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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PATNCIDTA MATTIEMATICA.
SFCTIC
De Inventione Orbium Ellipticorum, Parabolicorum  Hyperbolico-
rum ex umbilico dato.
L F MI M A XV.
Si ab Ellipseos vel Ryperbola cujusvis umbilicis duobus S, FI, ad
punctum quodvis tertium V inftectantur rectae duae SV, FIV.
quarum una TIV aequalis sit axi principali ficurae, altera SV a
perpendiculo TR in se demisso bi-
secetur in T; perpendiculum illud
TR sectionem Conicam alicubitan
set: e contra, si tangit, erit LIV
aequalis axi principali fiourae.
Secet enim perpendiculum Y R re-
ctam FTV productam, si opus Fuerie,
In R; ec jungatur SR. Ob aequalCs
S, TV, aequales CrUnE _ recta SK, V R ex anguli Z RS, Z RV.
Onde punctum R erit ad Sectionem Conicam, ec perpendiculum
TR tanset candem: _E CONETA. G. F. D.
PROPOSTTTO ZVIII. PROBLEMA Z.
Daris umbilico  axibus principalibus describere Trajectorias F. lipti
cas e Hyperbolicas, quae transibunt per puncta data,  rectas po-
sitione datas contingent.
Sic S communis umbilicus Rourarum; AB longicudo axis prin-
cipalis Frajectorix cujusvis; F punctum per quod Prajectoria de-
DEE FranSIrC; _ T R recta quam debet tangere. CCnErO F inter-
vallo AB =SP, A orbita sIC EILip (IS, vel AB F SF, RI C2 SIC IIY-
verbolas delcribatur circulus FC. Ad tangentem Y R demittatur
erpendiculum SF, ec producatur idem ad V, uE sic ZV aequalis
centroque V e interrallo AB describatur circulus P IL. IIaC
methodo
L.2
PRIMVS