Date: Mar 27, 2001 4:01 PM
Author: Antreas P. Hatzipolakis
Subject: Re: [HM] Theorem of tangents

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.

We get the tan formula:

b - c

----- = tan(A/2) * tan((B-C)/2) [and cyclically]

b + c

from these ones, which are known as "Mollweide Formulae"

b - c

----- * cos(A/2) = sin((B-C)/2)

a

b + c

----- * sin(A/2) = cos((B-C)/2)

a

Karl Brandan Mollweide (1774 - 1825) published his formulae in a

paper on plane and spheric trigonometry (in 1808, I think).

Antreas