SE N

Namgq; ex demonftratione.{uperioris Propofitionis, temporaquibus arcus quivis fimiles P.Q_& pgq deferibuntur,{unt in dimidiata ratione diftantiarum CP 8& SP vels p, hoc eft, in dimidia-ta, ratione corporis S ad{ummam corporum SP. Et compo-nendo,{ummz temporum quibus arcus omnes fimiles P 0.& P4deferibuntur, hoceft tempora tota quibus figurz totz fimiles de-feribuntur,{unt.in eadem dimidiata ratione. Q.E..D.

4 Prop. LX. Theor XXL

Si corpora duo S&» P, wiribus quadrato difkantie fung reciproce pro-\ portionalibus fe mutno trahentia, revoluntur circa'grawvitatis cen-trum commmwnne: dico quod Ellipfeos, quam corpus alterutrum P hocmin circa alternm S defcribit, Axis tranfverfus erit ad dxem tranf-verfum Ellipfeos, quam corpus idem P. circa alterum quiefcens Seodem tempore periodico defcribere poffet, ut fumma corporum dmu-orum S+P ad primam dunarum medie proportionalium inter hanc

Jummamı 9 corpus illnd alterum S.

Nam fi deferiptz Ellipfes eflent fibi invicem xquales, tempo-ra periodica, per Theorema fuperius, forent. in dimidiata ratienecorporis S ad{ummam corporum: S+P,. Minuatur in hac rati-ne tempus periodicum in Ellipfi pofteriore,& tempora periodi-ca evadent xqualia, Ellipfeos autem axis. tranfverfüs. per Theo-rema VIL minuetur in ratione cujus hac.eft fefquiplicata, id eftin ratione, cujus ratio Sad S-+P,eft triplicata; adeoq; ad ax-em tran{verfum Ellipfeos ‚alterius, ut prima duarum medie pro-portionalium inter S+P& Sad S-+P. Et inverfe, axis tranf-verfüs Ellipfeos circa corpus mobile deferiptz erit ad axem tranf-‚ verfum deferiptz circa immobile, ut. S-+ P ad primam duarum me-„die proportionalium inter S+P&$..Q.E.D.

‚Prop.