Philosophiae naturalis principia mathematica . p;um mutata, vertatur in Hyperbolam, movebitur corpus inhujus perimetro, vi centripeta in centrifugam verfa. XI SECT t:& ] S E C T. III. De motu Corpornm in Conicis Se&ionibtts Prob. VI. Revohatur corpus m EUipfii Requiritnr lex <vk centripet* tenden- tis ad umbilicnm EUipfeos. Efto Ellipieosfuperioris umbilicus S. Agatur SP fecans Ellip-feos tum diametrum DK in £, tum ordinatim applicatam Qjvin x, & compleaturparallelogrammum QxPR. Patet £P x-qualem effe femi- B axi majori AC^ eo quod a£ra ab altero Ellipfeos umbilico Hlinea
Philosophiae naturalis principia mathematica . p;um mutata, vertatur in Hyperbolam, movebitur corpus inhujus perimetro, vi centripeta in centrifugam verfa. XI SECT t:& ] S E C T. III. De motu Corpornm in Conicis Se&ionibtts Prob. VI. Revohatur corpus m EUipfii Requiritnr lex <vk centripet* tenden- tis ad umbilicnm EUipfeos. Efto Ellipieosfuperioris umbilicus S. Agatur SP fecans Ellip-feos tum diametrum DK in £, tum ordinatim applicatam Qjvin x, & compleaturparallelogrammum QxPR. Patet £P x-qualem effe femi- B axi majori AC^ eo quod a£ra ab altero Ellipfeos umbilico Hlinea HZipfiEC parallela, ( ob x- quales C S, C H ) sequcntur ES,£I,a- deo ut £P femifum- ma lit ipfarumPS, PJ, idcft(fobpa- rallelas HI, Pit& angulos xanales IP R, HPZ ; ipfo- rum P S, P H, qux conjunciim axern totum iAC ada-quant. Ad SP demittatur perpendicularis 0Ty & Ellipfeos Iatere reclo principali (Tcu iBC quad. ^ d-fio ^ crk. L x fiR ad L x P */ ut £R ad ? *; ideftutf£(f feu^C)ad?C: & LxP^ad G-z/P ut LadG^ Sc. &GvPad Qv CDqmul-jk(per Leni. VlJf.)^z/ Qx quad.^undiis QJk P coeuntibus, efr ratio arqua-litatis, & gjc qnad. feu £5/ f*Mfc/. eft ad OJJ qttad. ut E P P Fquad^ id eft ut C A qnad. ad P Fquad. tive (per Lem. XILJ)ut ^j^. ad CBquad, Et coivjun&is his omnibus rationi-bus, L x£JL fit ad gjT qnad. ut ^C ad P C -fL ad C<v-f C P c/adCE^-fCD^.adCi^.id eft utACxL( feu 2C£l7.)xC-P ^. adPCxG^xCB^. five ut 2 PC ad G^. Sed punclis OSc P coeuntibus, aequantur 2 P C SlGv. Ergo & his proportio-nalia LxQJK 8c Qjtquad. aequantur. Ducantur hax aqualiain —J~ & fiet L x S P y ^- % Ergo ( per l ^ QK &-*.*- Theor. V.^)vis centripeta reciproce efcut L xS P^. ideft recipro-ce inratione duplicata diftantiae S P. QJF. I. F adem brevitate qua traduximus Problema quintum ad Parabo-lam, & Hyperbolam, liceret idem hic facere: verum ob dignita-tem Problematis & ufum ejus in fequentibus, non pigebit cafuscaeteros demon
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