Philosophiae naturalis principia mathematica . 9T, necnon^^ tangentipa-rallelam & occurentem tum diametro TPG in^, tum diftantiseSP in x. Jam ob fimilia triangula Px^, MS P & aequalia uniuslateraSM, SP, aequalia funt alterius latera Px feu QK &lP<, ex Conicis, quadratum ordinatae Qjv a:quale eft re&angulofub laterereclo&fegmentodiametri P^, id eft ( per )re&angulo 4 P£x Pv feu^PSx Q_K; & pun&is P& 2_coeun-tibus, ratio Qjc ( per Lem. 8. ) fit xqualitatis. ErgoQxq. eo incaiu, aequale yeft re&angu-lo ^ Eft au-teni ( ob x-quales angu-los Qjc T, MPS, ?M0 )Qxq. ad Q7f.
Philosophiae naturalis principia mathematica . 9T, necnon^^ tangentipa-rallelam & occurentem tum diametro TPG in^, tum diftantiseSP in x. Jam ob fimilia triangula Px^, MS P & aequalia uniuslateraSM, SP, aequalia funt alterius latera Px feu QK &lP<, ex Conicis, quadratum ordinatae Qjv a:quale eft re&angulofub laterereclo&fegmentodiametri P^, id eft ( per )re&angulo 4 P£x Pv feu^PSx Q_K; & pun&is P& 2_coeun-tibus, ratio Qjc ( per Lem. 8. ) fit xqualitatis. ErgoQxq. eo incaiu, aequale yeft re&angu-lo ^ Eft au-teni ( ob x-quales angu-los Qjc T, MPS, ?M0 )Qxq. ad Q7f. ut ?Sq. ad SNq. hoc eft ( per Corol. I. Lem. X IV. ) ut P S adAS, id eft ut 4P^x£R ad /^ASxQJL, & inde ( per Lib. V Elem. ) Qjq. & 4^8 xQJl aequantur. Ducantur hafC^qualiainl^&flet^i^S: *qUale SP,^S:QJv. QJv & propterea Cper Corol. Theor. V.) vis centripeta eft recipro- ce ut S?q. x 4^S, id eft, ob datam^^S, reciproce in dupli- cata ratione diftaiitias S P. CL E. I. Corol. I. Ex tribus noviOnnis Propofitionibus confequens cfr,quod fl corpus quodvis P, fecundum lineam quamvis reclam P R,quacunq; cum velocitate exeat delocoP, & vi centripeta qua* fitreciproce proportionalis quadrato diflanf iae a centro, f imul agitc-tur ; movebitur hoc corpus in aliqua fedionum Conicarum unabi-licum habente in centro virium; & contra. Corol. il velocitas,quacum corpus exit de loco fuo P, ea f7r,qua lineola P K in minima aliqua temporis particula defcribi po-flit, & vis centripeta potis fit eodem tempore corpus idemmove-re per fpatium QJK.: movebiturhoccorpus ki Conica aliquafeft- ione cujuslatusreclum eft quantitas illa- f-quae ulcimo fit ubi lineolae P iv., QJl in infinitum diminuuntur. Circulum in hisCoroIIariis refero ad Ellipfm, &: cafum excipio ubi corpus recladefcendit ad centrum. $} corpora plura revohvantur circa cenirum commune^ & <vis centri-peta decrefcat in diiplicata ratione dtjiantiarnm a centro \ dico
Size: 2281px × 1095px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthornewtonisa, bookdecade1680, bookidphilosophiaenat00newt
