
Re: [HM] Theorem of tangents
Posted:
Mar 27, 2001 4:01 PM


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.
We get the tan formula:
b  c  = tan(A/2) * tan((BC)/2) [and cyclically] b + c
from these ones, which are known as "Mollweide Formulae"
b  c  * cos(A/2) = sin((BC)/2) a
b + c  * sin(A/2) = cos((BC)/2) a
Karl Brandan Mollweide (1774  1825) published his formulae in a paper on plane and spheric trigonometry (in 1808, I think).
Antreas

