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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
James Thomson
Affiliation:
Professor of Mathematics in the University of Glasgow.
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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
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 14 , Issue 1 , 1839 , pp. 217 - 223
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.