1ad sq,quæque conſtituat angulum vspangulo hsq& angulum
vshangulo psqæquales, triangula svh, spqerunt ſimilia, & prop
terea vherit ad pqut eſt shad sq,id eſt (ob ſimilia triangula
34[Figure 34]
VSP, hsq) ut eſt VSad SPſeu abad pqueÆquantur ergo
vh& ab.Porro ob ſimilia triangula VSH. vsh,eſt VHad
SHut vhad sh,id eſt, axis Conicæ ſectionis jam deſcriptæ ad
illius umbilieorum intervallum, ut axis abad umbilieorum inter
vallum sh; & propterea Figura jam deſeripta ſimilis eſt Figuræ
apb.Tranſit autem hæc Figura per punctum P,eo quod trian
gulum PSHſimile ſit triangulo psh; & quia VHæquatur ipſius
axi & VSbiſecatur perpendiculariter a recta TR,tangit eadem
rectam TR. q.E.F.
vshangulo psqæquales, triangula svh, spqerunt ſimilia, & prop
terea vherit ad pqut eſt shad sq,id eſt (ob ſimilia triangula
![](https://digilib.mpiwg-berlin.mpg.de/digitallibrary/servlet/Scaler?fn=/permanent/archimedes/newto_philo_039_la_1713/039-01-figures/039.01.091.1.jpg&dw=200&dh=200)
VSP, hsq) ut eſt VSad SPſeu abad pqueÆquantur ergo
vh& ab.Porro ob ſimilia triangula VSH. vsh,eſt VHad
SHut vhad sh,id eſt, axis Conicæ ſectionis jam deſcriptæ ad
illius umbilieorum intervallum, ut axis abad umbilieorum inter
vallum sh; & propterea Figura jam deſeripta ſimilis eſt Figuræ
apb.Tranſit autem hæc Figura per punctum P,eo quod trian
gulum PSHſimile ſit triangulo psh; & quia VHæquatur ipſius
axi & VSbiſecatur perpendiculariter a recta TR,tangit eadem
rectam TR. q.E.F.
LEMMA XVI.