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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 64, page id 1041163592:0098
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MIipiuiI
64
PHTLOSODMLE NATDRALIS
Be Moro ad NI  BE Cs M N ad AB, et crecta P R perpendiculari ad AB,
oncoron demissaque Z R perpendiculari ad P Re; crit, ex natura hujus FIY
verbolxe, Z R ad A Z uE est M N 2d AB. Simili discursu punctum
locabitur in alia IIrperbola, cujus umbilici Tunt A, C ec princi-
palis axis differentia inter Z e C Z. dueique porest S ips AC
perpendicularis, ad quam (i ab LIrperbolae hujus puncto quovis L
demittatur normalis Z 5, haec fuerit ad Z ut est disterentia inter
AZ e C= ad AC. Dantur ergo rationes iplarum Z R e Z, d
ad AZ, e idcirco datur carun-
dem =R _c ZS ratio ad invicem;
ideoque A rectae R P, SO) ConCUT-
ranE in P, SE aGatUE TZ, Fgura
TRZS, dabitur specie, et recta
TZ in qua punctum Z alicubi 10-
cacur, dabitur positione. Padem
methodo per IIxperbolam ter-
tiam, cujus umbilici TUnE B eC
ec axis principalis ditterentia re-
ctarum BZ, C Z inveniri pocest
alia recta in qua puctum Z locatur.
Elabicissaurem duobus Locis recti-
lineis, habetur punctum quaesitum L in eorum interfectionc. d. F. l.
Ca5. 2. Si dux ex tribus lincis, puta AZ _ B Z aequantur, pun-
ctum Z locabitur in perpendiculo bisecante distantiam AB, ee 10-
cus alius rectilineus invenictur ut suPra. G. F. I.
Cas. 3. Si omnes eres aequantur, locabitur punctum Z in CCnErO
Circuli per puncta A, B, C transcuntis. d. F. l.
Solvitur etiam hoc Lemma problematicum per Librum Pactio.
num Apollonii a Vieta reltitutum.
PROPOSITIOZXI PROBLEMA XITI.
Trajectoriam circa datum umbilicum describere, quae transibit per
puncta data e rectas positione datas contine et.
Decur umbilicus 5, punctum P, _ FanSeNS Z R, Se invenien-
dus SiE umbilicus alter FI. Ad tangentem demitte perpendiculum
ST, e produc idem ad Y, ut sIE YY aequalis ST, _ Crit YFI x-
qualis axi principali. Junse SP, FIP, ec erit S P differentia inter
D et anem principalem. Hoc modo s dencur plures cansen-
1C5
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