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Topic: [HM] Theorem of tangents
Replies: 5   Last Post: Mar 28, 2001 4:57 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: [HM] Theorem of tangents
Posted: Mar 27, 2001 4:17 PM
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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:
> (a-b)/(a+b) = tan (A-B)/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,

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 high-school 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

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