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XI.—Investigation of a New Series for the Computation of Logarithms; with a New Investigation of a Series for the Rectification of the Circle

Published online by Cambridge University Press:  17 January 2013

James Thomson
Affiliation:
Professor of Mathematics in the University of Glasgow.

Extract

The series l(1+ x) = M (x—½ x2 + ⅓ x3—¼ x4+&c.), discovered by Mercator, seems to be the origin from which, directly or indirectly, all the series may be derived which are usually employed in the computation of logarithms. A series, which affords remarkable facilities for such computations, and which lately occurred to me, may be investigated in the following manner.

Type
Transactions
Copyright
Copyright © Royal Society of Edinburgh 1839

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References

page 218 note * If the modulus of the common logarithms be supposed to be known, the common logarithm of 2 may be computed with great ease by finding, by Mercator's series, the logarithm of 1 + 0.024; by adding to the result 3, the logarithm of 1000, and thus finding the logarithm of 1024; and, lastly, by dividing by 10, because 1024 is the tenth power of 2.