Discorsi Propositions 2/03-th-03-cor Discorsi Proposition2/03-th-03-cor

 COLLARIUM. COROLLARY Hinc colligitur, tempora descensuum super planis diversimode inclinatis, dum tamen eorum eadem sit elevatio, esse inter se ut eorum longitudines. Hence we may infer that the times of descent along planes having different inclinations, but the same vertical height stand to one another in the same ratio as the lengths of the planes. Si enim intelligatur aliud planum AM ex A ad eundem horizontem CB terminatum, demonstrabitur pariter, tempus descensus per AM ad tempus per AB {10} esse ut linea AM ad AB; ut autem tempus AB ad tempus per AC, ita linea AB ad AC; ergo, ex aequali, ut AM ad AC, ita tempus per AM ad tempus per AC. For consider any plane AM extending from A to the horizontal CB; (Condition 2/03-th-03) then it may be demonstrated in the same manner that the time of descent along AM is to the time along AB as the distance AM is to AB; (Condition 2/03-th-03) but since the time along AB is to that along AC as the length AB is to the length AC, it follows, ex aequali, that as AM is to AC so is the time along AM to the time along AC.

 Discorsi Propositions 2/03-th-03-cor Discorsi Proposition2/03-th-03-cor