Newton Principia Lemma IX (and X)
AD:Ad :: AE:Ae
Rect. triangle ABD is always similar to rect. triangle Abd and same with ACE and Ace. Slide points B and C until they meet A; Abd and Ace will coincide with Afd and Age. To what areas are ABD and ACE always proportional as they recede toward A? So ultimately to what areas are they in proportion, and to what sides are their areas in a duplicate ratio?