> > 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, 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 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.