Discorsi Propositions 2/23-pr-09-schol5 Discorsi Proposition2/23-pr-09-schol5

 Quod vero sumptis utcunque duobus punctis D, E, aequaliter ab angulo B remotis, transitus per DB fiat {30} tempore aequali tempori reflexionis per BE, hinc colligere possumus. If now we assume any two points D and E, equally distant from the vertex B, we may then infer that the descent along BD takes place in the same time as the ascent along BE. Ducta DF, erit parallela ad BC; constat enim, descensum per AD reflecti per DF: quod si post D mobile feratur per horizontalem DE, impetus in E erit idem cum impetu in D; ergo ex E ascendet in C; ergo gradus velocitatis in D est aequalis gradui in E. Draw DF parallel to BC; we know that, after descent along AD, the body will ascend along DF; or, if, on reaching D, the body is carried along the horizontal DE, it will reach E with the same momentum [impetus] with which it left D; hence from E the body will ascend as far as C, proving that the velocity at E is the same as that at D.

 Discorsi Propositions 2/23-pr-09-schol5 Discorsi Proposition2/23-pr-09-schol5