Newton, Isaac - Philosophia naturalis principia mathematica

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1methodo ſive dentur duo puncta P, p,ſive duæ tangentes TR,
tr,ſive punctum P& tangens

29[Figure 29]
TR,deſcribendi ſunt circuli duo.
Sit Heorum interſectio com
munis, & umbilicis S, H,axe illo
dato deſcribatur Trajectoria.
Dico factum. Nam Trajecto
ctoria deſcripta (eo quod PH
+SPin Ellipſi, & PH-SP
in Hyperbola æquatur axi)
tranſibit per punctum P,&
(per Lemma ſuperius) tanget
rectam TR.Et eodem argu
mento vel tranſibit eadem per
puncta duo P, p,vel tanget re
ctas duas TR, tr. q.E.F.

DE MOTU
CORPORUM

PROPOSITIO XIX. PROBLEMA XI.

Circa datum umbilicum Trajectoriam Parabolicam deſcribere, quæ
tranſibit per puncta data, & rectas poſitione datas continget.

Sit Sumbilicus, Ppunctum & TRtangens Trajectoriæ deſcri
bendæ. Centro P,intervallo PSdeſcribe cir

30[Figure 30]
culum FG.Ab umbilico ad tangentem demit
te perpendicularem ST,& produc eam ad V,
ut ſit TVæqualis ST.Eodem modo deſcri
bendus eſt alter circulus fg,ſi datur alterum
punctum p; vel inveniendum alterum punctum
v,ſi datur altera tangens tr; dein ducenda re
cta IFquæ tangat duos circulos FG, fgſi
dantur duo puncta P, p,vel tranſeat per duo
puncta V, v,ſi dantur duæ tangentes TR, tr,vel
tangat circulum FG& tranſeat per punctum V,
ſi datur punctum P& tangens TR.Ad FIdemitte perpendicula
rem SI,eamque biſeca in K; & axe SK,vertice principali Kde
ſcribatur Parabola. Dico factum. Nam Parabola, ob æquales
SK& IK, SP& FP,tranſibit per punctum P; & (per Lem
matis XIV. Corol. 3.) ob æquales ST& TV& angulum rectum
STR,tanget rectam TR. q.E.F.

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