Philosophiae naturalis principia mathematica . hac ipfa ratione. Prop. XLI. Prob. XXVIII. Pejita cttjufcunq\ genervs z>i ccntripeta &> conceffis figuraruiu curvili- nearum quadraturis^ requiruntur tum TrajeBorix in quibm corpo- ra movebuntur^ tum tempora motuum in TrajeBoriis inventis. Tendat vis quaelibet ad centrum C & invenienda fit TrajecToria VlTKkz Detur circulus FXIcentro C intervallo quovis CV defcriptus, centroqj eodem defcribantur alii quivjs circuli JD, KE KE traje&oriam fecantes in I Sc K re&amq; CVm D & E. A-ge tum recTam CNIX fecantem circulos KE^VYin N & X,tumreclam CKTocc
Philosophiae naturalis principia mathematica . hac ipfa ratione. Prop. XLI. Prob. XXVIII. Pejita cttjufcunq\ genervs z>i ccntripeta &> conceffis figuraruiu curvili- nearum quadraturis^ requiruntur tum TrajeBorix in quibm corpo- ra movebuntur^ tum tempora motuum in TrajeBoriis inventis. Tendat vis quaelibet ad centrum C & invenienda fit TrajecToria VlTKkz Detur circulus FXIcentro C intervallo quovis CV defcriptus, centroqj eodem defcribantur alii quivjs circuli JD, KE KE traje&oriam fecantes in I Sc K re&amq; CVm D & E. A-ge tum recTam CNIX fecantem circulos KE^VYin N & X,tumreclam CKToccurrentem circuloFX2in Y. Sint autem pun&aI Sc K fibnhvicem viciniflima, &pergat corpus ab Vpev I>T8cK ad \ b fitq^ A ajtitudo illa de qua corpus aliud cadere debetut in loco D velocitatem acquirat aequalem velocitati corporisprioris in J; & ftantibus quae in Propofitione XXXIX, quoniamlineola IK^ dato tempore quam minimo defcripta, eft ut velocitasatq; adeo ut latus quadratum areae ABFD, Sc triangulumICK. tempori proportionale datur, adeoq, KN eft reciproce utaltitudo 1C, id eft, fi detur quantitas aliqua Q^ & altitu- uoIC nominetur A, ut^r-j quam nominemus Z. Ponamuse- am efle ma^nitudinem ipfius £_ut Cit V ABFD in aliquocafuadZuteftltfad KN, Sc erit femper V ABFD ad Z utlif adKN, Sc ABFDadZZ ut IKquad. ad KN quad. Sc divifimABFD—ZZ ad ZZ ut INquad. ad KNquad. adeoq; V ABFD-ZZ ad Z_ut IN ad KN, Sc propterea AxKNx- ^quale C ™9 1 gmle—g-glff Unde cum YXxXC fit ad AxKN VABFD-ZZ- in duplicata ratione YC ad KC, erit re&ang. YXxXC sequale QxlNxCXquad. ? ,. —_^—~==. Igiturfim perpendiculoi^f capiantur AA^/ABFD — ZZ 0_ _j2x C X ^M/i femper Db, Dc ipfis ^-^^f^ & ^A^TeFD^TZ sequales refpe£Hve, & defcribantur curvae lineae aby cd quaspun&a i>, c perpetuo tangunt; deq; punclo^ad lineam ^Ceriga-tur perpendiculum Va d abfcindens are^s curvilineas VD b a, VD~dcy & erigantur etiam ordinatae E%, Ex: quoniam reclangu-lum Db xlN {euDb^E sequale eft dimidio reda
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