Fromthe logarithm of the dividend, viz. 1425=3,15381 Take the logarithm of the divisor, viz. 57 = 1,75587 And the remainder is the loga rithm of the quotient, viz. } 3. IN THE RULE OF THREE. 25-1,3979 Three numbers given to find a fourth, in direct proportion. RULE. From the tables take the logarithms of each of the proposed numbers, then add the logarithms of the fecond and third together, and from the sum take the logarithm of the first and the remainder will be the logarithm of the fourth number. Let the three proposed numbers be 18, 24 and 33, and the operation will stand thus : 1,38021 the logarithm of 24, the 2d. term. 1,51851 the logarithm of 33, the 3d. term. 2,89872 the logarithm of their product. -1,25527 the logarithm of the 1st term 18. 1,64345 the logarithm of the 4th term required, which, by the Table answers to the natural number 44, the 4th proportional to the three proposed numbers. 4. IN INVOLUTION, OR RAISING POWERS. To find any power of any proposed number, or to involve any number to any proposed power, by logarithms. RULE. Multiply the logarithm of the given root by the power, viz. by 2 for the square, by 3 for the cube,&c. and the product is the logarithm of the power fought. Required to find the cube of 12? 1,07918=the logarithm of 12. X3=the third power, or cube. A 3,23754-1728 the cube of 12. To Extract any root of any proposed number. RULE. Divide the logarithm of the proposed number by the index of the required root, viz. by 2 for the square, by 3 for the cube, &c. and the quotient will be the logarithm of the root required. Required Required to find the cube root of 1728 ? 3,23754 the logarithm of 1728, and 3,237543=1,07918 is the logarithm of the cube root of 1728, Viz. 12. 6. IN COMPOUND INTEREST. To find the amount of any fum for any time, and at any rate at compound interest. RULE. Multiply the logarithm of the ratio (i. e. the amount of 11. for 1 year) by the number of years, and to the product add the logarithm of the principal; the fum will be the logarithm of the amount. What will 451. amount to forborne 12 years, at 6 per cent. per annum, compound interest ? Log. of 1,06, the ratio, is,02533 Multiply by the time 12 ,30396 Add Log. of 45, the principal 1,65321 The fum is 1,95717 which is the logarithm of 90,7-190 145. Anf. 7. IN DISCOUNT AT COMPOUND INTEREST. To find the present worth of any sum of money, due any time hence, at any rate, at compound interest. RULE. From the logarithm of the fum to be dif counted, fubtract the logarithm of the rate multiplied by the time; and the remainder is the logarithm of the present worth. What prefent money will pay a debt of gol. 145. due 12 years hence, discounting at the rate of 6 per cent. per annum ? From the logarithm of 901. 14=1,95717 Sub. product of the Log. of the ratio X by the time. } = 30396 The remainder 1,65421 is the logarithm of 451. Anf. N. Ham. 2 10 0 1 31502 11 18 35 52 10 2 28 70 6 40013,33 568 5003 50016,666134650 31793 87 10 7 10 0 4 13 4 105 60020,00 1 8 00 70023,333 968815 0 58108 122 10 80 026,663 10 13 4 10 006453140 100033,33 1368 12 10 0 7 15 68 175 Federal 347 A TABLE, directing how to buy and sell by the d. . s. d. s. d. ○○○○○○○○ 141234 24 48 666688 141234 Hundred. 3 17 0 I 3 194 I 42 7 140이 318 I 44 7164 4 40 I 1 1 94 4.11 0 I 10 55536 7 18 8 54 14123 34 6 880 I 34 I 58 104 I 80 11 1 10 4 II 1 12 8 11 34 1150 II 141234 5120 514 5 16 05190 1 48 677778888 74 2 89 2 11 4 2 13 8 14123-4 648104 68 128 68150 8 17 4 819 8 I 7호 9 20 74944 84990 I 81 1 914 9 130 9160 949 18 4 9 10 08 94 10 896 3억 6 141234 141234 2 18 4 63 08 I 2 141234 613 0 6154 6 17 8 3 4 1 10 10 12 74 3 12 4 3 14 8 1 141234 34 770 141-23-4 |