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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 65, page id 1041163592:0099
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PRTNOTPTA NATHIEMAEICAS
ces TR, vel plura puncta P, derenietur semper ad lincas tor L IBEU
rTP vel P HI, 2 dictis punctis Y vel
P ad umbilicum II ductas, qux vel
aequantur axibus, vel datis longitu
dinibus SF disterune ab iildem, at-
que adeo quae vel aequantur sibi invi-
cem, vel datas habent differentias; e
inde, per Lemma superius, datur umbi-
licus ille alter FI. Hlabitis autem um-
bilicis una cum axis longitudine (quae
vel est YHI; vel A Trajectoria FIlipsis eAt, PTY F SF; Cin LY.
verbola, P H -SP) habetur Trajectoria. 8. F.. 1.
Scholium.
Catus ubi dantur eria puncta sic solvitur expedicius. DenEUE
puncta B, C, D. Junctas BC, C D produc ad F, F, UE SIE F B ad
FC uE SB adSC, eE FC ad F D AE SC ad SD. Ad F. F ductam
ex productam demitre normales SG, BII, inque CS infinite
producta cape C  ad AS e G a ad aS ut eAt HB ad BS; de crit
A vertex, e Aa axis principalis Trajectorixe: quae, perinde ut Ci
major, aequalis, vel minor tuerit quam A5, erit EIlipsis, Parabola
vel Hyperbola; pun-
eto a in primo casu
cadente ad candem
Partem lineae G Y
cum puncto A; in
secundo casu abeunte
in intinicum; in certio
cadence ad concrari-
am partem lincae GF.
Nam (I dCMIETANEUE?
2d C F perpendicula
CT, DK; erit TC ad TYB UE F C 2d F B, hOc eH, uESC ad SB; de vi-
cissim TC adSC uETIB ad SB SIvC UEC A adS . EE Simili aEBUMCNEO
probabitur ene RD ad SD in cadem ratione. Pacent ergo puncta B,
C. Din Conifectione circa umbilicum Sita delcripta, ut rectae omnes
ab umbilico S’ad singula Sectionis puncta ductxe, sint ad perpendicula
a punctis iildem ad rectam G F demissa in data illa ratione.
Mechodo haud mulcum dissimili hujus problematis solutionem
cradir Clarissimus Ceometra de la Flire, Conicorum luorum L. ib.
E
VIIL. PFOD. ZZV
PRIOS
SE CTI