 3556 4435 4440 4445 5322 5328 5334 6209 6216 6223 7096 7104 7112 7983 7992 8001 890 891 892 893 894 895 896 897 898 899 1 2 3 4 5 6 7 8 9 890 1780 2670 3560 4450 5340 6230 7120 8010 891 892 893 1782 1784 1786 2673 2676 2679 3564 3568 3572 4455 4460 4465 5346 5352 5358 6237 6244 6251 7128 7136 7144 8019 8028 8037 894 895 896 1788 1790 1792 2682 2685 2688 3576 3580 3584 4470 4475 4480 5364 5370 5376 6258 6265 6272 7152 7160 7168 8046 8055 8064 897 898 899 1794 1796 1798 2691 2694 2697 3588 3592 3596 4485 4490 4495 5382 5388 5394 6279 6286 6293 7176 7184 7192 8073 8082 8091

The text on this page is estimated to be only 28.78% accurate

66 XVIII. MULTIPLES. 900 901 902 903 904 905 906 907 908 909 1 2 3 4 5 6 7 8 9 900 1800 2700 3600 4500 5400 6300 7200 8100 901 902 903 1802 1804 1806 2703 2706 2709 3604 3608 3612 4505 4510 4515 5406 5412 5418 6307 6314 6321 7208 7216 7224 8109 8118 8127 904 905 906 1808 1810 1812 2712 2715 2718 3616 3620 3624 4520 4525 4530 5424 5430 5436 6328 6335 6342 7232 7240 7248 8136 8145 8154 907 908 909 1814 1816 1818 2721 2724 2727 3628 3632 3636 4535 4540 4545 5442 5448 5454 6349 6356 6363 7256 7264 7272 8163 8172 8181 910 911 912 913 914 915 916 917 918 919 1 2 3 4 5 6 7 8 9 910 1820 2730 3640 4550 5460 6370 7280 8190 911 912 913 1822 1824 1826 2733 2736 2739 3644 3648 3652 4555 4560 4565 5466 5472 5478 6377 6384 6391 7288 7296 7304 8199 8208 8217 914 915 916 1828 1830 1832 2742 2745 2748 3656 3660 3664 4570 4575 4580 5484 5490 5496 6398 6405 6412 7312 7320 7328 8226 8235 8244 917 918 919 1834 1836 1838 2751 2754 2757 3668 3672 3676 4585 4590 4595 5502 5508 5514 6419 6426 6433 7336 7344 7352 8253 8262 8271 920 921 922 923 924 925 926 927 928 929 1 2 3 4 5 6 7 8 9 920 1840 2760 3680 4600 5520 6440 7360 8280 921 922 923 1842 1844 1846 2763 2766 2769 3684 3688 3692 4605 4610 4615 5526 5532 5538 6447 6454 6461 7368 7376 7384 8289 8298 8307 924 925 926 1848 1850 1852 2772 2775 2778 3696 3700 3704 4620 4625 4630 5544 5550 5556 6468 6475 6482 7392 7400 7408 8316 8325 8334 927 928 929 1854 1856 1858 2781 2784 2787 3708 3712 3716 4635 4640 4645 5562 5568 5574 6489 6496 6503 7416 7424 7432 8343 8352 8361 930 931 932 933 934 935 936 937 938 939 1 2 3 4 5 6 7 8 9 930 1860 2790 3720 4650 5580 6510 7440 8370 931 932 933 1862 1864 1866 2793 2796 2799 3724 3728 3732 4655 4660 4665 5586 5592 5598 6517 6524 6531 7448 7456 7464 8379 8388 8397 934 935 936 1868 1870 1872 2802 2805 2808 3736 3740 3744 4670 4675 4680 5604 5610 5616 6538 6545 6552 7472 7480 7488 8406 8415 8424 937 938 939 1874 1876 1878 2811 2814 2817 3748 3752 3756 4685 4690 4695 5622 5628 5634 6559 6566 6573 7496 7504 7512 8433 8442 8451 ~T~ 2 3 4 5 6 7 8 9 940 941 942 943 944 945 946 947 948 949 940 1880 2820 3760 4700 5640 6580 7520 8460 941 942 943 1882 1884 1886 2823 2826 2829 3764 3768 3772 4705 4710 4715 5646 5652 5658 6587 6594 6601 7528 7536 7544 8469 8478 8487 944 945 946 1888 1890 1892 2832 2835 2838 3776 3780 3784 4720 4725 4730 5664 5670 5676 6608 6615 6622 7552 7560 7568 8-t°* 8505 8514 947 948 949 1894 1896 1898 2841 2844 2847 3788 3792 3796 4735 4740 4745 5682 5688 5694 6629 6636 6643 7576 7584 7592 8523 8532 8541

The text on this page is estimated to be only 28.90% accurate

XVIII. MULTIPLES. 67 950 951 952 953 954 955 956 957 958 959 1 2 3 4 5 6 7 8 9 950 1900 2850 3800 4750 5700 6650 7600 8550 951 952 953 1902 1904 1906 2853 2856 2859 3804 3808 3812 4755 4760 4765 5706 5712 5718 6657 6664 6671 7608 7616 7624 8559 8568 8577 954 955 956 1908 1910 1912 2862 2865 2868 3816 3820 3824 4770 4775 4780 5724 5730 5736 6678 6685 6692 7632 7640 7648 8586 8595 8604 957 958 959 1914 1916 1918 2871 2874 2877 38-28 3832 3836 4785 4790 4795 5742 5748 5754 6699 6706 6713 7656 7664 7672 8613 8622 8631 960 961 962 963 964 965 966 967 968 969 1 2 3 4 5 6 7 8 9 960 1920 2880 3840 4800 5760 6720 7680 8640 961 962 963 1922 1924 1926 2883 2886 2889 3844 3848 3852 4805 4810 4815 576,6 5772 5778 6727 6734 6741 7688 7696 7704 8649 8658 8667 964 965 966 1928 1930 1932 2892 2895 2898 3856 3860 3864 4820 4825 4830 5784 5790 5796 6748 6755 6762 7712 7720 7728 8676 8685 8694 967 968 969 1934 1936 1938 2901 2904 2907 3868 3872 3876 4835 4840 4845 5802 5808 5814 6769 6776 6783 7736 7744 7752 8703 8712 8721 970 971 972 973 974 975 976 977 978 979 1 2 3 4 5 6 7 8 9 970 1940 2910 3880 4850 5820 6790 7760 8730 971 972 973 1942 1944 1946 2913 2916 2919 3884 3888 3892 4855 4860 4865 5826 5832 5838 6797 6804 6811 7768 7776 7784 8739 8748 8757 974 975 976 1948 1950 1952 2922 2925 2928 3896 3900 3904 4870 4875 4880 5844 5850 5856 6818 6825 6832 7792 7800 7808 8766 8775 8784 977 978 979 1954 1956 1958 2931 2934 2937 3908 3912 3916 4885 4890 4895 5862 5868 5874 6839 6846 6853 7816 7824 7832 8793 8802 8811 980 981 982 983 984 985 986 987 988 989 1 2 3 4 5 6 7 8 9 980 1960 2940 3920 4900 5880 6860 7840 8820 981 982 983 1962 1964 1966 2943 2946 2949 3924 3928 3932 4905 4910 4915 5886 5892 5898 6867 6874 6881 7848 7856 7864 8829 8838 8847 984 985 986 1968 1970 1972 2952 2955 2958 3936 3940 3944 4920 4925 4930 5904 5910 5916 6888 6895 6902 7872 7880 7888 8856 8865 8874 987 988 989 1974 1976 1978 2961 2964 2967 3948 3952 3956 4935 4940 4945 5922 5928 5934 6909 6916 6923 7896 7904 7912 8883 8892 8901 990 991 992 993 994 995 996 997 998 999 1 2 3 4 5 6 7 8 9 990 1980 2970 3960 4950 5940 6930 7920 8910 991 992 993 1982 1984 1986 2973 2976 2979 3964 3968 3972 4955 4960 4965 5946 5952 5958 6937 6944 6951 7928 7936 7944 8919 8928 8937 994 995 996 1988 1990 1992 2982 2985 2988 3976 3980 3984 4970 4975 4980 5964 5970 5976 6958 6965 6972 7952 7960 7968 8946 8955 8964 997 998 999 1994 1996 1998 2991 2994 2997 3988 3992 3996 4985 4990 4995 5982 5988 5994 6979 6986 6993 7976 7984 7992 8973 8982 8991

The text on this page is estimated to be only 28.73% accurate

68 XIX. OIEOUMPEEENOE OP CIRCLE n 0 123 456 7 8 9 PP 1.0 3.142 3.173 3.204 3.236 3.267 3.299 3.330 3.362 3.393 3.424 32^ 1.1 3.456 3.487 3.519 3.550 3.581 3.613 3.644 3.676 3.707 3.738 3 1.2 3.770 3.801 3.833 3.864 3.896 3 927 3.958 3.990 4.021 4.053 6 1.3 4.084 4.115 4.147 4.178 4.210 4.241 4.273 4.304 4.335 4.367 10 1.4 4.398 4.430 4.461 4.492 4.524 4.555 4.587 4.618 4.650 4.681 13 1.5 4.712 4.744 4.775 4.807 4.838 4.869 4.901 4.932 4.964 4.995 16 1.6 5.027 5.058 5.089 5.121 5.152 5.184 5.215 5.246 5.278 5.309 19 1.7 5.341 5.372 5.404 5.435 5.466 5.498 5.529 5.561 5.592 5.623 22 1.8 5.655 5.686 5.718 5.749 5.781 5.812 5.843 5.875 5.906 5.938 26 1.9 5.969 6.000 6.032 6.063 6.095 6.126 6.158 6.189 6.220 6.252 29 2.0 6.283 6.315 6.346 6.377 6.409 6.440 6.472 6.503 6.535 6.566 iT 2.1 6.597 6.629 6.660 6.692 6.723 6.754 6.786 6.817 6.849 6.880 3 2.2 6.912 6.943 6.974 7.006 7.037 7.069 7.100 7.131 7.163 7.194 6 2.3 7.226 7.257 7.288 7.320 7.351 7.383 7.414 7.446 7.477 7.508 9 2.4 7.540 7.571 7.603 7.634 7.665 7.697 7.728 7.760 7.791 7.823 12 2.5 7.854 7.885 7.917 7.948 7.9SO 8.011 8.042 8.074 8.105 8.137 16 2.6 8.168 8.200 8.231 8.262 8.294 8.325 8.357 8.388 8.419 8.451 19 2.7 8.482 8.514 8.545 8.577 8.608 8.639 8.671 8.702 8.734 8.765 22 2.8 8.796 8.828 8.859 8.891 8.922 8.954 8.985 9.016 9.048 9.079 25 2.9 9.111 9.142 9.173 9.205 9.236 9.268 9.299 9.331 9.362 9.393 28 3.0 9.423 9.456 9.488 9.519 9.550 9.582 9.613 9.645 9.676 9.708 4 3.1 9.739 9.770 9.802 9.833 9.865 9.896 9.927 9.959 9.990 10.02 0 3.2 10.05 10.08 10.12 10.1^ 10.18 10.21 10.24 10.27 10.30 10.34 1 3.3 10.37 10.40 10.43 10.46 10.49 10.52 10.56 10.59 10.62 J0.65 1 3.4 10.68 10.71 10.74 10.78 10.81 10.84 10.87 10.90 10.93 10.96 2 3.5 11.00 11.03 11.06 11.09 11.12 11.15 11.18 11.22 11.25 11.28 2 3.6 11.31 11.34 11.37 11.40 11.44 11.47 1L5Q 11.53 11.56 11.59 2 3.7 11.62 11.66 11.69 11.72 11.75 11.78 11.81 11.84 11.88 11.91 3 3.8 11.94 11.97 ]2.00 12.03 12.06 12.10 12.13 12.16 12.19 12.22 3 3.9 12.25 12.28 12.32 12.35 12.38 12.41 12.44 12.47 12.50 12.53 4 4.0 12.57 12.60 12.63 12.66 12.69 12.72 12.75 12.79 12.82 12.85 3 4.1 12.88 12.91 12.94 12.97 13.01 13.04 13.07 13.10 13.13 13.16 0 4.2 13.19 13.23 13.26 13.29 13.32 13.35 13.38 13.41 13.45 13.48 1 4.3 13.51 13.54 13.57 13.60 13.63 13.67 13.70 13.73 13.76 13.79 1 4.4 13.82 13.85 13.89 13.92 13.95 13.98 14.01 14.04 14.07 14.11 1 4.5 14.14 14.17 14.20 14.23 14.26 14.29 14.33 14.36 14.39 14.42 2 4.6 14.45 14.48 14.51 14.55 14.58 14.61 14.64 14.67 14.70 14.73 2 4.7 14.77 14.80 14.83 14.86 14.89 14.92 14.95 14.99 15.02 15.05 2 4.8 15.08 15.11 15.14 15.17 15.21 15.24 15.27 15.30 15.33 15.36 2 4.9 15.39 15.43 15.46 15.49 15.52 15.55 15.58 15.61 15.65 15.68 3 5.0 15.71 15.74 15.77 15.80 15.83 15.87 15.90 15.93 15.96 15.99 5.1 16.02 16.05 16.08 16.12 16.15 16.18 16.21 16.24 16.27 16.30 5.2 16.34 16.37 16.40 1643 16.46 16.49 16.52 16.56 16.59 16.62 5.3 16.65 16.68 16.71 16.74 16.78 16.81 16.84 16.87 16.90 16.93 5.4 16.96 17.00 17.03 17.06 17.09 17.12 17.15 17.18 17.22 17.25 5.5 17.28 17.31 17.34 17.37 17.40 17.44 17.47 17.50 17.53 17.56 5.6 17.59 17.62 17.66 17.69 17.72 17.75 17.78 17.81 17.84 17.88 5.7 17.91 17.94 17.97 18.00 18.03 18.06 18.10 18.13 18.16 18.19 5.8 18.22 18.25 18-28 18.32 18.35 18.38 .18.41 1844 18.47 18.50 5.9 18.54 18.57 18.60 18.63 18.66 18.69 18.72 18.76 18.79 18.82

The text on this page is estimated to be only 28.02% accurate

n BEING DIAMETER, 69 11 0 1 2 3 456 7 8 9 PP 6.0 18.85 18.88 18.91 18.94 18.98 19.01 19.04 19.07 19.10 19.13 4 6.1 19.16 19.20 19.23 19.26 19.29 19.32 19.35 19.38 19.42 19.45 0 6.2 19.48 19.51 19.54 19.57 19.60 19.63 19.67 19.70 19.73 19.76 1 6.3 19.79 19.82 19.85 19.89 19.92 19.95 19.98 20.01 20.04 20.07 1 6.4 20.11 20.14 20.17 20.20 20.23 20.26 20.29 20.33 20.36 20.39 2 6.5 20.42 20.45 20.48 20.51 20.55 20.58 20.61 20.64 20.67 20.70 2 6.6 20.73 20.77 20.80 20.83 20.86 20.89 20.92 20.95 20.99 21.02 2 6.7 21.05 21.08 21.11 21 .14 21.17 21.21 21.24 21.27 21.30 21.33 3 6.8 21.36 21.39 21.43 21 .46 21.49 21.52 21.55 21.58 21.61 21.65 3 6.9 21.68 21.71 21.74 21 .77 21.80 21.83 21.87 21.90 21.93 21.96 4 7.0 21.99 22.02 22.05 22.09 22.12 22.15 22.18 22.21 22.24 22.27 7.1 22.31 22.34 22.37 22.40 22.43 22.46 22.49 22.53 22.56 22.59 7.2 22.62 22.65 22.68 22.71 22.75 22.78 22.81 22.84 22.87 22.90 7.3 22.93 22.97 23.00 23.03 23.06 23.09 23.12 23.15 23.18 23.22 7.4 23.25 23.28 23.31 23 .34 23.37 23.40 23.44 23.47 23.50 23.53 7.5 23.56 23.59 23.62 23.66 23.69 23.72 23.75 23.78 23.81 23.84 7.6 23.88 23.91 23.94 23.97 24.00 24.03 24.06 24.10 24.13 24.16 7.7 24.19 24.22 24.25 24.28 24.32 24.35 24.38 24.41 24.44 24.47 7.8 24.50 24.54 24.57 24.60 24.63 24.66 24.69 24.72 24.76 24.79 7.9 24.82 24.85 24.88 24.91 24.94 24.98 25.01 25.04 25.07 25.10 8.0 25.13 25.16 25.20 25 .23 25.26 25.29 25.32 25.35 25.38 25.42 3 8.1 25.45 25.48 25.51 25 .54 25.57 25.60 25.64 25.67 25.70 25.73 0 8.2 25.76 25.79 25.82 25 .86 25.89 25.92 25.95 25.98 26.01 26.04 1 8.3 26.08 26.11 26.14 26 .17 26.20 26.23 26.26 26.30 26.33 26.36 1 8.4 26.39 26.42 26.45 26.48 26.52 26.55 26.58 26.61 26.64 26.67 1 8.5 26.70 26.73 26.77 26.80 26.83 26.86 26.89 26.92 26.95 26.99 2 8.6 27.02 27.05 27.08 27 .11 27.14 27.17 27.21 27.24 27.27 27.30 2 8.7 27.33 27.36 27.39 27.43 27.46 27.49 27.52 27.55 27.58 27.61 2 8.8 27.65 27.68 27.71 27.74 27.77 27.80 27.83 27.87 27.90 27.93 2 8.9 27.96 27.99 28.02 28.05 28.09 28.12 28.15 28.18 28.21 28.24 3 9.0 28.27 28.31 28.34 28.37 28.40 28.43 28.46 28.49 28.53 28.56 9.1 28.59 28.62 28.65 28.68 28.71 28.75 28.78 28.81 28.84 28.87 9.2 28.90 28.93 28.97 29.00 29.03 29.06 29.09 29.12 29.15 29.19 9.3 ^9.22 29.25 29.28 29.31 29.34 29.37 29.41 29.44 29.47 29.50 9.4 29.53 29.56 29.59 29.63 29.66 29.69 29.72 29.75 29.78 29.81 9.5 29.85 29.88 29.91 29.94 29.97 30.00 30.03 30.07 30.10 30.13 9.6 30.16 30.19 30.22 30.25 30.28 30.32 30.35 30.38 30.41 30.44 9.7 30.47 30.50 30.54 30.57 30.60 30.63 30.66 30.69 30.72 30.76 9.8 30.79 30.82 30.85 30.88 30.91 30.94 30.98 31.01 31.04 31.07 9.9 31.10 31.13 31.16 31 .20 31.23 31.26 31.29 31.32 31.35 31.38 value log recip. TTHF 0-0175 2.2419 57.2958 7T 3.1416 0.4971 0.3183 •S^f O.OOS7 3.9408 114.5916 27T 6.2832 0.7982 0.1592 ir2 9.86960.9943 0.1013 47T 12.5664 1.0992 0.0796 V^ 1.77250.2486 0.5642 IT 1.5708 0.1961 0.6366 I-3 31.0061.4914 0.0323 ir = 3.1415926536 •a T 0.7854 1.8951 1.2732 tfr 1.46460.1657 0.6828 f 0.5236 1.7190 1.9099 \/| 0.8060 1.9063 1.2407 ¥ 4.1888 0.6221 0.2387 •fyJJL 1 .6120 0.2074 0.6204

The text on this page is estimated to be only 28.80% accurate

7U 2L2L Al t±iA I)*1 U1RULJ J T r g in n 0 123 456 7 8 9 (1 1.0 0.785 O.S01 0.817 0.833 0.849 0.866 0.882 0.899 0.916 0.933 17 .1 0.950 0.968 0.985 1.003 1.021 1.039 1.057 1.075 1.094 1.112 19 .2 1.131 1.150 1.169 1.188 1.208 1.227 1.247 1.267 1.287 1.307 20 .3 1.327 1.348 1.368 1.389 1.410 1.431 1.453 1.474 1.496 1.517 22 .4 1.539 1.561 1.584 1.606 1.629 1.651 1.674 1.697 1.720 1.744 23 .5 1.767 1.791 1.815 1.839 1.863 1.887 1.911 1.936 1.961 1.986 25 .6 2.011 2.036 2.061 2.087 2.112 2.138 2.164 2.190 2.217 2.243 27 .7 2.270 2.297 2.324 2.351 2.378 2.405 2.433 2.461 2.488 2.516 29 .8 2.545 2.573 2.602 2.630 2.659 2.688 2.717 2.746 2.776 2.806 29 .9 2.835 2.865 2.895 2.926 2.956 2.986 3.017 3.048 3.079 3.110 32 2.0 3.142 3.173 3.205 3.237 3.269 3.301 3.333 3.365 3.398 3.431 33 2.1 3.464 3.497 3.530 3.563 3.597 3.631 3.664 3.698 3.733 3.767 34 2.2 3.801 3.836 3.871 3.906 3.941 3.976 4.011 4.047 4.083 4.119 36 2.3 4.155 4.191 4.227 4.264 4.301 4.337 4.374 4.412 4.449 4.486 38 2.4 4.524 4.562 4.600 4.638 4.676 4.714 4.753 4.792 4.831 4.870 39 2.5 4.909 4.948 4.988 5.027 5.067 5.107 5.147 5.187 5.228 5.269 40 2.6 5.309 5.350 5.391 5.433 5.474 5.515 5.557 5.599 5.641 5.683 43 2.7 5.726 5.768 5.811 5.853 5.896 5.940 5.983 6.026 6.070 6.114 44 2.8 6.158 6.202 6.246 6.290 6.335 6.379 6.424 6.469 6.514 6.560 45 2.9 6.605 6.651 6.697 6.743 6.789 6.835 6.881 6.928 6.975 7.022 47 3.0 7.069 7.116 7.163 7.211 7.258 7.306 7.354 7.402 7.451 7.499 49 3.1 7.548 7.596 7.645 7.694 7.744 7.793 7.843 7.892 7.942 7.992 50 3.2 8.042 8.093 8.143 8.194 8.245 8.296 8.347 8.398 8.450 8.501 52 3.3 8.553 8.605 8.657 8.709 8.762 8.814 8.867 8.920 8.973 9.026 53 3.4 9.079 9.133 9.186 9.240 9.294 9.348 9.402 9.457 9.511 9.566 55 3.5 9.621 9.676 9.731 9.787 9.842 9.898 9.954 10.01 10.07 10.12 6 3.6 10.18 10.24 10.29 10.35 10.41 10.46 10.52 10.58 10.64 10.69 6 3.7 10.75 10.81 10.87 10.93 10.99 11.04 11.10 11.16 11.22 11.28 6 3.8 11.34 11.40 11.46 11.52 11.58 11.64 11.70 11.76 11.82 11.88 7 3.9 11.95 12.01 12.07 12.13 12.19 12.25 12.32 12.38 12.44 12.50 7 4.0 12.57 12.63 12.69 12.76 12.82 12.88 12.95 13.01 13.07 13.14 6 4.1 13.20 13.27 13.33 13.40 13.46 13.53 13.59 13.66 13.72 13.79 6 4.2 13.85 13.92 13.99 14.05 14.12 14.19 14.25 14.32 14.39 14.45 7 4.3 14.52 14.59 14.66 14.73 14.79 14.86 14.93 15.00 15.07 1544 7 4.4 15.21 15.27 15.34 15.41 15.48 15.55 15.62 15.69 15.76 15.83 7 4.5 15.90 15.98 16.05 16.12 16.19 16.26 16.33 16.40 16.47 16.55 7 4.6 16.62 16.69 16.76 16.84 16.91 16.98 17.06 17.13 17.20 17.28 7 4.7 17.35 17.42 17.50 17.57 17.65 17.72 17.80 17.87 17.95 18.02 8 4.8 18.10 18.17 18.25 18.32 18.40 18.47 18.55 18.63 18.70 18.78 8 4.9 18.86 18.93 19.01 19.09 19.17 19.24 19.32 19.40 19.48 19.56 7 5.0 19.63 19.71 19.79 19.87 19.95 20.03 20.11 20.19 20.27 20.35 ~s 5.1 20.43 20.51 20.59 20.67 20.75 20.83 20.91 20.99 21.07 21.16 8 5.2 21.24 21.32 21.40 21.48 21.57 21.65 21.73 21.81 21.90 21.98 8 5.3 22.06 22.15 22.23 22.31 22.40 22.48 22.56 22.65 22.73 22.82 8 5.4 22.90 22.99 23.07 23.16 23.24 23.33 23.41 23.50 23.59 23.67 9 5.5 23.76 23.84 23.93 24.02 24.11 24.19 24.28 24.37 24.45 24.54 9 5.6 24.63 24.72 24.81 24.89 24.98 25.07 25.16 25.25 25.34 25.43 9 5.7 25.52 25.61 25.70 25.79 25.88 25.97 26.06 26.15 26.24 26.33 9 5.8 26.42 26.51 26.60 26.69 26.79 26.88 26.97 27.06 27.15 27.25 9 5.9 27.34 27.43 27.53 27.62 27.71 27.81 27.90 27.99 28.09 28.18 9

The text on this page is estimated to be only 28.08% accurate

n BEING DIAMETE3. 71 n 0 1 2 3 4 5 6 7 8 9 (1 6.0 28.27 28.37 28.46 28.56 28.65 28.75 28.84 28.94 29.03 29.13 9 6.1 29.22 29.32 29.42 29.51 29.61 29. 71 29.80 29.90 30.00 30.09 10 6.2 30.19 30.29 30.39 30.48 30.58 30.68 30.78 30.88 30.97 31.07 10 6.3 31.17 31.27 31.37 31.47 31.57 31.67 31.77 31.87 31 .97 32.07 10 6.4 32.17 32.27 32.37 32.47 32.57 32.67 32.78 32.88 32.98 33.08 10 6.5 33.18 33.29 33.39 33.49 33.59 33. 70 33.80 33.90 34.00 34.11 10 6.6 34.21 34.32 34.42 34.52 34.63 34.73 34.84 34.94 35.05 35.15 11 6.7 35.26 35.36 35.47 35.57 35.68 35.78 35.89 36.00 36 10 36.21 il 6.8 36.32 36.42 36.53 36.64 36.75 36.85 36.96 37.07 37 18 37.28 11 6.9 37.39 37.50 37.61 37.72 37.83 37.94 38.05 38.16 38.26 38.37 11 7.0 38.48 38.59 38.70 38.82 38.93 39.04 39.15 39.26 39.37 39.48 11 7.1 39.59 39.70 39.82 39.93 40.04 40.15 40.26 40.38 40.49 40.60 12 7.2 40.72 40.83 40.94 41.06 41.17 41. 28 41.40 41.51 41 62 41.74 11 7.3 41.85 41.97 42.08 42.20 42.31 42.43 42.54 42.66 42.78 42.89 12 7.4 43.01 43.12 43.24 43.36 43.47 43. 59 43.71 43.83 43.94 44.06 12 7.5 44.18 44.30 44.41 44.53 44.65 44.77 44.89 45.01 45 13 45.25 11 7.6 45.36 45.48*45.60 45.72 45.84 45.96 46.08 46.20 46.32 46.45 12 7.7 46.57 46.69 46.81 46.93 47.05 47.17 47.29 47.42 47.54 47.66 12 7.8 47.78 47.91 48.03 48.15 48.27 48.40 48.52 48.65 48.77 48.89 13 7.9 49.02 49.14 49.27 49.39 49.51 49.64 49.76 49.89 50.01 50.14 13 8.0 50.27 50.39 50.52 50.64 50.77 50.90 51.02 51.15 51 28 51.40 13 8.1 51.53 51.66 51.78 51.91 52.04 52. 17 52.30 52.42 52 55 52.68 13 8.2 52.81 52.94 53.07 53.20 53.33 53.46 53.59 53.72 53.85 53.98 13 8.3 54.11 54.24 54.37 54.50 54.63 54. 76 54.89 55.02 55 15 55.29 13 8.4 55.42 55.55 55.68 55.81 55.95 56.08 56.21 56.35 56.48 56.61 14 8.5 56.75. 56.88 57.01 57.15 57.28 57.41 57.55 57.68 57.82 57.95 14 8.6 58.09 58.22 58.36 58.49 58.63 58.77 58.90 59.04 59.17 59.31 14 8.7 59.45 59.58 59.72 59.86 59.99 60.13 60.27 60.41 60.55 60.68 14 8.8 60.82 60.96 61. 10 61.24 61.38 61.51 61.65 61.79 61.93 62.07 14 8.9 62.21 62.35 62.49 62.63 62.77 62.91 63.05 63.19 63 33 63.48 14 9.0 63.62 63.76 63.90 64.04 64.18 64.33 64.47 64.61 64.75 64.90 14 9.1 65.04 65.18 65.33 65.47 65.61 65.76 65.90 66.04 66.19 66.33 15 9.2 66.48 66.62 66.77 66.91 67.06 67.20 67.35 67.49 67.64 67.78 15 9.3 67.93 68.08 68.22 68.37 68.51 68.66 68.81 68.96 69.10 69.25 15 9.4 69.40 69.55 69.69 69.84 69.99 70. 14 70.29 70.44 70.58 70.73 15 9.5 70.88 71.03 71.18 71.33 71.48 71.63 71.78 71.93 72.08 72.23 15 9.6 72.38 72.53 72.68 72.84 72.99 73. 14 73.29 73.44 73.59 73.75 15 9.7 73.90 74.05 74.20 74.36 74.51 74.66 74.82 74.97 75 12 75.28 15 9.8 75. 1 3 75.58 75.74 75.89 76.05 76.20 76.36 76.51 76.67 76.82 16 9.9 76.98 77.13 77.29 77.44 77.60 77. 76 77.91 78.07 78.23 78.38 16 32nds 36ths 10 .3125 .2(7) 20 .625 .(5) 30 .9375 .8(3) 1 .03125 .02(7) 11 .34375 .30(5) 21 .65625 .58(3) 31 .96875 .86(1) 2 .0625 .0(5) 12 .375 .(3) 22 .6875 .6(1) 32 .(8) 3 .09375 .08(3) 13 .40625 .36(1) 23 .71875 .63(8) 33 .91(6) 4 .125 .(1) 14 .4375 .3(8) 24 .75 .(6) 34 .9(4) 6 .15625 .13(8) 15 .46875 .41(6) 25 .78125 .69(4) 35 .97(2) 6 .1875 .1(6) 16 .5 .(4) 26 .8125 .7(2) 36 7 .21875 .19(4) 17 .53125 .47(2) 27 .84375 .75 8 .25 .(2) 18 .5625 .5 28 .875 .(7) 9 .28125 .25 19 .59375 .52(7) 29 .90625 .80(5)

The text on this page is estimated to be only 28.81% accurate

72 XXI. CONTENT OF SPHEKE 11 0 123 456 789 d 1.0 .5236 .539^ .5556 .5722 .5890 .6061 .6236 .6414 .6596 .6781 188 .1 .6969 .7161 .7356 .7555 .7757 .7963 .8173 .8386 .8603 .8823 225 .2 .9048 .9276 .9508 .9743 .9983 1.023 1.047 1.073 1.098 1.124 26 .3 1.150 1.177 1.204 1.232 1.260 1.288 1.317 1.346 1.376 1.406 31 .4 1.437 1.468 1.499 1.531 1.563 1.596 1.630 1.663 1.697 1.732 35 .5 1.767 1.803 1.839 1.875 1.912 1.950 1.988 2.026 2.065 2.105 40 .6 2.143 2.185 2.226 2.268 2.310 2.352 2.395 2.439 2.483 2.527 45 .7 2.572 2.618 2.664 2.711 2.758 2.806 2.855 2.903 2.953 3.003 51 .8 3.054 3.105 3.157 3.209 3.262 3.315 3.369 3.424 3.479 3.535 56 .9 3.591 3.648 3.706 3.764 3.823 3.882 3.942 4.003 4.064 4.126 63 2.0 4.189 4.252 4.316 4.380 4.445 4.511 4.577 4.644 4.712 4.780 ~69 2.1 4.849 4.919 4.989 5.060 5.131 5.204 5.277 5.350 5.423 5.500 75 2.2 5.575 5.652 5.729 5.806 5.883 5.964 6.044 6.123 6.206 6.288 83 2.3 6.371 6.454 6.538 6.623 6.709 6.795 6.882 6.970 7.059 7.148 90 2.4 7.238 7.329 7.421 7.513 7.606 7.700 7.795 7.890 7.986 8.083 98 2.5 8.181 8.280 8.379 8.479 8.580 8.682 8.785 8.888 8.992 9.097 106 2.6 9.203 9.309 9.417 9.525 9.634 9.744 9.855 9.966 10.08 10.19 12 2.7 10.31 10.42 10.54 10.65 10.77 10.89 11.01 11.13 11.25 11.37 12 2.8 11.49 11.62 11.74 11.87 11.99 12.12 12.25 12.38 12.51 12.64 13 2.9 12.77 12.90 13.04 13.17 13.31 13.44 13.58 13.72 13.86 14.00 14 ITo 14.14 14.28 14.42 14.57 14.71 14.86 15.00 15.15 15.30 15.43 15 3.1 15.60 15.73 15.90 16.06 16.21 16.37 16.52 16.68 16.84 17.00 16 3.2 17.16 17.32 17.48 17.64 17.81 17.97 18.14 18.31 18.48 18.65 17 3.3 18.82 18.99 19.16 19.33 19.51 19.68 19.86 20.04 20.22 ,20.40 18 3.4 20.58 20.76 20.94 21.13 21.31 21.50 21.69 21.88 22.07 22.26 19 3.5 22.45 22.64 22.84 23.03 23.23 23.43 23.62 23.82 24.02 24.23 20 3.6 24.43 24.63 24.84 25.04 25.25 25.46 25.67 25.88 26.09 26.31 21 3.7 26.52 26.74 26.95 27.17 27.39 27.61 27.83 28.06 28.28 28.50 23 3.8 28.73 28.96 29.19 29.42 29.63 29.88 30.11 30.35. 30.58 30.82 24 3.9 31.06 31.30 31.54 31.78 32.02 32.27 32.52 32.76 33.01 33.26 25 4.0 33.51 33.76 34.02 34.27 34.53 34.78 35.04 35.30 35.56 35.82 27 4.1 36.09 36.35 36.62 36.88 37.15 37.42 37.69 37.97 38.24 38.52 27 4.2 38.79 39.07 39.35 39.63 39.91 40.19 40.48 40.76 41.05 41.34 29 4.3 41.63 41.92 42.21 42.51 42.80 43.10 43.40 43.70 44.00 44.30 30 4.4 44.60 44.91 45.21 45.52 45.83 46.14 46.45 46.77 47.08 47.40 31 4.5 47.71 48.03 48.35 48.67 49.00 49.32 49.65 49.97 50.30 50.63 34 4.6 50.97 51.30 51.63 51.97 52.31 52.63 52.99 53.33 53.67 54.02 34 4.7 54.36 54.71 55.06 55.41 55.76 56.12 56.47 56.83 57.19 57.54 37 4.8 57.91 58.27 58.63 59.00 59.37 59.73 60.10 60.48 60.85 61.22 38 4.9 61.60 61.98 62.36 62.74 63.12 63.51 63.89 64.28 64.67 65.06 39 5.0 65.45 65.84 66.24 66.64 67.03 67.43 67.83 68.24 68.64 69.05 41 5.1 69.46 69.87 70.28 70.69 71.10 71.52 71.94 72.36 72.78 73.20 42 5.2 73.62 74.03 74.47 74.90 75.33 75.77 76.20 76.64 77.07 77.51 44 5.3 77.95 78.39 78.84 79.28 79.73 80.18 80.63 81.08 81.54 81.99 46 5.4 82.45 82.91 83.37 83.83 84.29 84.76 85.23 85.70 86.17 86.64 47 5.5 87.11 87.59 88.07 88.55 89.03 89.51 90.00 90.48 90.97 91.46 49 5.6 91.95 92.43 92.94 93.44 93.94 94.44 94.94 95.44 95.93 96.46 51 5.7 96.97 97.48 97.99 98.51 99.02 99.54 100.1 100.6 101.1 101.6 6 5.8 102.2 102.7 103.2 103.8 104.3 104.8 105.4 105.9 106.4 107.0 5 5.9 107.5 108.1 108.6 109.2 109.7 110.3 110.9 111.4 112.0 112.5 6

The text on this page is estimated to be only 28.63% accurate

TT q 6n n BEING DIAMETER. 73 n 0 1 2 3 456 7 8 9 d 6.0 113.1 113.7 114.2 114.8 115.4 115.9 116.5 117.1 117.7 118.3 5 6.1 118.8 119.4 120.0 120.6 121.2 121.8 122.4 123.0 123.6 124.2 6 6.2 124.8 125.4 126.0 126.6 127.2 127.8 128.4 129.1 129.7 130.3 6 6.3 130.9 131.5 132.2 132.8 133.4 134.1 134.7 135.3 136.0 136.6 7 6.4 137.3 137.9 138.5 139.2 139.8 140.5 141.2 141.8 142.5 143.1 7 6.5 143.8 144.5 145.1 145.8 146.5 147.1 147.8 148.5 149.2 149.8 7 6.6 150.5 151.2 151.9 152.6 153.3 154.0 154.7 155.4 156.1 156.8 7 6.7 157.5. 158.2 158.9 159.6 160.3 161.0 161.7 162.5 163.2 163.9 7 6.8 164.6 165.4 166.1 166.8 167.6 168.3 169.0 169.8 170.5 171.3 7 6.9 172.0 172.8 173.5 174.3 175.0 175.8 176.5 177.3 178.1 178.8 8 7.0 179.6 180.4 181.1 181.9 182.7 183.5 184.3 185.0 185.8 186.6 8 7.1 187.4 188.2 189.0 189.8 190.6 191.4 192.2 193.0 193.8 194.6 8 7.2 195.4 196.2 197.1 197.9 198.7 199.5 200.4 201.2 202.0 202.9 8 7.3 203.7 204.5 205.4 206.2 207.1 207.9 208.8 209.6 210.5 211.3 9 7.4 212.2 213.0 213.9 214.8 215.6 216.5 217.4 218.3 219.1 220.0 9 7.5 220.9 221.8 222.7 223.6 224.4 225.3 226.2 227.1 228.0 228.9 9 7.6 229.8 230.8 231.7 232.6 233.5. 234.4 235.3 236.3 237.2 238.1 9 7.7 239.0 240.0 240.9 241.8 242.8 243.7 244.7 245.6 246.6 247.5 10 7.8 248.5 249.4 250.4 251.4 252.3 253.3 254.3 255.2 256.2 257.2 10 7.9 258.2 259.1 260.1 261.1 262.1 263.1 264.1 265.1 266.1 267.1 10 8.0 268.1 269.1 270.1 271.1 272.1 273.1 274.2 275.2 276.2 277.2 11 8.1 278.3 279.3 280.3 281.4 282.4 283.4 284.5 285.5 286.6 287.6 11 8.2 288.7 289.8 290.8 291.9 292.9 294.0 295.1 296.2 297.2 298.3 11 8.3 299.4 300.5 301.6 302.6 303.7 304.8 305.9 307.0 308.1 309.2 11 8.4 310.3 311.4 312.6 313.7 314.8 315.9 317.0 318.2 319.3 320.4 12 8.5 321.6 322.7 323.8 325.0 326.1 327.3 328.4 329.6 330.7 331.9 11 8.6 333.0 334.2 335.4 336.5 337.7 338.9 340.1 341.2 342.4 343.6 12 8.7 344.8 346.0 347.2 348.4 349.6 350.8 352.0 353.2 354.4 355.6 12 8.8 356.8 358.0 359.3 360.5 361.7 362.9 364.2 365.4 366.6 367.9 12 8.9 369.1 370.4 371.6 372.9 374.1 375.4 376.6 377.9 379.2 380.4 13 9.0 381.7 383.0 384.3 385.5 386.8 388.1 389.4 390.7 392.0 393.3 13 9.1 394.6 395.9 397.2 398.5 399.8 401.1 402.4 403.7 405.1 406.4 13 9.2 407.7 409.1 410.4 411.7 413.1 414.4 415.7 417.1 418.4 419.8 14 9.3 421.2 422.5 423.9 425.2 426.6 428.0 429.4 430.7 432.1 433.5 14 9.4 434.9 436.3 437.7 439.1 440.5 441.9 443.3 444.7 446.1 447.5 14 9.5 448.9 450.3 451.8 453.2 454.6 456.0 457 5. 458.9 460.4 461.8 14 9.6 463.2 464.7 466.1 467.6 469.1 470.5 472.0 473.5 474.9 476.4 15 9.7 477.9 479.4 480.8 482.3 483.8 485.3 486.8 488.3 489.8 491.3 15 9.8 492.8 494.3 495.8 497.3 498.9 500.4 501.9 503.4 505.0 506.5 15 9.9 50S.O 509.6 511.1 512.7 514.2 515.8 517.3 518.9 520.5 522.0 16 n log n! log 2» 10 6.5598 3.0103 20 18.3861 6.0206 1 0.0000 0.3010 11 7.6012 3.3113 21 19.7083 6.3216 2 0.3010 0.6021 12 8.6803 3.6124 22 21.0508 66227 3 0.7782 0.9031 13 9.7943 3.9134 23 22.4125 6.9237 4 1.3802 1.2041 14 10.9404 4.2144 24 23.7927 7.2247 5 2.0792 1.5051 15 12.1165 4.5154 25 25.1906 7.5257 6 2.8573 1.8062 16 13.3206 4.8165 26 26.6056 7.8268 7 3.7024 2.1072 17 14.5511 5.1175 27 28.0370 8.1278 8 4.6055 2.4082 18 15.8063 5.4185 28 29.4841 8.4288 9 5.5598 2.7093 19 17.0851 5.7196 29 30.9465 8.7299

The text on this page is estimated to be only 28.69% accurate

74 XXII. HYPEEBOLIO LOGAEITHMS. n 0 123 456 7 8 9 (1 1.0 0.0000 0100 0198 0296 0392 0488 0583 0677 0770 0862 91 1.1 0953 1044 1133 1222 1310 1398 1484 1570 1655 1740 83 1.2 1823 1906 1989 2070 2151 2231 2311 2390 2469 2546 78 1.3 2624 2700 2776 2852 2927 3001 3075 3148 3221 3293 72 1.4 3365 3436 3507 3577 3646 3716 3784 3853 3920 3988 67 1.5 4055 4121 4187 4253 4318 4383 4447 4511 4574 4637 63 1.6 4700 4762 4824 4886 4947 5008 5068 5128 5188 5247 59 1.7 5306 5365 5423 5481 5539 5596 5653 5710 5766 5822 56 1.8 5878 5933 5988 6043 6098 6152 6206 6259 6313 6366 53 1.9 6419 6471 6523 6575 6627 6678 6729 6780 6831 6881 50 2.0 0.6931 6981 7031 7080 7129 7178 7227 7275 7324 7372 47 2.1 7419 7467 7514 7561 7608 7655 7701 7747 7793 7839 46 2.2 7885 7930 7975 8020 8065 8109 8154 8198 8242 8286 43 2.3 8329 8372 8416 8459 8502 8544 8587 8629 8671 8713 42 2.4 8755 8796 8838 8879 8920 8961 9002 9042 9083 9123 40 2.5 9363 9203 9243 9282 9322 9361 9400 9439 9478 9517 38 2.6 9555 9594 9632 9670 9708 9746 9783 9821 9858 9895 38 2.7 9933 9969*0006*0043 *0080*0116*0152 *0188*0225*0260 36 2.8 1.0296 0332 0367 0403 0438 0473 0508 0543 0578 0613 34 2.9 0647 0682 0716 0750 0784 0818 0852 0886 0919 0953 33 3.0 1.0986 1019 1053 1086 1119 1151 1184 1217 1249 1282 ~32 3.1 1314 1346 1378 1410 1442 1474 1506 1537 1569 1600 32 3.2 1632 1663 1694 1725 1756 1787 1817 1848 1878 1909 30 3.3 1939 1969 2000 2030 2060 2090 2119 2149 2179,2208 30 3.4 2238 2267 2296 2326 2355 2384 2413 2442 2470 2499 29 3.5 2528 2556 2585 2613 2641 2669 2698 2726 2754 2782 27 3.6 2809 2837 2865 2892 2920 2947 2975 3002 3029 3056 27 3.7 3083 3110 3137 3164 3191 3218 3244 3271 3297 3324 26 3.8 3350 3376 3403 3429 3455 3481 3507 3533 3558 3584 26 3.9 3610 3635 3661 3686 3712 3737 3762 3788 3813 3838 25 4.0 1.3863 3SSS 3913 3938 3962 3987 4012 4036 4061 4085 25 4.1 4110 4134 4159 4183 4207 4231 4255 4279 4303 4327 24 4.2 4351 4375 4398 4422 4446 4469 4493 4516 4540 4563 23 4.3 4586 4609 4633 4656 4679 4702 4725 4748 4770 4793 23 4.4 4816 4839 4861 4884 4907 4929 4951 4974 4996 5019 22 4.5 5041 5063 5085 5107 5129 5151 5173 5195 5217 5239 22 4.6 5261 5282 5304 5326 5347 5369 5390 5412 5433 5454 22 4.7 5476 5497 5518 5539 5560 5581 5602 5623 5644 5665 21 4.8 5686 5707 5728 5748 5769 5790 5810 5831 5851 5872 20 4.9 5892 5913 5933 5953 5974 5994 6014 6034 6054 6074 20 5.0 1.6094 6114 6134 6154 6174 6194 6214 6233 6253 6273 19 5.1 6292 6312 6332 6351 6371 6390 6409 6429 6448 6467 20 5.2 6487 6506 6525 6544 6563 6582 6601 6620 6639 6658 19 5.3 6677 6696 6715 6734 6752 6771 6790 6808 6827 6845 19 5.4 6864 6882 6901 6919 6938 6956 6974 6993 7011 7029 18 5.5 7047 7066 7084 7102 7120 7138 7156 7174 7192 7210 18 5.6 7228 7246 7263 7281 7299 7317 7334 7352 7370 7387 18 5.7 7405 7422 7440 7457 7475 7492 7509 7527 7544 7561 18 5.8 7579 7596 7613 7630 7647 7664 7681 7699 7716 7733 17 5.9 7750 7766 7783 7800 7817 7834 7851 7867 7884 7901 17

The text on this page is estimated to be only 28.23% accurate

XXII. EYPEKBOLIO LOGAKITHMS. 7o n 0 123 4 5 6 789 d 6.0 1.7918 7934 7951 7967 7984 8001 8017 8034 8050 8066 17 6.1 8083 8099 8116 8132 8148 8165 8181 8197 8213 8229 16 6.2 8245 8262 8278 8294 8310 8326 8342 8358 8374 8390 15 6.3 8405 8421 8437 8453 8469 8485 8500 8516 &532 8547 16 6.4 8563 8579 8594 8610 8625 8641 8656 8672 8687 8703 15 6.5 8718 8733 8749 8764 8779 8795 8810 8825 8840 8856 15 6.6 8871 8886 8901 8916 8931 8946 8961 8976 8991 9006 15 6.7 9021 9036 9051 9066 9081 9095 9110 9125 9140 9155 14 6.8 9169 9184 9199 9213 9228 9242 9257 9272 9286 9301 14 6.9 9315 9330 9344 9359 9373 9387 9402 9416 9430 9445 14 7.0 1.9459 9473 9488 9502 9516 9530 9544 9559 9573 9587 ~14~ 7.1 9601 9615 9629 9643 9657 9671 9685 9699 9713 9727 14 7.2 9741 9755 9769 9782 9796 9810 9824 9838 9851 9865 14 7.3 9879 9892 9906 9920 9933 9947 9961 9974 9988*0001 14 7.4 2.0015 0028 0042 0055 0069 0082 0096 0109 0122 0136 13 7.5 0149 0162 0176 0189 0202 0215 0229 0242 0255 0268 13 7.6 0281 0295 0308 0321 0334 0347 0360 0373 0386 0399 13 7.7 0412 0425 0438 0451 0464 0477 0490 0503 0516 0528 13 7.8 0541 0554 0567 0580 0592 0605 0618 0631 0643 0656 13 7.9 0669 0681 0694 0707 0719 0732 0744 0757 0769 0782 12 8.0 2.0794 0807 0819 0832 0844 0857 0869 0882 0894 0906 13 8.1 0919 0931 0943 0956 0968 0980 0992 1005 1017 1029 12 8.2 1041 1054 1066 1078 1090 1102 1114 1126 1138 1150 13 8.3 1163 1175 1187 1199 1211 1223 1235 1247 1258 1270 12 8.4 1282 1294 1306 1318 1330 1342 1353 1365 1377 1389 12 8.5 1401 1412 1424 1436 1448 1459 1471 1483 1494 1506 12 8.6 1518 1529 1541 1552 1564 1576 1587 1599 1610 1622 11 8.7 1633 1645 1656 1668 1679 1691 1702 1713 1725 1736 12 8.8 1748 1759 1770 1782 1793 1804 1815 1827 1838 1849 12 8.9 1861 1872 1883 1894 1905 1917 1928 1939 1950 1961 11 9.0 2.1972 1983 1994 2006 2017 2028 2039 2050 2061 2072 IT 9.1 2083 2094 2105 2116 2127 2138 2148 2159 2170 2181 11 9.2 2192 2203 2214 2225 2235 2246 2257 2268 2279 2289 11 9.3 2300 2311 2322 2332 2343 2354 2364 2375 2386 2396 11 9.4 2407 2418 2428 2439 2450 2460 2471 2481 2492 2502 11 9.5 2513 2523 2534 2544 2555 2565 2576 2586 2597 2607 11 9.6 2618 2628 2638 2649 2659 2670 2680 2690 2701 2711 10 9.7 2721 2732 2742 2752 2762 2773 2783 2793 2803 2814 10 9.8 2824 2834 2844 2854 2865 2875 2885 2895 2905 2915 10 9.9 2925 2935 2946 2956 2966 2976 2986 2996 3006 3016 10 n i 1st 2d 3d 4th m loge 10» loge 10-" 1 2.3026 0.2303 0.0230 0.0023 0.0002 0.4343 2.3026 3.6974 2 4.6052 0.4605 0.0461 0.0046 0.0005 0.8686 4.6052 5.3948 3 6.9078 0.6908 0.0691 0.0069 0.0007 1.3029 6.9078 7.0922 4 9.2103 0.9210 0.0921 0.0092 0.0009 1.7372 9.2103 10.7897 5 11.5129 1.1513 0.1151 0.0115 0.0012 2.1715 11.5129 12.4871 6 13.8155 1.3816 0.1382 0.0138 0.0014 2.6058 13.8155 14.1845 7 16.1181 1.6118 0.1612 0.0161 0.0016 3.0401 16.1181 17.8819 8 18.4207 1.8421 0.1842 0.0184 0.0018 3.4744 18.4207 19.5793 9 20.7233 2.0723 0.2072 0.0207 0.0021 3.9087 20.7233 21.2767

The text on this page is estimated to be only 28.70% accurate

76 XXIII. AMOUNT AT THE END OP n YEABS. (•> , r \n 1 + n 3 3£ 4 4J 5 6 7 8 9 10 0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1 1.030 1.035 1.040 1.045 1.050 1.060 1.070 1.080 1.090 1.100 2 1.061 1.071 1.082 1.092 1.103 1.124 1.145 1.166 1.188 1.210 8 1.093 1.109 1.12^ 1.141 1.158 1.191 1.225 1.260 1.295 1.331 4 1.126 1.148 1.170 1.193 1.216 1.262 1.311 1.360 1.412 1.464 5 1.159 1.188 1.217 1.246 1.276 1.338 1.403 1.469 1.539 1.611 6 1.194 1.229 1.265 1.302 1.340 1.419 1.501 1.587 1.677 1.772 7 1.230 1.272 1.316 1.361 1.407 1.504 1.606 1.714 1.828 1.949 8 1.267 1.317 1.369 1.422 1.477 1.594 1.718 1.851 1.993 2.144 9 1.30^ 1.363 1.423 1.486 1.551 1.689 1.838 1.999 2.172 2.358 10 1.344 1.411 1.480 1.553 1.629 1.791 1.967 2.159 2.367 2.594 11 1.384 1.460 1.539 1.623 1.710 1.898 2.105 2.332 2.580 2.853 12 1.426 1.511 1.601 1.696 1.796 2.012 2.252 2.518 2.813 3.138 13 1.469 1.564 1.665 1.772 1.886 2.133 2.410 2.720 3.066 3.452 14 1.513 1.619 1.732 1.852 1.980 2.261 2.579 2.937 3.342 3.797 15 1.558 1.675 1.801 1.935 2.079 2.397 2.759 3.172 3.642 4.177 16 1.605 1.734 1.873 2.022 2.183 2.540 2.952 3.426 3.970 4.595 17 1.653 1.795 1-948 2.113 2.292 2.693 3.159 3.700 4.328 5.054 18 1.702 1.857 2.026 2.208 2.407 2.854 3.380 3.996 4.717 5.560 19 1.754 1.923 2.107 2.308 2.527 3.026 3.617 4.316 5.142 6.116 20 1.806 1.990 2.191 2.412 2.653 3.207 3.870 4.661 5.604 6.727 21 1.860 2.059 2.279 2.520 2.786 3.400 4.141 5.034 6.109 7.400 22 1.916 2.132 2.370 2.634 2.925 3.604 4.430 5.437 6.659 8.140 23 1.974 2.206 2.465 2.752 3.072 3.820 4.741 5.871 7.258 8.954 24 2.033 2.283 2.563 2.876 3.225 4.049 5.072 6.341 7.911 9.850 25 2.094 2.363 2.666 3.005 3.386 4.292 5.427 6.848 8.623 10.83 26 2.157 2.446 2.772 3.141 3.556 4.549 5.807 7.396 9.399 11.92 27 2.221 2.532 2.883 3.282 3.733 4.822 6.214 -7.988 10.25 13.11 28 2.288 2.620 2.999 3.430 3.920 5.112 6.649 8.627 11.17 14.42 29 2.357 2.712 3.119 3.584 4.116 5.418 7.114 9.317 12.17 15.86 30 2.427 2.807 3.243 3.745 4.322 5.743 7.612 10.06 13.27 17.45 31 2.500 2.905 3.373 3.914 4.538 6.088 8.145 10.87 14.46 19.19 32 2.575 3.007 3.508 4-.090 4.765 6.453 8.715 11.74 15.76 21.11 33 2.652 3.112 3.648 4.274 5.003 6.841 9.325 12.68 17.18 23.23 34 2.732 3.221 3.794 4.466 5.253 7.251 9.978 13.69 18.73 25.55 35 2.814 3.334 3.946 4.667 5.516 7.686 10.68 14.79 20.41 28.10 36 2.898 3.450 4.104 4.877 5.792 8.147 11.42 15.97 22.25 30.91 37 2.985 3.571 4.268 5.097 6.081 8.636 12.22 17.25 24.25 34.00 38 3.075 3.696 4.439 5.326 6.385 9.154 13.08 18.63 26.44 37.40 39 3.167 3.825 4.616 5.566 6.705 9.704 13.99 20.12 28.82 41.14 40 3.262 3.959 4.801 5.816 7.040 10.29 14.97 21.72 31.41 45.26 41 3.360 4.098 4.993 6.078 7.392 10.90 16.02 23.46 34.24 49.79 42 3.461 4.241 5.193 6.352 7.762 11.56 17.14 25.34 37.32 54.76 43 3.565 4.390 5.400 6.637 S.15Q 12.25 18.34 27.37 40.68 60.24 44 3.671 4.543 5.617 6.936 8.557 12.99 19.63 29.56 44.34 66.26 45 3.782 4.702 5.841 7.248 8.985 13.76 21.00 31.92 48.33 72.89 46 3.895 4.867 6.075 7.574 9.434 14.59 22.47 34.47 52.68 80.18 47 4.012 5.037 6.318 7.915 9.906 15.47 24.05 37.23 57.42 88.20 48 4.132 5.214 6.571 8.271 10.40 16.39 25.73 40.21 62.59 97.02 49 4.256 5.396 6.833 8.644 10.92 17.38 27.53 43.43 68.22 106.7

The text on this page is estimated to be only 28.93% accurate

1000 XXIV. PRESENT VALUE OF 1000 ..r_\n DUE n YEARS HENCE. 77 n 3 3* 4 4^ 5 6 7 8 9 10 0 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1 970.9 966.2 961.5 956.9 952.4 943.4 934.6 925.9 917.4 909.1 2 942.6 933.5 924.6 915.7 907.0 890.0 873.4 857.3 841.7 826.4 3 915.1 901.9 889.0 876.3 863.8 839.6 816.3 793.8 772.2 751.3 4 888.5 871.4 854.8 838.6 822.7 792.1 762.9 735.0 708.4 683.0 5 862.6 842.0 821.9 802.5 783.5 747.3 713.0 680.6 649.9 620.9 6 837.5 813.5 790.3 767.9 746.2 705.0 666.3 630.2 596.3 564.5 7 813.1 786.0 759.9 734.8 710.7 665.1 622.7 583.5 547.0 513.2 8 789.4 759.4 730.7 703.2 676.8 627.4 582.0 540.3 501.9 466.5 9 766.4 733.7 702.6 672.9 644.6 591.9 543.9 500.2 460.4 424.1 10 744.1 708.9 675.6 643.9 613.9 558.4 508.3 463.2 422.4 385.5 11 722.4 684.9 649.6 616.2 584.7 526.8 475.1 428.9 387.5 350.5. 12 701.4 661.8 624.6 589.7 556.8 497.0 444.0 397.1 355.5 318.6 13 681. 0 639.4 600.6 564.3 530.3 468.8 415.0 367.7 326.2 289.7 14 661.1 617.8 57.7.5 540.0 505.1 442.3 387.8 340.5 299.2 263.3 15 641.9 596.9 555.3 516.7 481.0 417.3 362.4 315.2 274.5 239.4 16 623.2 576.7 533.9 494.5 458.1 393.6 338.7 291.9 251.9 217.6 17 605.0 557.2 513.4 473.2 436.3 371.4 316.6 270.3 231.1 197.8 18 587.4 538.4 493.6 452.8 415.5 350.3 295.9 250.2 212.0 179.9 19 570.3 520.2 474.6 433.3 395.7 330.5 276.5 231.7 194.5 163.5 20 553.7 502.6 456.4 414.6 376.9 311.8 258.4 214.5 178.4 148.6 21 537.5 485.6 438.8 396.8 358.9 294.2 241.5 198.7 163.7 135.1 22 521.9 469.2 422.0 379.7 341.8 277.5 225.7 183.9 150.2 122.8 23 506.7 453.3 405.7 363.4 325.6 261.8 210.9 170.3 137.8 111.7 24 491.9 438.0 390.1 347.7 310.1 247.0 197.1 157.7 126.4 101.5 25 477.6 423.1 375.1 332.7 295.3 233.0 184.2 146.0 116.0 92.30 26 463.7 408.8 360.7 318.4 281.2 219.8 172.2 135.2 106.4 83.91 27 450.2 395.0 346.8 304.7 267.8 207.4 160.9 125.2 97.61 76.28 28 437.1 381.7 333.5 291.6 255.1 195.6 150.4 115.9 89.55 69.34 29 424.3 368.7 320.7 279.0 242.9 184.6 140.6 107.3 82.15 63.04 30 412.0 356.3 308.3 267.0 231.4 174.1 131.4 99.38 75.37 57.31 31 400.0 344.2 296.5 255.5 220.4 164.3 122.8 92.02 69.15. 52.10 32 388.3 332.6 285.1 244.5 209.9 155.0 114.7 85.20 63.44 47.36 33 377.0 321.3 274.1 234.0 199.9 146.2 107.2 78.89 58.20 43.06 34 366.0 310.5 263.6 223.9 190.4 137.9 100.2 73.05 53.39 39.14 35 355.4 300.0 253.4 214.3 181.3 130.1 93.66 67.63 48.99 35.58 36 345.0 289.8 243.7 205.0 172.7 122.7 87.54 62.62 44.94 32.35 37 335.0 280.0 234.3 196.2 164.4 115.8 81.81 57.99 41.23 29.41 38 325.2 270.6 225.3 187.8 156.6 109.2 76.46 53.69 37.83 26.73 39 315.8 261.4 216.6 179.7 149.1 103.1 71.46 49.71 34.70 24.30 40 306.6 252.6 208.3 171.9 142.0 97.22 66.78 46.03 31.84 22.09 41 297.6 244.0 200.3 164.5 135.3 91.72 62.41 42.62 29.21 20.09 42 289.0 235.8 192.6 157.4 128.8 86.53 58.33 39.46 26.80 18.26 43 280.5 227.8 185.2 150.7 122.7 81.63 54.51 36.54 24.58 16.60 44 272.4 220.1 178.0 144.2 116.9 77.01 50.9$ 33.83 22.55 15.09 45 264.4 212.7 171.2 138.0 111.3 72.65 47.61 31.33 20.69 13.72 46 256.7 205.5 164.6 132.0 106.0 68.54 44.50 29.01 18.98 12.47 47 249.3 198.5 158.3 126.3 100.9 64.66 41.59 26.86 17.42 11.34 48 242.0 191.8 152.2 120.9 96.14 61.00 38.87 24.87 15.98 10.31 49 235.0 1S5.3 146.3 115.7 91.56 57.55 36.32 23.03 14.66 9.370

The text on this page is estimated to be only 28.86% accurate

78 XXV. AMOUNT OF AN ANNUITY PAID AT THE END OP EACH YEAK, r 100 n 3 3£ 4 4J 5 6 7 8 9 10 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1 2 3 1.000 1.000 1.000 2.030 2.035 2.040 3.091 3.106 3.122 1.000 1.000 1.000 2.045 2.050 2.060 3.137 3.153 3.184 1.000 1.000 1.000 2.070 2.080 2.090 3.215 3.246 3.278 1.000 2.100 3.310 4 5 6 4.184 4.215 4.246 5.309 5.362 5.416 6.468 6.550 6.633 4.278 4.310 4.375 5.471 5.526 5.637 6.717 6.802 6.975 4.440 4.506 4.573 5.751 5.867 5.985 7.153 7.336 7.523 4.641 6.105 7.716 7 8 9 7.662 7.779 7.898 8.892 9.052 9.214 10.16 10.37 10.58 8.019 8.142 8.394 9.380 9.549 9.897 10.80 11.03 11.49 8.654 8.923 9.200 10.26 10.64 11.03 11.98 12.49 13.02 9.487 11.44 13.58 10 11.46 11.73 12.01 12.29 12.58 13.18 13.82 14.49 15.19 15.94 11 12 13 12.81 13.14 13.49 14.19 14.60 15.03 15.62 16.11 16.63 13.84 14.21 14.97 15.46 15.92 16.87 17.16 17.71 18.88 15.78 16.65 17.56 17.89 18.98 20.14 20.14 21.50 22.95 18.53 21.38 24.52 14 15 16 17.09 17.68 18.29 18.60 19.30 20.02 20.16 20.97 21.82 18.93 19.60 21.02 20.78 21.58 23.28 22.72 23.66 25.67 22.55 24.21 26.02 25.13 27.15 29.36 27.89 30.32 33.00 27.97 31.77 35.95 17 18 19 21.76 22.71 23.70 23.41 24.50 25 .65 25.12 26.36 27.67 24.74 25.84 28.21 26.86 28.13 30.91 29.06 30.54 33.76 30.84 33.75 36.97 34.00 37.45 41.30 37.38 41.45 46.02 40.54 45.60 51.16 20 26.87 28.28 29.78 31.37 33.07 36.79 41.00 45.76 51.16 57.27 21 22 23 28.68 30.27 31.97 30.54 32.33 34.25 32.45 34.46 36.62 33.78 35.72 39.99 36.30 38.51 43.39 38.94 41.43 47.00 44.87 50.42 5.76 49.01 55.46 62.87 53.44 60.89 69.53 64.00 71.40 79.54 24 25 26 34.43 36.67 39.08 36.46 38.95 41.65 38.55 41.31 44.31 41.69 44.50 50.82 44.57 47.73 54.86 47.57 51.11 59.16 58.18 66.76 76.79 63.25 73.11 84.70 68.68 79.95 93.32 88.50 98.35 109.2 27 28 29 40.71 43.76 47.08 42.93 46.29 49.97 45.22 48.91 52.97 50.71 54.67 63.71 53.99 58.40 68.53 57.42 62.32 73.64 74.48 87.35 102.7 80.70 95.34 113.0 87.35 104.0 124.1 121.1 134.2 148.6 30 47.58 51.62 56.08 , 61.01 66.44 79.06 94.46 113.3 136.3 164.5 31 32 33 50.00 54.43 59.33 52.50 57.33 62.70 55.08 60.34 66.21 64.75 70.76 84.80 68.67 75.30 90.89 72.76 80.06 97.34 102.1 123.3 149.6 110.2 134.2 164.0 118.9 146.0 179.8 181.9 201.1 222.3 34 35 36 57.73 63.45 69.86 60.46 66.67 73.65 63.28 70.01 77.60 77.03 85.07 104.2 81.50 90.32 111.4 86.16 95.84 119.1 128.3 158.6 197.0 138.2 172.3 215.7 148.9 187.1 236.1 245.5 271.0 299.1 37 38 39 66.17 73.46 81.70 69.16 77.03 85.97 72.23 80.72 90,41 91.04 101.6 127.3 96.14 107.7 135.9 101.5 114.1 145.1 160.3 203.1 258.4 172.6 220.3 282.6 185.6 238.9 309.1 330.0 364.0 401.4 40 75.40 84.55 95.03 107.0 120.8 154.8 199.6 259.1 337.9 442.6 41 42 43 78.66 88.51 99.83 82.02 92.61 104.8 85.48 96.85 110.0 112.8 127.8 165.0 118.9 135.2 176.0 125.3 143.0 187.5 214.6 280.8 369.3 230.6 304.2 403.5 247.8 329.6 440.8 487.9 537.6 592.4 44 45 46 89.05 101.2 115.4 92.72 105.8 121.0 96.50 110.5 126.9 131.9 151.1 199.8 138.8 159.7 212.7 146.1 168.7 226.5 266.1 356.9 481.5 285.7 386.5 525.9 306.8 418.4 574.2 652.6 718.9 791.8 47 48 49 100.4 115.4 132.9 104.4 120.4 139.3 108.5 125.6 145.8 153.7 178.1 241.1 161.6 188.0 256.6 169.9 198.4 273.0 329.2 452.9 626.9 353.3 490.1 684.3 379.0 530.3 746.9 872.0 960.2 1057

The text on this page is estimated to be only 28.90% accurate

— 100 V — 100 XXVI, PRESENT, VALUE OF AN ANNUITY PAID AT THE END OF EACH YEAE, 79 n 3 3| 4 4£ 5 6 7 8 9 10 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1 .9709 .9662 .9615 .9569 .9524 .9434 .9346 .9259 .9174 .9091 2 1.913 1.900 1.886 1.873 1.859 1.833 1.808 1.783 1.759 1.736 8 2.829 2.802 2.775 2.749 2.723 2.673 2.624 2.577 2.531 2.487 4 3.717 3.673 3.630 3.588 3.546 3.465 3.387 3.312 3.240 3.170 5 4.580 4.515 4.452 4.390 4.329 4.212 4.100 3.993 3.890 3.791 6 5.417 5.329 5.242 5.158 5.076 4.917 4.767 4.623 4.486 4.355 7 6.230 6.115 6.002 5.893 5.786 5.582 5.389 5.206 5.033 4.868 8 7.020 6.874 6.733 6.596 6.463 6.210 5.971 5.747 5.535 5.335 9 7.786 7.608 7.435 7.269 7.108 6.802 6.515 6.247 5.995 5.759 10 8.530 8.317 8.111 7.913 7.722 7.360 7.024 6.710 6.418 6.145 11 9.253 9.002 8.760 8.529 8.306 7.887 7.499 7.139 6.805 6.495 12 9.954 9.663 9.385 9.119 8.863 8.384 7.943 7.536 7.161 6.814 13 10.63 10.30,9.986 9.683 9.394 8.853 8.358 7.904 7.487 7.103 14 11.30 10.92 10.56 10.22 9.899 9.295 8.745 8.244 7.786 7.367 15 11.94 11.52 11.12 10.74 10.38 9.712 9.108 8.559 8.061 7.606 16 12.56 12.09 11.65 11.23 10.84 10.11 9.447 8.851 8.313 7.824 17 13.17 12.65 12.17 11.71 11.27 10.48 9.763 9.122 8.544 8.022 18 13.75 13.19 12.66 12.16 11.69 10.83 10.06 9.372 8.756 8.201 19 14.32 13.71 13.13 12.59 12.09 11.16 10.34 9.604 8.950 8.365 20 14.88 14.21 13.59 13.01 12.46 11.47 10.59 9.818 9.129 8.514 21 15.42 14.70 14.03 13.40 12.82 11.76 10.84 10.02 9.292 8.649 22 15.94 15.17 14.45 13.78 13.16 12.04 11.06 10.20 9.442 8.772 28 16.44 15.62 14.86 14.15 13.49 12.30 11.27 10.37 9.580 8.883 24 16.94 16.06 15.25 14.50 13.80 12.55 11.47 10.53 9.707 8.985 25 17.41 16.48 15.62 14.83 14.09 12.78 11.65 10.67 9.823 9.077 26 17.88 16.89 15.98 15.15 14.38 13.00 11.83 10.81 9.929 9.161 27 18.33 17.29 16.33 15.45 14.64 13.21 11.99 10.94 10.03 9.237 28 18.76 17.67 16.66 15.74 14.90 13.41 12.14 11.05 10.12 9.307 29 19.19 18.04 16.98 16.02 15.14 13.59 12.28 11.16 10.20 9.370 30 19.60 18.39 17.29 16.29 15.37 13.76 12.41 11.26 10.27 9.427 31 20.00 18.74 17.59 16.54 15.59 13.93 12.53 11.35 10.34 9.479 32 20.39 19.07 17.87 16.79 15.80 14.08 12.65 11.43 10.41 9.526 33 20.77 19.39 18.15 17.02 16.00 14.23 12.75 11.51 10.46 9.569 34 21.13 19.70 18.41 17.25 16.19 14.37 12.85 11.59 10.52 9.609 35 21.49 20.00 18.66 17.46 16.37 14.50 12.95 11.65 10.57 9.644 36 21.83 20.29 18.91 17.67 16.55 14.62 13.04 11.72 10.61 9.677 37 22.17 20.57 19.14 17.86 16.71 14.74 13.12 11.78 10.65 9.706 38 22.49 20.84 19.37 18.05 16.87 14.85 13.19 11.83 10.69 9.733 39 22.81 21.10 19.58 18.23 17.02 14.95 13.26 11.88 10.73 9.757 40 23.11 21.36 19.79 18.40 17.16 15.05 13.33 11.92 10.76 9.779 41 23.41 21.60 19.99 18.57 17.29 15.14 13.39 11.97 10.79 9.799 42 23.70 21.83 20.19 18.72 17.42 15.22 13.45 12.01 10.81 9.817 43 23.98 22.06 20.37 18.87 17.55 15.31 13.51 12.04 10.84 9.834 44 24.25 22.28 20.55 19.02 17.66 15.38 13.56 12.08 10.86 9.849 45 24.52 22.50 20.72 19.16 17.77 15.46 13.61 12.11 10.88 9.863 46 24.78 22.70 20.88 19.29 17.88 15.52 13.65 12.14 10.90 9.875 47 25.02 22.90 21.04 19.41 17.98 15.59 13.69 12.16 10.92 9.887 48 25.27 23.09 21.20 19.54 18.08 15.65 13.73 12.19 10.93 9.897 49 25.50 23.28 21.34 19.65 18.17 15.71 13.77 12.21 10.95 9.906

The text on this page is estimated to be only 28.86% accurate

80 XXVII. AMOUNT OF AN ANNUITY WHEN PAID AT THE BEGINNING OP EACH YEAE. 1 + 100 r 100 11 3 3| 4 4] 5 6 7 8 9 10 0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1 1.030 1.035 1.040 1.045 1.050 1.060 1.070 1.080 1.090 1.100 2 2.091 2.106 2.122 2.137 2.153 2.184 2.215 2.246 2.278 2.310 8 3.184 3.215 3.246 3.278 3.310 3.375 3.440 3.506 3.573 3.641 4 4.309 4.362 4.416 4.471 4.526 4.637 4.751 4.867 4.985 5.105 5 5.468 5.550 5.633 5-717 5.802 5.975 6.153 6.336 6.523 6.716 6 6.662 6.779 6.898 7019 7.142 7.394 7.654 7.923 8.200 8.487 7 7.892 8-052 8.214 8.380 8.549 8.897 9.260 9.637 10.03 10.44 8 9.159 9.368 9.583 9.802 10.03 10.49 10.98 11.49 12.02 12.58 9 10.46 10.73 11.01 11.29 11-58 12.18 12.82 13.49 14.19 14.94 10 11.81 12.14 12.49 12.84 13.21 13.97 14.78 15.65 16.56 17.53 11 13.19 13.60 14.03 14.46 14.92 15.87 16.89 17.98 19.14 20.38 12 14.62 15.11 15.63 16.16 16.71 17.88 19.14 20.50 21.95 23.52 13 16.09 16.68 17-29 17.93 18.60 20.02 21.55 23.21 25.02 26.97 14 17.60 18.30 19.02 19.78 20.58 22.28 24.13 26.15 28.36 30.77 15 19.16 19.97 20.82 21.72 22.66 24.67 26.89 29.32 32.00 34.95 16 20.76 21.71 22.70 23.74 24.84 27,21 29.84 32.75 35.97 39.54 17 22.41 23.50 24.65 25.86 27.13 29.91 33.00 36.45 40.30 44.60 18 24.12 25.36 26.67 28.06 29.54 32.76 36.38 40.45 45.02 50.16 19 25.87 27.28 28.78 30.37 32.07 35.79 40.00 44.76 50.16 56.27 20 27.68 29.27 30.97 32.78 34.72 38.99 43.87 49.42 55.76 63.00 21 29.54 31.33 33.25 35.30 37.51 42.39 48.01 54.46 61.87 70.40 22 31.45 33.46 35.62 37.94 40.43 46.00 52.44 59.89 68.53 78.54 23 33.43 35.67 38.08 40.69 43.50 49.82 57.18 65.76 75.79 87.50 24 35.46 37.95 40.65 43.57 46.73 53.86 62.25 72.11 83.70 97.35 25 37.55 40.31 43.31 46.57 50.11 58.16 67.68 78.95 92.32 108.2 26 39.71 42.76 46.08 49.71 53.67 62.71 73.48 86.35 101.7 120.1 27 41.93 45.29 48.97 52.99 57.40 67.53 79.70 94.34 112.0 133.2 28 44.22 47.91 51.97 56.42 61.32 72.64 86.35 103.0 123.1 147.6 29 46.58 50.62 55.08 60.01 65.44 78.06 93.46 112.3 135.3 163-i 30 49.00 53.43 58.33 -63.75 69.76 83.80 101.1 122.3 148.6 180.9 31 51.50 56.33 61.70 67.67 74.30 89.89 109.2 133.2 163.0 200.1 32 54.08 59.34 65.21 71.76 79.06 96.34 117.9 145.0 178.8 221.3 33 56.73 62.45 68.86 76.03 84.07 103.2 127.3 157.6 196.0 244.5 34 59.46 65.67 72.65 80.50 89.32 110.4 137.2 171.3 214.7 270.0 35 62.28 69.01 76.60 85.16 94.84 118.1 147.9 186.1 235.1 298.1 36 65.17 72.46 80.70 90.04 100.6 126.3 159.3 202.1 257.4 329.0 37 68.16 76.03 84.97 95.14 106.7 134.9 171.6 219.3 281.6 363.0 38 71.23 79.72 89.41 100.5 113.1 144.1 184.6 237.9 308.1 400.4 39 74.40 83.55 94.03 106.0 119.8 153.8 198.6 258.1 336.9 441.6 40 77.66 87.51 98.83 111.8 126.8 164.0 213.6 279.8 368.3 486.9 41 81.02 91.61 103.8 117.9 134.2 175.0 229.6 303.2 402.5 536.6 42 84.48 95.85 109.0 124.3 142.0 186.5 246.8 328.6 439.8 591.4 43 88.05 100.2 114.4 130.9 150.1 198.8 265.1 355.9 480.5 651.6 44 91.72 104.8 120.0 137.8 158.7 211.7 284.7 385.5 524.9 717.9 45 95.50 109.5 125.9 145.1 167.7 225.5 305.8 417.4 573.2 790.8 46 99.40 114.4 131.9 152.7 177.1 240.1 328.2 451.9 625.9 871.0 47 103. \ 119.4 138.3 160.6 187.0 255.6 352.3 489.1 683.3 959.2 48 107.5 124.6 144.8 168.9 197.4 272.0 37S.O 529.3 745.9 1056 49 111.8 130.0 151.7 177.5 208.3 289.3 405.5 572.8 814.1 1163

The text on this page is estimated to be only 29.06% accurate

XXVIII. SUM TO BE PAID AT THE END OF EACH OF n YEARS TO EXTINGUISH A DEBT OF 1000. 81 n 3 3} 4 4| 5 6 7 8 9 10 1 1030 1035 1040 1045 1050 1060 1070 1080 1090 1100 2 522.6 526.4 530.2 534.0 537.8 545.4 553.1 560.8 568.5 576.2 8 353.5 356.9 360.3 363.8 367.2 374.1 381.1 388.0 395.1 402.1 4 269.0 272.3 275.5 278.7 282.0 288.6 295.2 301.9 308.7 315.5 5 218.4 221.5 224.6 227.8 231.0 237.4 243.9 250.5 257.1 263.8 6 184.6 187.7 190.8 193.9 197.0 203.4 209.8 216.3 222.9 229.6 7 160.5 163.5 166.6 169.7 172.8 179.1 185.6 192.1 198.7 205.4 8 142.5 145.5 14S.5 151.6 154.7 161.0 167.5 174.0 180.7 187.4 9 128.4 131.4 134.5 137.6 140.7 147.0 153.5 160.1 166.8 173.6 10 117.2 120.2 123.3 126.4 129.5 135.9 142.4 149.0 155.8 162.7 11 108.1 111.1 114.1 117.2 120.4 126.8 133.4 140.1 146.9 154.0 12 100.5 103.5 106.6 109.7 112.8 119.3 125.9 132.7 139.7 146.8 13 94.03 97.06 100.1 103.3 106.5 113.0 119.7 126.5 133.6 140.8 14 88.53 91.57 94.67 97.82 101.0 107.6 114.3 121.3 128.4 135.7 15 83.77 86.83*89.94 93.11 96.34 103.0 109.8 116.8 124.1 131.5 16 79.61 82.68 85.82 89.02 92.27 98.95 105.9 113.0 120.3 127.8 17 75.95 79.04 82.20 85.42 88.70 95.44 102.4 109.6 117.0 124.7 18 72.71 75.82 78.99 82.24 85.55 92.36 99.41 106.7 114.2 121.9 19 69.81 72.94 76.14 79.41 82.75 89.62 96.75 104.1 111.7 119.5 20 67.22 70.36 73.58 76.88 80.24 87.18 94.39 101.9 109.5 117.5 21 64.87 68.04 71.28 74.60 78.00 85.00 92.29 99.83 107.6 115.6 22 62.75 65.93 69.20 72.55 75.97 83.05 90.41 98.03 105.9 114.0 23 60.81 64.02 67.31 70.68 74.14 81.28 88.71 96.42 104.4 112.6 24 59.05 62.27 65.59 68.99 72.47 79.68 87.19 94.98 103.0 111.3 25 57.43 60.67 64.01 67.44 70.95 78.23 85.81 93.68 101.8 110.2 26 55.94 59.21 62.57 66.02 69.56 76.90 84.56 92.51 100.7 109.2 27 54.56 57.85 61.24 64.72 68.29 75.70 83.43 91.45 99.73 108.3 28 53.29 56.60 60.01 63.52 67.12 74.59 82.39 90.49 98.85 107.5 29 52.11 55.45 58.88 62.41 66.05 73.58 81.45 89.62 98.06 106.7 30 51.02 54.37 57.83 61.39 65.05 72.65 80.59 88.83 97.34 106.1 31 50.00 53.37 56.86 60.44 64.13 71.79 79.80 88.11 96.69 105.5 32 49.05 52.44 55.95 59.56 63.28 71.00 79.07 87.45 96.10 105.0 33 48.16 51.57 55.10 58.74 62.49 70.27 78.41 86.85 95.56 104.5 34 47.32 50.76 54.31 57.98 61.76 69.60 77.80 86.30 95.08 104.1 35 46.54 50.00 53.58 57.27 61.07 68.97 77.23 85.80 94.64 103.7 36 45.80 49.28 52.89 56.61 60.43 68.39 76.72 85.34 94.24 103.3 37 45.11 48.61 52.24 55.98 59.84 67.86 76.24 84.92 93.87 ! 103.0 38 44.46 47.98 51.63 55.40 59.28 67.36 75.80 84.54 93.54 102.7 39 43.84 47.39 51.06 54.86 58.76 66.89 75.39 84.19 93.24 102.5 40 43.26 46.83 50.52 54.34 58.28 66.46 75.01 83.86 92.96 102.3 41 42.71 46.30 50.02 53.86 57.82 66.06 74.66 83.56 92.71 102.0 42 42.19 45.80 49.54 53.41 57.39 65.68 74.34 83.29 92.48 101.9 43 41.70 45.33 49.09 52.98 56.99 65.33 74.04 83.03 92.27 101.7 44 41.23 44.88 48.66 52.58 56.62 65.01 73.76 82.80 92.08 101.5 45 40.79 44.45 48.26 52.20 56.26 64.70 73.50 82.59 91.90 101.4 46 40.36 44.05 47.88 51.84 55.93 64.41 73.26 82.39 91.74 101.3 47 39.96 43.67 47.52 51.51 55.61 64.15 73.04 82.21 91.60 101.1 48 39.58 43.31 47.18 51.19 55.32 63.90 72.83 82.04 91.46 101.0 49 39.21 42.96 46.86 50.89 55.04 63.66 72.64 81.89 91.34 100.9

The text on this page is estimated to be only 26.84% accurate

82 XXIX. LEAST DIVISOKS. 0 1 2 3 4 n 1379 1379 1379 1379 1379 ~0 3 3 — 3 — O O 7 1 „ 3—37 11 3 — 3 7 3 11 3 — 2 3 7 3 11 — 3 7 3 13 3 — 3 — — 3 13 3 3 73—3 11 3 17 3 7 — 3 — 3 11 7 4 — 13 11 — 373 — — 3 7 3 19 — 3 — 3 — 5 3 — 3 — 7 3 11 3 17 23 3 13 3 7 — 3 — 3 6 — 3 — 3 13 3 7 3 17 — 3 7 3 11 7 — 19 7 — 3 23 3 — 73—3 17 — 11 — 3—37 8 3 11 3 — — 3 19 3 373 — 29 3 7 3 9 17 3 — 3 — 11 7 — 3 13 3 — 73—3 — 23 — 13 10 7 17 19 — 3 — 3 — - 3 13 3 17 — 373 — 11 3 — 3 — 11 3 — 3 19 — 7 — 3 11 3 17 7 3 31 3 12 — 3 17 3 7 23 3 — 3 — — 3 — 3 17 11 29 13 7 3 13 3 — — 3 — 3 11 31 7 13 3 17 3 19 14 3 23 3 — 17 3 13 3 7 3 — 3 — 11 3 — 3 15 19 3 11 3 — 17 37 7 3 — 3 11 — 3 29 3 23 — 7 — 16 — 7 3 — 3 — — 3 — 3 7 23 — 11 3 31 3 17 17 3 13 3 — 29 3 17 3 11 7 3 — 3 37 — 3—3 18 — 3 13 3 — 7 23 17 3 — 3 31 — 3 11 3 7 19 — 43 19 — 11 - 23 3 — 3 19 17 3 41 3 13 7 3 29 3 — 20 3—37 — 3—3 43 7 3 19 3 — 13 3 23 3 21 11 3 7 3 29 13 3 11 3 — — 3—3 19 7 22 31 47 3—37 — 3 17 3 23 7 3 — 3 13 23 373 — -373 11 23 13 17 3 — 3 — —.3—3 24 7 3 29 3 — 19 — 41 3—37 11 3 — 3 — 7 — 31 25 41 — 23 13 3 7 3 11 — 373 — 17 43 — 3 — 3 — 26 3 19 3 — 73—3 — 43 37 11 3—37 19 3 — 3 27 37 3 — 3 11 _ 373 — — 373 — 13 41 — 28 7 53 3 29 3 — 7 3 11 3 19 17 3—37 29 3 — 3 — 41 3 — 3 23 37 — 29 373 — 17 3 7 3 30 — 3 31 3 — 23 7 — 3 — 3 13 73—3 — 17 11 — 31 7 29 13 — 3 11 3 — — 3 53 3 31 13 — 43 3 7 3 47 32 3 — 3 — 13 3—3 — 11 7 — 3 53 3 41 7 3 17 3 33 — 3 — 3 7 — 31 — 3 — 3 — — 3 47 3 13 17 34 19 41 — 7 3 — 3 13 11 3 23 3 47 — 7 19 3 11 3 — 35 3 31 3.11 — 3—3 7 13 3 — 3 — — 3—3 36 13 3 — 3 23 7 3 — 3 19 — 3—3 11 — 7 41 37 — 7 11 — 3 47 3 — 61 3 — 3 7 — 37 — 3 19 3 23 38 3 — 3 13 37 3 11 3 43 7 3 — 3 11 23 3 — 3 39 47 3 — 3 — 7 3 — 3 — — 3 31 3 7 11 40 19 3 — 3 — — 3—3 29 37 11 7 3 13 3 — 41 3 11 3 7 - 3 23 3 13 7 3 — 3 — 41 3 11 3 42 — 373 11 3 41 3 — — 3 19 3 31 7 43 11 13 59 31 3 19 3 7 29 3 — 3 61 7 3 43 3 — 44 373 — 11 3 7 3 19 43 3 11 3 23 — 3—3 45 73—3 13 3—37 23 3 13 3 19 7 46 43 — 17 11 3 7 3 31 — 373 11 41 3 — 3 — 47 3 — 3 17 7 3 53 3 29 — 3—37 11 3 47 3 48 — 3 11 3 17 61 3 7 3 11 - 3 7 3 47 29 37 13 49 13 — 7 — 3 17 3 — 7 3 13 3 - 11 3—37

The text on this page is estimated to be only 27.38% accurate

XXIX. LEAST DIVISORS. 83 11 5 1«> - < j 6 10 17 o 7 8 9 o 7 9 o 7 9 0 3 — 3 — — 3 — 3 7 — 3 — 3 — 73—3 1 2 3 — 3—3 — 11 — 7 3 — 3 — 7 13 3 — 3 — 19 3 — 3 3 — 3 — — 3 — 3 7 — 13 — — 3 11 3 7 17 o o 3 — 3 13 17 3 — 3 4 5 6 11 3 — 3 19 7 — 13 3 — 3 — 7 3 — 3 — — 3 23 3 3 11 3 — — 3 — 3 11 7 13 3 — 3 7 11 — 19 3 — 3 13 — 17 7 — 3 — 3 — — 3 17 3 7 8 9 — 3—3 23 3—37 — 7 13 — 3 — 3 11 31 3 — 3 3 — 3 19 13 3 — 3 — 7 — 11 11 3 — 3 7 3 — 3 23 7 13 — 17 3 19 3 29 — 3 — 3 10 — 373 11 — 3 29 3 13 23 3 — 3 7 11 12 13 13 19 373 — 7 3 23 3 3—37 13 3 7 3 — 29 — 37 — 3 11 3 31 19 3—37 — 7 — 29 3 — 3 — — 3 19 3 3 — 3 11 — 3 — 3 13 7 11 — 14 15 16 31 — 3 — 3 — 13 3 — 3 3 7 3 13 tl-. — 3 7 3 — 11 19 — 3 7 3 23 3—37 41 3 7 3 3 — 3 — 37 3 — 3 19 17 18 19 17 — 7 — 3 17 3 11 — 3 19 3 3 41 3 29 — 3 — 3 37 13 7 11 73-3 3 — 3 — 13 373 — 73—3 3 11 3 7 31 3 7 3 11 20 7 — 11 29 3 — 3 — 19 3 31 3 373 — 21 22 23 3 — 3 17 — 3 37 3 — 13 — 7 — 3 11 3 7 31 3 17 3 23 13 41 7 — 3 — 3 43 — 3 — 3 3 37 3 11 — 3—3 7 7 3 13 3 29 11 3 — 3 — 24 25 26 3 11 3 — — 3—3 jj 7 23 3 — 3 13 11 17 7 3 — 3 17 7 37 3 31 3 — — 3—3 3 13 3 19 29 3 13 3 7 47 3 11 3 7 23 3 — 3 — 27 28 29 3 — 3 31 — 3—3 13 11 11 3 — 3 — 7 47 19 3 — 3 — 17 47 — 7 3 13 3 — — 3 13 3 3 11 3 — 43 3 — 3 11 19 29 7 — 3 — 3 7 11 — 13 3 41 3 — 30 3 43 3 7 — 3—3 37 7 17 — 3 — 3 — 11 3 19 3 31 32 33 23 3 7 3 373 — 29 3 13 3 7 — 373 3 19 3 11 — 3 29 3 11 31 — 3—3 17 7 19 11 3 17 3 — — 31 23 7 3 37 3 — — 3 43 3 34 35 36 73—3 53 11 3 13 3 — 3 7 3 43 7 3 19 3 3 23 3 7 — 3 7 3 13 59 3 11 3 17 37 3 29 3 7 — 7 13 — 3 — 3 59 — 3 — 3 37 38 39 11 3 13 3 7 17 3 59 3 37 — 53 3 — 3 53 17 3 — 3 373 — 73—3 11 29 41 23 19 3 7 3 — 11 13 — 373 — 17 29 3 17 3 7 13 3 7 3 40 — 3—3 31 17 7 13 3 — 3 — 7 3 61 3 17 41 42 43 7 3 — 3 — 19 3 — 3 3 23 3 11 — 3 17 3 7 — 11 17 43 3 — 3 7 11 3 — 3 29 37 47 53 59 3 — 3 — 13 3 41 3 3 7 3 13 73—3 — 23 — 53 44 45 46 — 61 — 7 3 29 3 47 — 3—3 3 — 3 41 — 3—3 59—13 7 17 3 11 3 7 17 23 19 3 — 3 — 7 67 3 — 3 13 31 3 43 3 3 — 3 11 — 3—3 — 13 7 37 47 48 49 — 7 67 — 3 23 3 43 — 3—3 3 11 3 19 — 3 31 3 11 7 13 3 17 3 — 11 — 7 3 — 3 13 7 3 19 3 — 17 3 — 3 3 - 3 67 3 59 3 7 — 19 —

The text on this page is estimated to be only 27.42% accurate

84 XXIX. LEAST DIVISOES. 0 i 2 3 4 u IA m g\ o 7 9 50 3 — 3 — — 3 29 3 11 47 373 — 71 3 7 3 51 — 3 — 3 19 — 7 — 3 47 3 23 7 3 11 3 53 37 — 19 52 7 11 41 — 3 13 3 17 23 3 — 3 13 3 7 3 29 53 3 — 3 — 47 3 13 3 17 — 7 73 3 — 3 19 73—3 54 11 3 — 3 7 3 11 3 61 — 3 — 3 13 — 55 7 3 37 3 — — 3 — 3 — 11 7 29 3 23 3 31 56 3 13 3 71 31 3 41 3 7 — 17 13 3 43 3 — - 3 - 3 57 — 3 13 3 — 29 — 7 3 59 3 17 11 3 — 3 7 _ 58 — 7 — 37 3 — 3 11 -3—3 7 19 13 — 3 — 3 — 59 3 — 3 19 23 3 61 3 31 7 3 17 3 — 13 3 19 3 60 17 3 — 3 — 7 11 13 3 19 3 — 37 3 — 3 7 23 61 — 17 31 41 3 — 3 29 — 3 11 3 17 7 3 — 3 11 62 3—37 — 3—3 — 7 13 — 3 23 3 17 79 3 — 3 68 — 373 - 59 — 71 3 — 3 — 13 3 — 3 17—11 7 64 37 19 43 13 3 11 3 7 — 3—3 59 7 41 47 3 17 3 — 65 3 7 3 23 17 3 7 3 — 11 61 — 3 47 3 13 31 3 — 3 66 73—3 11 17 13 — 3 37 3 7 19 3 — 3 29 7 17 61 67 19 — 373 — 11 3 7 3 53 23 3 11 3 17 68 3 — 3 11 7 3 17 3 19 3—37 — 3 41 3 69 67 3 — 3 — 31 — 11 3 7 3 13 29 3 7 3 11 53 70 — 47 7 43 3 — 3 — 73—3 79 13 31 — 3—37 71 3 — 3 — 13 3 11 3 - 17 3 7 3 11 37 3 7 3 72 19 3 — 3 7 _ 3 31 3 — 73—3 13 u 73 7 67 3 71 3 13 — 3 17 3 11 41 373 — 74 3 11 3 31 -3-3 41 13 7 17 3 — 3 43 7 3 11 3 75 76 13 3 — 3 11 7 7 11 — 73 3 23 3 19 3 — 3 — — 3 29 3 17 ,3 — 3 13 17 7 — — 19 3 — 3 — 77 3 — 3 13 11 3 — 3 7 59 3 11 3 71 — 3 61 3 78 29 3 37 3 73 13 — 7 3 — 3 — 41 3 17 3 — 11 7 47 79 — 7 — 11 3 41 3 — 89 3 — 3 7 17 3 13 3 — 80 3 53 3 — — 3—3 13 71 23 7 3 29 3 — 11 3 13 3 81 — 3 11 3 — 7 — 23 3 — 3 11 47 3 79 3 7 17 — 29 82 59 13 29 — 3 43 3 — — 3 19 3 fj 3 — 3 73 83 3 19 3 7 — 3—3 53 7 11 — 3 13 3 31 19 3 17 3 84 31 3 7 3 13 47 19 _ 3 — 3 — — 3 11 3 23 7 85 — 11 47 67 3—37 — 3—3 19 7 3 — 3 83 86 373 — 79 3 7 3 37 3 89 3 53 — 3—3 87 73—3 31 _ 23 — 3 11 3 7 — 3—3 — 7 — 13 88 13 23 373 — — 373 — 11 3 37 3 — 89 3 29 3 59 7 3 37 3 11 — 79 — 3-37 — 3 23 3 90 — 3—3 71 29 373 — 11 3 7 3 83 — 91 19 — 7 — 3 13 3 11 73—3 23 13 3 41 3 7 92 3 — 3 — 61 3 13 3 — 23 — 11 373 — — 373 93 71 3 41 3 — 67 7 — 3 — 3 19 73—3 13 — 94 7 — 23 97 3 — 3 — — 3 11 3 3 7 3 11 95 3 13 3 37 — 3 31 3 — 89 7 13 3 - 3 73—3 96 — 3 13 3 7 — 59 — 3 — 3 — — 3 23 3 31 - 11 97 89 31 17 7 3 11 3 — — 3 71 3 37 — 7 — 3—398 3 — 3 17 — 3—3 7 11 31 — 3 — 3 — 13 3 43 3 99 - *3 ~~~ «j 11 23 47 7 3 — 3 — — 3 19 3 — 61 7 —

The text on this page is estimated to be only 27.66% accurate

XXIX. LEAST DIVISORS. 85 5 6 7 8 9 11 1379 1379 1379 1379 1379 50 _ 31 13 — 3 61 3 37 11 3 — 3 — 13 — 7 3 11 3 — 51 3—37 13 3 — 3 — 7 31 — 3 71 3 — 29 3 — 3 52 59 3 7 3 — 19 23 11 3 — 3 — — 3 17 3 11 67 — 7 53 — 53 11 23 3 31 3 7 41 3 19 3 — 7 — 17 3 — 3 — 54 3 7 3 53 43 3 7 3 — 13 3 — 3 11 17 3 23 3 55 73-3 67 — 19 — 3—37 — 3 37 3 — 7 29 11 56 •r M 311 ^ 1 1 373 — 7*j ni "J 53 3 7 3 or* O'? r *? 13 — 11 — 3 — 3 41 o7 58 11 3 13 — 3—3 3 73 3 — 11 29 23 53 — 373 — — 373 43 71 — 17 59 11 — 7 59 3 67 3 47 7 3 43 3 — 31 — 53 3 13 3 7 60 3 — 3 73 11 3 — 3 13 — 59 373— 373 61 — 3 47 3 61 — 7 31 3 — 3 37 7 3 23 3 41 11 62 7 13 — 11 3 — 3 — — 3—3 11 61 — 19 373 — 63 3 — 3 — — 3—3 23 — 7 — 3 13 3 — 73—3 64 — 3 11 3 7 23 29 — 3 — 3 11 — 3 13 3 — 43 73 67 65 79 7 3'- 3 — 3 — 3 — 29 7 11 3 19 3 — 66 3 — 3 — — 3 59 3 7 — 11 — 3 41 3 — — 3 37 3 67 43 3 29 3 67 7 3 13 3 — — 3 11 3 7 13 68 13 7 — 19 3 — 3 — — 3 13 3 7 — 71 83 3 61 3 — 69 3 17 3 — — 3—3 — 19 — 7 3 — 3 29 — 3 — 3 70 11 3 — 3 23 7 37 — 3 11 3 — 73 3 19 3 7 41 47 31 71 — 23 17 — 3 13 3 67 71 3 — 3 43 11 — 7 3 — 3 23 72 3—37 53 3 13 3 11 7 19 29 3 — 3 37 23 3 — 3 73 — 373 17 37 53 — 3 73 3 47 11 3 83 3 19 — 13 7 74 — 29 3 17 3 7 31 3 — 3 — 7 3 59 3 — 75 373 — — 373 67 11 3 — 3 — — 3 71 3 76 7 3 13 3 47 79 11 3—37 — 3—3 — 7 43 — 77 23 3 7 3 17 19 3 7 3 31 43 13 — 3 — 3 11 78 3 — 3 29 73—3 17 3—37 13 3 53 3 79 — 3 73 3 19 — 31 13 3 7 3 79 23 3 7 3 61 — 11 19 80 83 — 7 — 3 11 3 — 7 3 41 3 — 59 3—37 81 3 31 3 41 — 3—3 — 11 13 — 3 7 3 19 — 3 7 3 82 37 3 23 3 11 — 7 — 3 — 3 17 73—3 43 83 7 — 61 13 3 — 3 — 11 3 — 3 17 83 3 7 3 37 84 3 79 3 11 — 3—3 43 37 7 61 3 17 3 13 7 3 29 3 85 17 3 43 3 7 — 13 11 3 — 3 23 — 3 31 3 11 13 86 41 17 11 7 3 — 3 — 13 3 — 3 — 19 7 — 3 — 3 — 87 3 — 3 19 — 3 11 3 7 31 67 — 3 — 3 11 59 3 19 3 88 53 3 17 3 7 3 19 3 13 83 3 — 3 17 — 7 11 89 — 7 13 17 3 — 3 — — 3 47 3 7 13 11 89 3 17 3 — 90 3 11 3 13 3 — 3 47 43 29 7 3 31 3 61 — 3 11 3 91 — 3 — 3 — 7 89 53 3 — 3 67 — 3 — 3 7 29 17 — 92 11 19 — 47 3 59 3 13 73 3 — 3 37 7 3 — 3 17 93 3 47 3 7 11 3 17 3 — 7 — 83 3 11 3 41 — 3 — 3 94 13 3 7 3 17 3 — 3 — 19 3 53 3 — 11 — 7 95 — 41 19 11 3 73 3 7 17 3 61 3 11 7 — 43 3 53 3 29 96 3 7 3 13 — 3 7 3 19 17 3 23 3 — 11 3 — 3 97 7 3 11 3 43 13 3 29 3 7 — 3 — 3 — 7 97 41 98 — 59 3 7 3 71 — 3 7 3 41 11 3 13 3 19 99 3 37 3 23 73—3 13 — 11 17 3 67 3 7 97 3 13 3

The text on this page is estimated to be only 28.18% accurate

86 XXX. EXPONENTIALS. en n 0 123 4 5 6 7 8 9 .0 1.000 1.010 1.020 1.030 1.041 1.051 1.062 1.073 1.083 1.094 .1 1.105 1.116 1.127 1.139 1.150 1.162 1.174 1.185 1.197 1.209 .2 1.221 1.234 1.246 1.259 1.271 1.284 1.297 1.310 1.323 1.336 .3 1.350 1.363 1.377 1.391 1.403 1-419 1.433 1.448 1.462 1.477 A 1.492 1.507 1.522 1.537 1.553 1.568 1.584 1.600 1.616 1.632 .5 1.649 1.665 1.682 1.699 1.716 1.733 1.751 1.768 1.786 1.804 .6 1.822 1.840 1.859 1.878 1.896 1.916 1.935 1.954 1.974 1.994 .7 2.014 2.034 2.054 2.075 2.096 2.117 2.138 2.160 2.181 2.203 .8 2.226 2.248 2.270 2.293 2.316 2.340 2.363 2.387 2.411 2.435 .9 2.460 2.484 2.509 2.535 2.560 2.586 2.612 2.638 2.664 2.691 1. 2.718 3.004 3.320 3.669 4.055 4.482 4.953 5.474 6.050 6.686 2. 7.389 8.166 9.025 9.974 11.02 12.18 13.46 14.88 16.44 18.17 3. 20.09 22.20 24.53 27. 11 29.96 33.12 36.60 40.45 44.70 49.40 4. 54.60 60.34 66.69 73.70 81.45 90.02 99.48 109.9 121.5 134.3 5. 148.4 164.0 181.3 200.3 221.4 244.7 270.4 298.9 330.3 365.0 6. 403.4 445.9 492.7 544.6 601.8 665.1 735.1 812.4 897.8 992.3 7. 1097 1212 1339 1480 1636 1808 1998 2208 2441 2697 8. 2981 3294 3641 4024 4447 4915 5432 6003 6634 7332 9. 8103 8955 9897 10938 12088 13360 14765 16318 18034 19930 6-n n 0 123 4 5 6 789 .0 1.000 *990 *980 *970 *961 *951 *942 *932 *923 *914 .1 0.905 896 887 878 869 861 852 844 «35 827 .2 0.819 811 803 795 787 779 771 763 756 748 .3 0.741 733 726 719 712 705 698 691 684 677 .4 0.670 664 657 651 644 638 631 625 619 613 .5 0.607 600 595 589 583 577 571 566 560 554 .6 0.549 543 538 533 527 522 517 512 507 502 .7 0.497 492 487 482 477 472 468 463 458 454 .8 0.449 445 440 436 432 427 423 419 415 411 .9 0.407 403 399 395 391 387 383 379 375 372 1. 0.368 333 301 273 247 223 202 183 165 150 2. 0.135 122 111 100 *907 *S21 *743 *672 *608 *550 3. 0.0498 450 408 369 334 302 273 247 224 202 4. 0.0183 166 150 136 123 HI 101 *910 *823 *745_ 5. 0.00674 610 552 499 452 409 370 335 303 274 6. 0.00248 224 203 184 166 150 136 123 111 101 7. 0.000912 825 747 676 611 553 501 453 410 371 8. 0.000335 304 275 249 225 203 184 167 151 136 9. 0.000123 112 101 091 083 075 068 061 055 050 1 1 i HIT «1T n ne ne en e n e9 e ~z 1 2.718282 .367879 2.718 .368 4.811 .208 2 5.436564 .735759 1.649 .607 23.14 .0432 3 8.154845 1.103638 1.396 .717 111.3 .00898 4 10.873127 1.471518 1.284 .779 535.5 .00187 5 13.591409 1.839397 1.221 .819 2576 .000388 6 16.309691 2.207277 1.181 .847 12392 .0000807 7 19.027973 2.575156 1.154 .867 59610 .0000168 8 21.746255 2.943036 1.133 .883 286752 .00000349 9 24.464536 3.310915 1.118 .895 1379406 .000000725

The text on this page is estimated to be only 28.29% accurate

EXPLANATION OF TABLES. THROUGHOUT these tables the figures of the argument are printed in thick type, the initial figures being printed in the left-hand column, and the terminal figures in the top row. The entry is found in the intersection of the row of the initial figures with the celumn of the terminal figure. A bar below a terminal 5 or 0 shows that the final 5 has been increased ; hence, when the entry is further contracted, the terminal figure ought not to be increased by one. . I. Common Logarithms, pp. 2-5. Pages 2 and 3 give the logarithm to four places of any sequence of three significant figures. The column headed d gives the difference between the last logarithm of the row and the first logarithm of the next row ; it facilitates the finding of the difference between any two successive logarithms in the row. The small table at the bottom of page 3 gives the proportional parts of the tabular differences from 4 to 23. The tabular difference is printed in the top row, and the tenths in the left-hand column. Pages 4 and 5 give the logarithms of any sequence of 4 figures from 1000 to 1900. The proportional parts of the tabular differences are given in the right column ; only the difference is printed, the tenth being understood from the location of the proportional part. The small table at the bottom of page 5 gives the logarithm to six places of the numbers 1.000 to 1.100 which occur in calculations of interest. The initial pair of figures are given only for the 0 entry and are understood for the remaining entries of the row ; unless an asterisk is printed in front, which indicates that the initial figures are those printed in front of the next row.

The text on this page is estimated to be only 28.08% accurate

88 EXPLANATION OF TABLES. Given a number to find its logarithm, or, to use the table directly. The characteristic or integral part of the required logarithm is obtained by counting the number of places by which the first figure of the number is removed to the left or to the right of the unit's place ; if to the left, the characteristic is positive ; if to the right, negative. Thus the characteristic of 1234 is 3, while that of .01234 is 2. The mantissa, or fractional part of the required logarithm, is obtained from the table thus. If the number has not more than two significant figures, then the mantissa is found in the column headed 0. If there are three significant figures, the mantissa is found in the intersection of the row for the first two figures with the column headed by the third figure. For example, the mantissa of 23 is .3617, that of 234 is .3692. When the number contains four significant figures, the mantissa can be obtained directly from pages 4 and 5 provided the number is not greater than 1900. When the number is greater, the required mantissa is found from pages 2 and 3 by interpolation. Find the mantissa for the first three significant figures ; find the difference between it and the next higher mantissa in the table (it will in general be nearly equal to that printed under d) ; find from the table at the bottom of page 3 the proportional part of this tabular difference for the fourth significant figure and add it to the lower mantissa. Thus log 2345. is .3692 plus five-tenths of 19, that is 10 ; hence .3702. For log 23456 we add besides six-hundredths of 19, that is 1 ; hence .3703. Or we multiply 19 by .56 and take the nearest integer to the value, namely, 11. Given a logarithm to find the corresponding number; or, to use the table inversely. When the number is wanted to not more than three significant figures, find the mantissa in the table which is nearest to the given mantissa ; the corresponding argument gives three figures of the number, and the position of the decimal point is determined by the characteristic. Thus the number corresponding to 2.5015 is 317, that to 2.5020 is .0318. Suppose four significant figures are wanted. If the mantissa does not exceed .2785, the nearest mantissa on pages 4-5 will point out the number to four figures. If it exceeds the above

The text on this page is estimated to be only 26.90% accurate

EXPLANATION OF TABLES. 89 number, the fourth, figure is obtained by interpolation. Find the next lower mantissa 5 find the difference between the said mantissa and the next higher, also the difference between said mantissa and the given mantissa, and find from the table of page 3 what proportional part the latter difference is of the former. For example, the next lower to .7370 is .7364, hence the first part of the number is 545, and the fourth figure is that part of ten which 6 is of 8 : namely 7 ; hence 5.457. To find the logarithm of a product. Take the sum of the logarithms of the factors. Thus, log (123x4567) =2.0899 3.6590 6 5.7495 To find the logarithm of a quotient. Subtract the logarithm of the denominator from the logarithm of the numerator. Thus, log ^gW = 2.0899 3.6596 2.4303 To find the logarithm of a power. Multiply the logarithm of the base by the index of the power. Thus, log 9872 = 2 (2.9943) = 5.9886 log (.987)2 = 2 (1.9943) =1.9886 To find the logarithm of a root. Divide the logarithm of the base by the index of the root. Thus, log V987 = |(2.9943) =1.4972 log V.~987 = £( 1.9943) = 1.9972 II. Antilogarithms, pp. 6-7. This is a table of the fractional powers of 10 from 10 -000 to 10 .999 The first two figures of the fraction or mantissa are given in the left column, and the third in the top row.

The text on this page is estimated to be only 26.78% accurate

90 EXPLANATION OF TABLES. To find the number corresponding to a logarithm. This is given by a direct use of the table. Find the entry for the first three figures of the mantissa, take the difference between that entry and the next higher, and from the column of proportional parts find the part which requires to be added to the entry on account of the fourth figure. Insert the decimal point in the place indicated by the characteristic of the logarithm. For example, to find the antilogarithm of 2.9876. For 987 we have 9705, difference is 22 ; the proportional part of 22 for 6 is 13, therefore 9705 + 13 = 9718, and inserting the decimal point, 971.8. The direct use of a table of antilogarithms serves the same purpose as the inverse use of a table of logarithms. III. Addition Logarithms, pp. 8-9. The argument is log n, where n is a fraction less than unity. Thus the characteristic of log n is negative ; it is not printed so, but is indicated by its complement to 10. Thus the argument 9.713 means 9.713 - 10, or 1.713. Given the logarithm of each of two numbers, to find the logarithm of their sum. Let a and b denote the two numbers, of which b is the less. Then log (o + 6) = loga + logfl + ^\ (1) and log n = log - = log b — log a. (2) Having found log n by means of (2), we get log (1 4- n) from the table, and by adding it to log a obtain log (a -f- b) . Example, log a = 3.8060, log b = 2.1618. Therefore, log n = log - = 2.1618 3.8060 2.3558 therefore, from the table, log (1 -f n) = 0.0097 therefore, log (a 4- b) = 3.8060 0.0097 3.8157

The text on this page is estimated to be only 24.81% accurate

EXPLANATION OF TABLES. 91 To solve the same question by means of Tables I. and II. : a = 6397, 6 = 1449 + 2 = 145.1, a + b = 6542, log (a + b) = 8156 + 1 = 3.8157. IV. Subtraction Logarithms, pp. 1O-13. This table is arranged similarly to the preceding, excepting that the tenth decade is expanded on pages 12-13. Given the logarithm of each of two numbers, to find the logarithm of their difference. Let a and b denote the two numbers, of which b is the less. Then, log (a - b) = log a(l - -\ = log a + log (l --\ \ aJ \ a/ = loga-log _. 1 — a Let log n = log -, then from the table we get log , which a L — n subtracted from log a, gives log (a — b). Example. Given log a = 1.9876 and log 6 = 1.5432. Then log n = log- = 1.5432 a 1.9876 1.5556 i.e., 9.5556 - 10. Now, from the table, 9.555 gives 0.1931 and 6 gives 3, .-. log— — =0.1934, 1 — n .-. log (a - b) = 1.9876 0.1934 1.7942 Suppose that log (1 + n) is known (n being less than unity) and its position in Table III., then log can be found in JL — — n the corresponding position in Table IV., and log — 3— ? can be 1 — n found by adding these two logarithms together. Logarithms of addition and subtraction are sometimes called Gaussian logarithms.

The text on this page is estimated to be only 27.88% accurate

92 EXPLANATION OF TABLES. V. Logarithmic Sines and Cosines, pp. 14-17. Pages 14-15 give the logarithm of the sine to every tenth of a degree, that is, every six minutes. The logarithm of the cosine is obtained by taking the right-hand argument and reading backwards. The d column gives the difference between the two last entries of a row, the last entry of one row being identical with the first of the succeeding. As the sines and cosines are all less than unity, the characteristics of the logarithms are all negative ; they are indicated by their complement to 10. Pages 16-17 give the sines and cosines for the first nine degrees to every hundredth of a degree. Given an arc, to find its log sin. If the arc is less than 90°, its log sin is found by the direct use of the table. For example, to find log sin 17°. 66. By the table log sin 17°.6 is 9.4805 — 10, the difference is 24, and the proportional part for 6 is 14 ; hence, 9.4819 — 10. If the arc is > 90° but < 180°, find the log sin of the difference between 180° and the arc ; if > 180° but < 270° find .that of the difference between the arc and 180°, and if > 270° but < 360°, find that of the difference between 360° and the arc. Given the log sin, to find the arc. For example, to find the arc in degrees the log sin of which is 9.6669. The next lower log sin in the table is 9.6659, which corresponds to 27°. 6 ; the tabular difference is 14, and the given difference is 10 ; hence, the arc is 27°. 67. At the bottom of page 17 there are two auxiliary tables. The one gives the equivalent in minutes of the fractions of a degree; thus, 0°.63 is equivalent to 37'.8. The other is called a Delambre's table ; it is used to find the log sin of a small arc. On account of the table, pages 16-17, this auxiliary table is not required, except when the arc is less than 0°.4. By S is here meant the logarithm of the ratio of the number expressing the degree to the number expressing the corresponding sine. To find the sine of a small arc. Let n denote the number of degrees ; then, log sin n° = log n — S.

The text on this page is estimated to be only 26.87% accurate

EXPLANATION OF TABLES. 93 Example : to find log sin 0°.123. Log .123 is 9.0899 — 10, and S is 1.7581 ; hence, logsinO°.123 is 7.3318 - 10. To find a small arc, given its* log sin. We have log n = log sin n° -f- S. For example, given log sin to be 7.1234 — 10. As the log sin is less than 8.2872-10, the value of S to add is 1.7581. Hence, 8.8815 — 10, the number corresponding to which is .0761, hence 0°.0761. VI. Logarithmic Tangents and Cotangents, pp. 18-21. This table is similar to the preceding. After 45° the tangent is greater than unity, the characteristic is no longer negative ; hence, the true characteristic is printed. Of the two auxiliary tables at the bottom of page 21, the one gives the equivalent in degrees of so many minutes ; the other is a Delambre's table of T for the first four degrees. By T is here meant the logarithm of the ratio of the number of degrees to the number expressing the tangent. It is used in finding the log tan of a very small arc. We have, log tan n° = log n— T and log n = log tan n° -f- T. VII. Logarithmic Sines and Cosines for Minutes, pp. 22-23. Here the log sin is given directly to every ten minutes, and by interpolation to every minute. The same table gives log cos when read backwards. Pages 22-25 give the proportional parts for all the differences from 1 to 100. Example: to find log cos 19° 28'. Log cos 19° 20' is 9.9748 — 10, the tabular difference is —5, the proportional part of —5 for 8 is -4 ; hence, 9.9744 - 10. At the end we have a table of S for the range between 0° and 7°, where the change in the value of the tabular difference is too rapid to allow of interpolation by proportional parts. Here S is the logarithm of the ratio of the number of minutes expressing the arc to the sine of the arc. Thus, 3.5372 is the log of the ratio of 378 to .1097.

The text on this page is estimated to be only 28.09% accurate

94 EXPLANATION OF TABLES. VIII. Logarithmic Tangents and Cotangents for Minutes, pp. 24-25This table is similar to the preceding. By T is meant the log of the ratio of the number of minutes expressing the arc to the tangent of the arc. IX. Natural Sines and Cosines, pp. 26-27. The natural sine is given to each tenth of a degree ; that is, to every six minutes. The equivalent minutes are printed alongside of the tenths of a degree. At the bottom of page 27 there is a table of proportional parts, the whole interval being six, to facilitate the interpolation to a minute. What is the sine of 34° 46' ? The sine of 34° 42' is .5693, the tabular difference is 14, and the pp. of 14 for 4 is 9 ; hence, .5702. What is the arc whose cosine is .4326 ? The arc of .4321 is 64° 24', the tabular difference is 16, the difference of given cosine is 5, corresponding to a pp. of 5 for a tabular difference of 16 we have 2' ; hence, the arc is 64° 22'. X. Natural Tangents and Cotangents, pp. 28-29. XI. Natural Secants and Cosecants, pp. 30-31. These tables are similar to the preceding. At the end of each we have a continuation of the table of proportional parts, the interval being six. XII. Radians, pp. 32-33. By a radian is meant the unit of circular measure of an angle. The table gives directly the number of radians equivalent to any number of degrees expressed by not more than three significant figures. The integer figure of the entry is printed only in the 0 column. Thus, the equivalent of 67°.8 is 1.1833 radians, and the equivalent of 1 radian is 57°.3. The tabular difference is either 17 or 18 ; hence, to find the equivalent for 4 significant figures, we add the proper pp. of either 18 or 17, as the case may be. The column headed h m gives the equivalent in hours and minutes of the corresponding number of degrees in the left

The text on this page is estimated to be only 28.31% accurate

EXPLANATION OF TABLES. 95 column ; and the adjacent column headed p gives that fraction of a whole period or perigon which is equivalent to the ratio of the corresponding number of degrees to 360°. The small table at bottom of page 33 gives the number of radians equivalent to the given number of minutes, while the column headed p gives that fraction of a period or perigon which the corresponding number of minutes bears to 360°. When the decimal point is changed by any number of places in the argument, the decimal point is changed by an equal number of places in the entry. Thus, 3°.6=. 06283 and 360° =6.283. XIII. Reciprocals, pp. 34-35. The reciprocal* is given directly for any sequence of three figures, the decimal point being after the first. When the decimal point in the argument is shifted any number of places, the decimal point in the entry is shifted an equal number of places in the opposite direction. Thus, 1 78.9 ^ = .001267, * At the bottom of page 35 we have the first nine multiples of the fractions -J-, ^, etc., up to -^. A bracket indicates that the figures included repeat themselves. XIV. Squares, pp. 36-37. This table gives directly to four significant figures the square of any sequence of three figures, the decimal point being after the first. When the decimal point changes in the number, the decimal point in the square changes by double the number of places in the same direction. Thus the square of 3.76 is 14.14, that of 37.6 is 1414, and that of .376 is .1414. When the number consists of more than three figures, the square may be found by means of the table of proportional parts. For example, to find the square of 1889 to four significant figures. The square of 188 is 35,340, the pp. of 38 for 9 is 34 ; therefore the square of 1889 is 3,568,000. Here the zeros are not significant, but only indicate the position of the decimal point.

The text on this page is estimated to be only 29.06% accurate

96 EXPLANATION OF TABLES. To find the complete square for any sequence of three figures. The complete square of any two figures is given in the zero column. If the number of three figures is less than 317, we have to find the square of the third figure, and append the terminal figure to the entry of the table, diminishing the terminal figure of the entry by one if the number appended is equal to or greater than 5. For instance, take 234. The square of 4 is 16, hence 6 is to be appended to 5476, but the fourth figure reduces to 5 because it has been increased by one when the 6 was cut off. Hence the complete square is 54,756. When the number exceeds 316, find the square of the two terminal figures in the zero column, take the last two figures of it and append them to the entry, diminishing the terminal figure of the entry by one if the addendum equals or exceeds 50. For example, the last two figures of the square of 96 is 16, the entry for 896 is 8028, hence the complete square is 802,816. The table at the bottom of page 37 gives the square of the reciprocal of any number of two digits. Thus the square of — is .0865. When the decimal point is shifted in the 3.4 argument, the decimal point of the entry requires to be shifted by twice the number of places in the opposite direction. Thus the square of — is 1.32. .87 XV. Cubes, pp. 38-39. This table gives to four figures the cube of any number of three figures, and in the 0 column the complete cube of any number of two figures. When the decimal point is shifted in the number, the decimal point of the cube requires to be shifted thrice the number of places in the same direction. Thus the cube of 1.23 is 1.861, that of 12.3 is 1861, that of .123 is .001861. The small table of page 39 gives the cube of the reciprocal of the number. Thus the cube of — is .00142. When the 8.9 decimal point is shifted in the number, the decimal point in the reciprocal of the cube is shifted thrice the number of places in the opposite direction.

The text on this page is estimated to be only 26.98% accurate

EXPLANATION OF TABLES. 97 XVI. Square Roots, pp. 40-43The first part of the table, pages 40-41, gives the square root of any number of three significant figures, when the decimal point is after the first figure, or is any even number of places to the right or left of that position ; while the second part of the table, pages 42-43, gives the square root, when the decimal point is after the second figure or any even number of places to the right or left of that position. The square root is given to five figures, the initial figure being printed only in the 0 column. When the decimal point of the number is shifted any even number of places from its position after either the first digit or after the second digit, the decimal point in the corresponding entry shifts by half the number of places in the same direction. Thus, V087 = 3.1417, V9&7 = 9.9348, V987 = 31.417, V9870 = 99.348, V."987 = .99348, Vi0987 = .31417. The small table of page 41 gives the square root of the reciprocal of any number of two figures, the decimal point being after the first figure ; while the small table of page 43 gives the same when the decimal point is after the second figure. Thus, = .319, -4r = .101, -1- = 1.01, -4= = .0319. V9.8 V98 V.98 V980 XVII. Cube Roots, pp. 44-49. The first part of the table gives the cube root, when the decimal point is after the first significant figure, or when displaced any multiple of three places to the right or left of that position ; the second part similarly when the decimal point is after the second significant figure ; and the third part when it is after the third. A displacement of three places in the number causes a displacement of one place in the same direction in the cube root. Thus, -v/123 = 1.0714, ^12^ = 2.3084, -\/123 = 4.9732, ^1230 = 10.714, ^0123 = .23084, ^123 = .49732. Similarly the three small tables give the cube root of the reciprocal of any two figures for the three distinct positions of the decimal point.

The text on this page is estimated to be only 28.57% accurate

98 EXPLANATION OF TABLES. XVIII. Multiples, pp. 5O-67. This table gives the first nine multiples of any number of three figures, and the folding table at the end gives the same for any number of two figures. By means of this table and our knowledge of the ordinary multiplication table we can write down any of the nine multiples of a number of four figures, and with the help of the folding table we can do the same for any number of five figures. By a double reference to the table we obtain a multiple of six figures, and so on. Thus, 8 times 789 = 6312 8 times 6789 = 8 times 56789 = 8 times 456789 = 6312 48 54312 6312 448 454312 6312 3648 3654312 To multiply any two numbers together. Consider, for example, the product of 123,456,789 and 6987. Turn up the multiples of 789, and write down the 7, 8, 9, and 6 multiples under one another in the usual manner, only space is to be left between each pair of multiples for another row of figures ; then turn up the multiples of 456, write down the 7 multiple with its initial figure below the fourth figure of the 7 multiple of 789, and similarly for the other multiples ; then turn up the multiples of 123, write down the 7 multiple with its first figure above the fourth figure of the 7 multiple of 456, and so on, as follows : 861 5523 3192 . 984 6312 3648 1107 7101 4104 738 4734 2736 862592584743

The text on this page is estimated to be only 28.60% accurate

EXPLANATION OF TABLES. 99 To divide one number by another. For example, to divide 4,567,890 by 567. Turn up the multiples of 567 ; find the next lower to 4567, deduct it ; take down another figure, find the next lower multiple to the number so forned, and so on, as follows : 567)4567890(8056 4536 3189 2835 3540 3402 138 If the divisor consist of four figures, as 5678, turn up the multiples of 567,and correct them mentally for the additional figure 8. If there are five figures, as 56,789, correct the multiples of 567 by adding the multiples of 89 from the folding table. XIX. Circumference of Circle, pp. 68-69. When the decimal point is changed in the diameter, the decimal point in the circumference changes by an equal number of places in the same direction. When n represents the radius, the circumference is obtained by doubling the entry. The small table, page 69, gives the value, the logarithm, and the reciprocal of frequently occurring constants, which involve TT. The mantissa of the logarithm of the reciprocal is the complement to 1 of the mantissa of the logarithm of the constant. Thus, log - is 1.5029. 7T XX. Area of Circle, pp. 70-71. When n denotes the radius, the area is obtained by multiplying the entry by 4. When the decimal point is changed in the diameter, the decimal point of the area changes by double the number of places in the same direction. Thus, when the diameter is 3.96 the area is 12.32, when 39.6 then 1232, when .396 then .1232. The diameter of a circle of given area is obtained by the inverse use of the table. When n denotes the diameter of a sphere, the surface is

The text on this page is estimated to be only 27.97% accurate

100 EXPLANATION OF TABLES. irn2. Hence the surface of a sphere of given diameter is obtained by multiplying the entry of the table by 4. The auxiliary table, page 71, gives the decimal equivalents of the binary divisions of the inch, and also the decimal equivalents of a number of inches as part of the foot or of the yard. Thus, the area of a circle of 3f inch diameter, is that of 3.375 inch; hence, 8.920 + 26, that is, 8.946 square inches. XXI. Content of Sphere, pp. 72-73. This table gives the content of a sphere of which n is the diameter. When the radius is given, the spherical content is obtained by multiplying the tabular entry by 8. When the decimal point is changed in the diameter, the decimal point of the content is changed thrice the number of places in the same direction. The small table at the bottom of page 73 gives the logarithm of the product of successive integers from 1 up to n, and the logarithm of the powers of 2 up to the 29th. For example, log 1-2. 3- 4- 5- 6 is 2.8573. XXII. Hyperbolic Logarithms, pp. 74-75. This table gives directly the hyperbolic or natural logarithm of any sequence of three significant figures, the decimal point being after the first. When the decimal point of the sequence is shifted n places to the right from the above position, find the logarithm of 10n in the auxiliary table and add it to the entry ; and when the decimal point is shifted n places to the left, add the logarithm of 10~n. Thus, log 56.7 = 1.7352 log 567 = 1.7352 2.3026 4.6052 4.0378 6.3404 log .567 = 1.7352 log. .0567 = 1.7352 3.6974 5.3948 1.4326 3.1300 By m in the auxiliary table is meant the modulus or multiplier for converting the natural or hyperbolic logarithm of a number into the common logarithm of the number, and by — is in meant the reciprocal modulus or multiplier for converting the common log of a number into the natural.

The text on this page is estimated to be only 27.44% accurate

EXPLANATION OF TABLES. 101 Example : To find the hyperbolic log of 1889, given the common log to be 3.2762. The equivalent of 3 = 6.9078 The equivalent of .2 = 0.4605 The equivalent of .07 = 0.1612 The equivalent of .006 = 0.0138 The equivalent of .0002 = 0.0005 Therefore hyp. log. of 1889 = 7.5438 XXIII. Amount of One Unit of Money at the End of a Given Number of Years, p. 76. The argument in the left-hand column is the number of years during which one unit of money (whether dollar, pound, franc, or mark) has been allowed to accumulate at compound interest, while the argument in the top row is the rate of interest expressed as so much per cent per year. The general expression for the amount of one unit in n years at r per cent per year is (l + Jj_ Given the principal, the number of years, and the rate, to find the amount. Find from the table the amount of one unit of money for the given number of years and rate, and multiply that number by the principal. For example, to find the amount of $123 at the end of 25 years at 6 per cent per year. The entry for 25 years and 6 per cent is 4.292 ; to find the product of this, number and 123, turn up the multiples of 123. 4.292x123= 246 1107 246 492 527.916 As the fourth figure of 4.292 is inexact, the figures 1 and 6 of the product are not significant; hence the result is $527.9. Given the amount, the number of years, and the rate, to find the principal. Find from the table the amount of one unit for the given number of years and rate, and divide the total amount by it ; the quotient is the principal.

The text on this page is estimated to be only 28.46% accurate

102 EXPLANATION OF TABLES. Given the principal, the rate, and the amount, to find the number of years. Divide the amount by the principal and compare the quotient with the entries in the column under the given rate. For example, to find the number of years in which $456 becomes $742.82 at 5 per cent per year. Dividing 742.82 by 456, we get 1.629, which is the entry in the 5 per cent column for 10 years. Given the principal, the amount, and the number of years, to find the rate. Divide the amount by the principal and compare the quotient with the entries in the row of the given number of years. To find the amount of a unit of money for a number of years and a fraction of a year. Find the difference between the entry for the number of years and the next higher entry, multiply it by the fraction of the year, and add the result to the lower entry. For example, to find it for 7 years and 3 months, the rate of interest being 8 per cent. The entry for 7 years is 1.714, and that for 8 is 1.851 ; the difference is 137, the fourth part of which is 34, which added to 1.714 gives 1.748. To find the amount of a unit of money for an intermediate rate of interest. The value may be found approximately by applying the principle of proportional parts as above. For example, the amount for 9 years at 5£ per cent is 1.551, plus one-half of 138; hence, 1.620. To find the amount of one unit of money for a number of years greater than 49. Break the number of years into parts each not greater than 49, multiply together the entries for the several parts ; the result is the amount for the given number of years. For example, to find the amount of one unit of money for 70 years at 10 per cent. The entry for 40 years is 45.26, and that for 30 years is 17.45. To find the product of 45.26 by 17.45, turn up the multiples of 745 and correct them for the 1 ; the result is 789.7870, but the last three figures are not significant; hence, 789.8. The true value is 789.747.

The text on this page is estimated to be only 28.38% accurate

EXPLANATION OF TABLES. 103 This problem may also be solved by means of the small table of logarithms, page 5, where the logs of the coefficients from 1.000 up to 1.100 are given to six places in order that their multiples may be obtained exact to four places. The log of 1.10 is .041393, which multiplied by 70 gives 2.8975, the antilogarithm of which is 789.8. XXIV. Present Value of 1000 Units of Money, p. 77. This table gives the present value of 1000 units of money due n years hence, the rate of interest having any one of the values in the top row. The entry is given, not for 1, but for 1000, in order to simplify the specification of the decimal point. When an entry is taken out, the decimal point ought to be shifted three places to the left. The method of using this table is the same as that for Table XXIII. XXV. Amount of an Annuity when paid at the End of Bach Year, p. 78. This table gives the amount of an annuity of one unit of money per year, when the annuity is allowed to accumulate for n years, the first payment being made at the end of one year from the time of reckoning. The method of using Table XXIII. applies to this table, " one unit of money per year" being substituted for "one unit of money," excepting the rule at the end for extending the table. In order to extend the table, the value of ( 1 -f -^- ) must be \ 10(v found by that rule, and the result substituted in the formula at the top of the table. XXVI. Present Value of the Preceding, p. 79. This table gives the value at the beginning of the time of reckoning of an annuity of one unit of money per year allowed to accumulate for a given number of years, the first payment being made at the end of one year from the beginning of the time of reckoning. The method of using the table is the same as for Table XXV.

The text on this page is estimated to be only 28.15% accurate

104 EXPLANATION OF TABLES. XXVII. Amount of an Annuity when paid at the Beginning of Bach Year, p. 8O. This table gives the amount of an annuity of one unit of money per year, when the several payments are allowed to grow at any one of the rates of interest specified, the first payment being made at the beginning of the time of reckoning. The method of using the table is the same as for Table XXV. XXVIII. Annuity required to extinguish a Debt of 1000, p. 81. This table gives the annual sum to be paid for a given number of years, the first payment being made one year from the present time, in order to extinguish a present debt of 1000 units of money. Here the 1000 is introduced for the same reason as in the case of Table XXIV. To extend the table, the extended value of (1 + r)n must be found and substituted in the formula printed at the top. XXIX. Least Divisors, pp. 82-85. This table gives the least divisor of any number up to 10,000. The first two figures of the number are given in the left-hand column, the third figure in the top row and the terminal figure in the row beneath. The only terminal figures entered are 1, 3, 7, 9, because any number which terminates otherwise is evidently divisible by 2 or 5. To find the factors of any number less than 10,000. If it is an even number, divide out 2 until the remainder is odd ; if it then ends in 5, divide out the power of 5 ; then enter the table with the remaining quotient to find its least divisor ; divide out that divisor, and with the then remaining quotient enter the table again ; and so on until the remaining quotient is a prime, which is indicated in the table by a bar. Example : 1889 is a prime. 9876 = 2 x 4938 = 22 x 2469. Now 2469 has least divisor 3, and quotient is 823, and 823 is a prime. Hence, 9876 = 22 x 3 x 823.

The text on this page is estimated to be only 28.52% accurate

EXPLANATION OF TABLES. 105 XXX. Exponentials, p. 86. The upper part of the table contains the ascending powers of e from .00 to .99 and from 1.0 to 9.9; and the lower part the corresponding descending powers. The upper part forms a small table of hyperbolic antilogarithms. At the bottom of the page we have the first nine multiples of e and of the reciprocal of e, the first nine fractional powers of e, both positive and negative, and the powers of e given by the first nine multiples of -, both positive and negative. 2 XXXI. Multiples (Folding Leaf). This table contains the first nine multiples of the numbers from 1 to 99. It may be used as a table of proportional parts for tenths by inserting a decimal point before the last figure, and for hundredths by inserting the point before the second last figure.

The text on this page is estimated to be only 16.98% accurate

% s University of Toronto Library 1 DO NOT / w // 1 £ 0 REMOVE /