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Posito quod vis centripeta proportionalis sit altitudini seu distantiae loco∣rum a centro, dico quod cadentium tempora, velocitates & spatia descripta sunt arcubus arcuum{que} sinibusversis & sinibus rectis respective pro∣portionales.[illustration]
Cadat corpus de loco quovis A secun∣dum rectam AS; & centro virium S, in∣tervallo AS, describatur circuli quadrans AE, sit{que} CD sinus rectus arcus cujus∣vis
AD, & corpus A, tempore AD, cadendo describet spatium AC, in{que} loco C acquisierit velocitatem CD. Demonstratur eo∣dem modo ex Propositione X. quo Propositio XXXII. ex Pro∣positione XI. demonstrata fuit. Q.E.D.
Corol. 1. Hinc aequalia sunt tempora quibus corpus unum de loco A cadendo provenit ad centrum S, & corpus aliud revolven∣do describit arcum quadrantalem ADE.
Corol. 2. Proinde aequalia sunt tempora omnia quibus corpora de locis quibusvis ad us{que} centrum cadunt. Nam revolventium tempora omnia periodica (per Corol. 3. Prop. IV.) aequan∣tur.