linguistic:paraphrasing
Case of an obtuse angle

Euclid proved this theorem by applying the Pythagorean theorem to each of the two right triangles in Fig. 2 (AHB and CHB). Using d to denote the line segment CH and h for the height BH, triangle AHB gives us

and triangle CHB gives

Expanding the first equation gives

Substituting the second equation into this, the following can be obtained:

This is Euclid's Proposition 12 from Book 2 of the Elements. To transform it into the modern form of the law of cosines, note that