Philosophiae naturalis principia mathematica . um afcenfu de-fcriptum, ^ Aa diiierentiam arcuum: & ftantibus quae in Propo- fitione PRINCIPrA MATHEMATICA. 277 fitione XXV. conftruda & demonftrata funt, erit vis qua corpus Liberofcillans urgetur in loco quovis Z> , ad vim refiftenticB ut arcus ^^*=****CSadarcumCO, qui femiflis eft difierentias illius Aa. Ideoquevis qua corpus ofcillans urgetur in Cycloidis principio feu punctoaltifTimo, id eft, vis gravitatis , erit ad refiftentiam ut arcus Cy-cloidis inter punftum illud fupremum & punftum infimum C adarcum C0\ id eft (fi arcus duplicentur)
Philosophiae naturalis principia mathematica . um afcenfu de-fcriptum, ^ Aa diiierentiam arcuum: & ftantibus quae in Propo- fitione PRINCIPrA MATHEMATICA. 277 fitione XXV. conftruda & demonftrata funt, erit vis qua corpus Liberofcillans urgetur in loco quovis Z> , ad vim refiftenticB ut arcus ^^*=****CSadarcumCO, qui femiflis eft difierentias illius Aa. Ideoquevis qua corpus ofcillans urgetur in Cycloidis principio feu punctoaltifTimo, id eft, vis gravitatis , erit ad refiftentiam ut arcus Cy-cloidis inter punftum illud fupremum & punftum infimum C adarcum C0\ id eft (fi arcus duplicentur) ut Cycloidis totius arcus,feu dupla penduli longitudo, ad arcum Aa. ^ E. 2). PROPOSITIO XXIX. PROBLEMA VI. Pofito quod Corpori m Cycloide ofctllanu refiflttur m du-plicata ratione velocitatis: mvenire reftflentiam in locisfnguUs. Sit Ba (Fig. Prop. xxv.) arcus ofcillatione integra defcripfus,fitque C infimum Cycloidis pun£tum, & C-ZTemiflis arcus Cycloi-distotius, longitudini Penduli aequalisi & quaeratur refiftentia cor-. c p rR (.* poris in loco quovis T>. Secetur refta infinita O^^in punftls OC, T, ^, ealegeut (fi erigantur perpendicula OA,Cr,!P/ §Ecentroque O & Afymptotis Oir,0^defcribatur Hyperbola r/C^fecans perpendicula CT TI, ^^ in r, I^E,ik per punftum /agatur A/parallela Afymptoto O^occurrens Afymptoto OK inK, &perpendiculis Cr& ^E m L & F) fuerit area HyperbolicaTIE^zA aream Hyperbolicam TITCm arcus ^Cdefcenfu cor-poris delcnptus ad arcum Ca afcenfu defcriptura, & area lEF ad Mm 3. aream xyZ PHILOSOPHItE naturalis DkMotu aream ILT ut O^ad OC. Dein perpendiculo il/iVabfcindatur? Hyperbolica TINMqus fit ad aream Hyperbolicam TIE^ucarcusCZad arcum BC defcenfu defcriptum. Et fi perpendi-culo i?G abfcindatur area Hyperbolica TIGR, quae fit ad areamT I E ^wt arcus quilibet CT> ad arcum B C defcenfu toto de-fcriptum : erit refiitentia in loco T> ad vim gravitatis , ut area ^J-7£F—7Gi7ad aream TIENM. Nam eum vires a gravitate oriundae quibus corpu
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