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Elementary Treatment of Logarithms

Published online by Cambridge University Press:  03 November 2016

T. J. I’A. Bromwich
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On previous occasions in the Gazette (and in other places) I have repeatedly expressed the opinion that the most natural line of approach to the logarithmic function is the historical one (followed both by Napier and by Newton) in which the logarithm is effectively defined as an integral. From conversation with boys (from eleven to fourteen) I am still convinced that the idea of an area is much easier to grapple with than the idea of a limit. In spite, then, of other suggestions (which appear in the Gazette three or four times a year on the average), I still accept this method as the best: more details will be found in Appendix II. of my book on Infinite Series (both editions).

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Type
Research Article
Information
The Mathematical Gazette , Volume 14 , Issue 197 , December 1928, pp. 260 - 265
Copyright
Copyright © Mathematical Association 1928

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References

page note 261 * It Is evident that the logarithmic property, log(XY)=log X + log Y, will persist if we divide by any factor μ: and (if μ =log 10) In the new scheme we shall have unity for log 10.

page note 262 * Derived at once from the figure, which givea 1 +cos 2θ=2 cos2 θ, 1 −cos 2θ =2 sin2 θ.

page note 264 * Results equivalent to these formulae are given in several sets of tables, but I do not recollect having seen the theory in any of the commoner text-books; and perhaps I may emphasize the fact that I have saved myself much labour (at various times) by a knowledge of the results.

page note 265 * The actual slip is In the course of Napier’s Second Table, containing ; the error in is indicated on p. 446 of my book, quoted above.