Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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ad
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sq,
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quæque conſtituat angulum
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vsp
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angulo
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hsq
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& angulum
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vsh
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angulo
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psq
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æquales, triangula
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svh, spq
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erunt ſimilia, & prop
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terea
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vh
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erit ad
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pq
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ut eſt
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sq,
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id eſt (ob ſimilia triangula
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VSP, hsq
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) ut eſt
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VS
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ad
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SP
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ſeu
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Æquantur ergo
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&
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ab.
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Porro ob ſimilia triangula
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VSH. vsh,
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eſt
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VH
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ad
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SH
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ut
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ad
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sh,
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id eſt, axis Conicæ ſectionis jam deſcriptæ ad
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illius umbilieorum intervallum, ut axis
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ab
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ad umbilieorum inter
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vallum
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sh
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; & propterea Figura jam deſeripta ſimilis eſt Figuræ
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apb.
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Tranſit autem hæc Figura per punctum
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P,
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eo quod trian
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gulum
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PSH
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ſimile ſit triangulo
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psh
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; & quia
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VH
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æquatur ipſius
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axi &
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VS
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biſecatur perpendiculariter a recta
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TR,
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tangit eadem
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rectam
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TR. q.E.F.
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LIBER
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PRIMUS.</
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LEMMA XVI.
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A datis tribus punctis ad quartum non datum inflectere tres rectas
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quarum differentiæ vel dantur vel nullæ ſunt.
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Cas.
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1. Sunto puncta illa data
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A, B, C
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& punctum quartum
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Z,
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quod invenire oportet; Ob datam differentiam linearum
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AZ, BZ,
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locabitur punctum
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Z
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in Hyperbola cujus umbilici ſunt
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A
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&
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B,
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&
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principalis axis differentia illa data. </
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MN.
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Cape
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PM.
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