Philosophiae naturalis principia mathematica . nicis Seftionibus, & cora-ponentes corporum Sphasricorum Vires centripefas eadem Lege ,in recefiTu a centro ,decrefcentes vel crefcentes cum feipfis: Quodefl notatu dignum. Cafus caeteros, qui cdnclufiones minus elegan-tes exhibent, figillatim percurrere longum elfet. Malim cundosmethodo generaU fimul comprehendere ac determinare, ut fequitur. L E M M A XXIX. Si defcrthantur centro S ctrculi4s qmltbet AEB,^ centro Pctrcult duo E F, e f, fecantes pftorem in E, e , /ineam-que P S /^ F , f; ^ adV% demittanturperpendtcula E D,ed. dtco quody ft diftant
Philosophiae naturalis principia mathematica . nicis Seftionibus, & cora-ponentes corporum Sphasricorum Vires centripefas eadem Lege ,in recefiTu a centro ,decrefcentes vel crefcentes cum feipfis: Quodefl notatu dignum. Cafus caeteros, qui cdnclufiones minus elegan-tes exhibent, figillatim percurrere longum elfet. Malim cundosmethodo generaU fimul comprehendere ac determinare, ut fequitur. L E M M A XXIX. Si defcrthantur centro S ctrculi4s qmltbet AEB,^ centro Pctrcult duo E F, e f, fecantes pftorem in E, e , /ineam-que P S /^ F , f; ^ adV% demittanturperpendtcula E D,ed. dtco quody ft diftantia arcuum E F, tiin infimtmnminui tntelligatur , ratio ulttma Itnea evanefcentis D d ^dItneam evanefcentem F f ea fit, qu^e Itnece ^Ead ItneamPS. Nam PRINCIPIA MATHEMATICA. 183 .,Nam fi linea T e fecet arcum EF m q -, &: refta Ee, quae cumarcu evanefcente ^*^ coincidit, produfta occurrat redtae ^*? in 7;& ab S demittatur in T E normalis SG: ob fimilia triangu1a2)7£^,dTe, T>ES; erit©Jad^?, ut T>T&dTE, feu T>E ad E S;. LlBERPlll MU*. ,& ob triangula £? f ^, EtyC TperLem. viii, &Corol,^. Lem vii.)fimilia, erit ^^ad^^ feu Ff, ut ES ad SG; & ex Eequo, 2)^ad FZ-uc ©£ ad J*G; hoc eft (ob fimilia triangula TT>E, TGS)uiTEzdiTS. ^;. PROPOSITIO LXXIX. THEOREMA XXXIX. St fuperfictes ob lautudmem mfimte dimmutam jamjam eva-nefcem E F fe, convoluttone fm ctrca axem P S, defcrihatfolidum Sphartcum concavo-convexum , ad cujus pariicu^las ftngulas aquales tendant dequales vtres centrtpetce: di-co qtiod Vts , qua foltdum tllud trahtt corpufculum fitumm^ j efi in rattone compofttaex ratione foltdt DE^X F f^ rattone vts quaparttcula data tn loco Vitraheret tdem. corpufculum. Nam fi primo confideremus vim fuperficiei Sphasricffi FE, quagconvolutione-arcus FE generatur, & a linea de ubivis iecatur in r;erit fuperficiei pars annularis , convolutione arcus rE genita , utiineola T>U-, manente Sphaerffi radio ^*^, (uti demonltravit Ar-chimedes in Lib. de Spbara & Cyttndro.) Et
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