...the multiplication of numbers is performed by adding together their logarithms ; division of numbers, by subtracting the logarithm of the divisor from that of the dividend ; involution of numbers, by multiplying (he logarithm of the root into the logarithm or index of the...

...means of the property (203), relating to division, we obtain the logarithm of a fractional number, by subtracting the logarithm of the divisor from that of the dividend. 205. By supposing a first table of logarithms already constructed, it is easy to construct as many...

...numbers in the tables ; for, by the property of division (No. 215) we obtain the logarithm of a fraction by subtracting the logarithm of the divisor from that of the dividend. 218. If we had a table of logarithms constructed, it would be easy to construct from this as many as...

...And thus might any number, within the limits of our Tables, be divided by any smaller number, merely by subtracting the logarithm of the divisor from that of the dividend, and then finding the difference. 326. It appears, however, in the latter instance, that we do not find,...

...in the tables ; for, by the property of division (Art. 242), we obtain the logarithm of a fraction by subtracting the logarithm of the divisor from that of the dividend. 246. Resuming the equation 10*=y, if we make a;=0, 1, 2, 3, 4, 5, ... n— 1, n. we have y=l, 10, 100,1000,...

...altering their nature. Multiplication is performed by adding the logarithm ot tin, factors; and Division by subtracting the logarithm of the divisor from that of the dividend. If a number of successive multiplications and divisions, without any intervening additions or subtractions,...

...numbers in the tables; for, by the property of division (Art. 259), we obtain the logarithm of a fraction by subtracting the logarithm of the divisor from that of the dividend. 263. Resuming the equation 10*=y, if we make a;=0, 1, 2, 3, 4, 5, ... n— 1, n. we have y=l, 10, 100,1000,...

...73 79 83 89 97 1.8512583 1.8633229 1.8976271 1.9190781 1.9493900 1.9867717 quotient = the remainder obtained by subtracting the logarithm of the divisor from that of the dividend. _, ma z-» ji im\ ii ror — = —Q = a , and .-. logl— ) =x— y=iogm— logn. n a" ' evn' . & to...

...by member, we have a1~* = y-: : hence a; — a;' = log (^Л or, log у — log y' = log ^ j That is, the logarithm of a quotient is obtained by subtracting...logarithm of the divisor from that of the dividend. 11. If all the numbers y, >/, y", &c. be equal in equation (2), and there be m of them, this equation...

...dividend, is to be divided by any other, the divisor, the logarithm of the result or quotient is found by subtracting the logarithm of the divisor from that of the dividend, and then the quotient itself can be found from its logarithm. The only difficulty which division will...