Philosophiae naturalis principia mathematica . in Curva illa Vp i^quampun&um p perpetuo tangit, eritreci-proce ut cubus altitudinis Cp. Namcorpus F, per vim inertiae, nulla alia viurgente, uniformiter progredi poteftin re £ta V P. Addatur vis in centrumC, cubo altitudinis C P vel Cp reci-proce proportionalis, & (per jam de-monftrata) detorquebitur motus ille re&ilineus in lineam curvamVph^. Eft autem hsec Curva Vp\ eadem cum Curva illa V P Q^_in Corol. 3. Prop. XLIinventa, in quaibi diximus corpora hiijus-modi viribus aitra&a oblique afcendere. Prop. XLV. Prob. XXXI. Orbium quifunt Circulis ma
Philosophiae naturalis principia mathematica . in Curva illa Vp i^quampun&um p perpetuo tangit, eritreci-proce ut cubus altitudinis Cp. Namcorpus F, per vim inertiae, nulla alia viurgente, uniformiter progredi poteftin re £ta V P. Addatur vis in centrumC, cubo altitudinis C P vel Cp reci-proce proportionalis, & (per jam de-monftrata) detorquebitur motus ille re&ilineus in lineam curvamVph^. Eft autem hsec Curva Vp\ eadem cum Curva illa V P Q^_in Corol. 3. Prop. XLIinventa, in quaibi diximus corpora hiijus-modi viribus aitra&a oblique afcendere. Prop. XLV. Prob. XXXI. Orbium quifunt Circulis maxime finitimi requiruntur motus folvitur Arithmetice faciendo ut orbis, quem corpusin Ellipfi mobili, ut in Propofitionis fuperioris Corol. 2. vel , defcribit in plano immobili, accedat ad foimam orbiscujus Apfides requiruntur, & qua?rendo Apfides orbis quem cor-pus illud in plano immobili defcribit. Orbes autem eandem ac-quirent iormam, fi vires centripetae quibus defcribuntur, inter fe T col-. C38]collatse, in ^qu?IibiTs altitLdimbus reddantur prnclum V Apfis fumma, & fcribantur T pro altitudine max-ima CV, A pro altitudine quavis alia C P vel Cp, & X pro al-titudinum differentia C V — C P; & vis qua corpus in Ellipficirca umbilicum ejus C ( ut in Corollario 2. ) revolvente move- tur, quaeq; in Corollario 2. erat ut-j^ ?] ^—7 -id eft Ji. G. Jl CHb. ^ + ^ fubftitLlendo T_x pro A, erit ut ^ cub. ——^ ^—j—^ £—-. Reduccnda fimiiiter eft vis alia quajvis centripeta ad fra&ionem cujus denominator fit A cnb., Scnumeratores, facla homologorum terminorum collatione, ftatu-endi funt analogi. Res Exemplis patebit, Exempl. 1. Ponamus vim centripetam uniformem eife, adeoq; ut_—, five ( fcribendo T— X prp A in Numeratore ) ut 1 cub. ~ 2 T q. X-4 3 TXq. ~ Xcub. Q „ . xT ? 2—i ^__ ^ ; & coliatis Numeratorum A cub. terminis correfpondentibus, nimirum datis cum datis & non datis cumnon datis,fiet RGq.—
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