Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1
LIBER
PRIMUS.
SECTIO IV.
De Inventione Orbium Elliptieorum, Parabolieorum & Hyperbolico­
rum ex umbilico dato.
LEMMA XV.
Si ab Ellipſeos vel Hyperbolæ cujuſvis umbilicis duobusS, H, ad
punctum quodvis tertiumV inflectantur rectæ duæSV, HV,
quarum unaHV æqualis ſit axi principali figuræ, alteraSV a
perpendiculoTR in ſe demiſſo bi-
28[Figure 28]
ſecetur inT; perpendiculum illud
TR ſectionem Conicam alicubi tan­
get: & contra, ſi tangit, eritHV
æqualis axi principali figuræ.
Secet enim perpendiculum TRre­
ctam HVproductam, ſi opus fuerit,
in R; & jungatur SR.Ob æquales
TS, TV,æquales erunt & rectæ SR, VR& anguli TRS, TRV.
Unde punctum Rerit ad Sectionem Conicam, & perpendiculum
TRtanget eandem: & contra. Q.E.D.
PROPOSITIO XVIII. PROBLEMA X.
Datis umbilico & axibus principalibus deſcribere Trajectorias Ellipti­
cas & Hyperbolicas, quæ tranſibunt per puncta data, & rectas po­
ſitione datas contingent.
Sit Scommunis umbilicus figurarum; ABlongitudo axis prin­
cipalis Trajectoriæ cujuſvis; Ppunctum per quod Trajectoria de­
bet tranſire; & TRrecta quam debet tangere. Centro Pinter­
vallo AB-SP,ſi orbita ſit Ellipſis, vel AB+SP,ſi ea ſit Hy­
perbola, deſcribatur circulus HG.Ad tangentem TRdemittatur
perpendiculum ST,& producatur idem ad V,ut ſit TVæqualis
ST; centroque V& intervallo ABdeſcribatur circulus FH.Hac

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