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
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.
LIBER
PRIMUS.
PRIMUS.
LEMMA XVI.
A datis tribus punctis ad quartum non datum inflectere tres rectas
quarum differentiæ vel dantur vel nullæ ſunt.
quarum differentiæ vel dantur vel nullæ ſunt.
Cas.1. Sunto puncta illa data A, B, C& punctum quartum Z,
quod invenire oportet; Ob datam differentiam linearum AZ, BZ,
locabitur punctum Zin Hyperbola cujus umbilici ſunt A& B,&
principalis axis differentia illa data. Sit axis ille MN.Cape PM.
quod invenire oportet; Ob datam differentiam linearum AZ, BZ,
locabitur punctum Zin Hyperbola cujus umbilici ſunt A& B,&
principalis axis differentia illa data. Sit axis ille MN.Cape PM.
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