Table of the Reciprocals of Numbers from 1 to 100,000: With Their Differences, by which the Reciprocals of Numbers May be Obtained Up to 10,000,000

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C. & E. Layton, 1865 - Reciprocals - 205 pages
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Page 1 - C2500 and 62501, each to 7 places, and without indices. The sum of these is an initial value, to which adding the differences of the logs. of 62499 and 62501 , or, in general, the difference of the logs. of (n — 1) and (n+1), we readily obtain the logarithms of the difference required, and of the successive differences. The numerical differences being then taken out, the reciprocals of the numbers are obtained by summation.
Page 1 - The difference of two reciprocals, divided by the difference of the corresponding numbers, is I he reciprocal of the product of those numbers.
Page 4 - If the number be 10,000 and under 100,000, find the first four figures in the margin, then on a line with these, and in the column headed by the last figure, the reciprocal will be found.

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