Tables of logarithms of numbers; and of logarithmic sines, tangents and secants, to seven places of decimals: together with other tables of frequent ... of mathematics, and in practical calculations

by Anthony Dumond Stanley

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1854 ...preceding rule, may be found most conveniently by cutting off figures from the divisor, instead of annexing ciphers to the dividend when there would be occasion for this in the common mode of dividing. It will be best however to add one cipher to the dividend at the outset. And when the dividend is thus multiplied by 10, if we multiply the divisor also by 10, the value of the quotient will not be affected. Now for the first 90 pages of the table, the divisors (which are the tabular differences for 1",) have one decimal figure, and multiplying them by 10 makes them all integral. So far as these 90 pages are concerned, the following example will serve to show how the division is to be performed. Let 2442 be the number to be divided, and 335.3 the tabular difference for 1" by which it is to be divided. Then annexing a cipher to 2442 and dividing by the whole'number 3353, we obtain 7 for the first figure of the quotient and 949 for a remainder; if the division is continued, the rest of the quotient will be a to obtain the next figure, instead of annexing a cipher to 949, we cut off the right hand figure of the divisor and divide 949 by 335; the quotient is 2: this multiplied by 335 gives 670, and if we have regard to the figure cut off, so far as to see what ought to be carried from it to the product obtained from the other figures, we find that this product must be increased by 1, as six tenths is nearer one than nothing; then subtracting 671 from 949 we find the remainder 278,which divided by 33 gives 8 for the third quotient figure; multiplying by this and carrying 4 as we should do, we obtain 268; this taken from 278 leaves 10, which divided by 3 gives 3 for a fourth quotient figure. This process may be exhibited as follows. 3353)24420(7....

26 pages, Paperback

Published January 1, 2012