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Re: [HM] Theorem of tangents
Posted:
Mar 27, 2001 4:17 PM


On Tue, 27 Mar 2001, Francine F. Abeles wrote:
> > I'm interested in finding a reference in English to the origin and use of > the theorem of tangents: > > (ab)/(a+b) = tan (AB)/2 x tan C/2, where a,b are the sides of a > triangle; A,B,C are its angles. >
Hello Fran. I expect that what you really want is a reference that tells you who first found this theorem, which I can't give, although I think it likely that Napier was the originator. But I can give you two English references of moderate age wherein I've seen the theorem, namely
A.P.(?) Workman's "Memoranda Mathematica"
and a trigonometry textbook by Durell
which I'd guess are respectively just under and just over a century old.
Unfortunately my copies of both books are at home, so I can't be more precise just now.
The Workman book is a wonderful one that I first met when I was at school in the 50s, learned a lot from then, and still occasionally use as a reference.
The Durell of the other book is not the British Clement V. Durell who wrote many other highschool textbooks, but an American who taught at the Lawrenceville School (near Princeton). It is unusual for a textbook in containing some historical remarks about the origins of trigonometry.
John Conway



