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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 62, page id 1041163592:0096
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IIIIIMIIIIII
62
PHITLOSOPMLA NATURALIS
DE MOrD UE V_ = VK ad RS = XS, id CA UE 2V X ad 2 H X dC 2 R X ad
Conronvn 25 X, adeoque uc V X ad IIX ec FI X ad SX, similia crunt eri-
angula VX FL, TIXS, eE PrOPterCa V IP erit ad S IPUEV X ad XII,
adeoque ur VK ad KS. Haber isitur Trajectorix descripex axis
principalis  eam rationem ad iplius umbilicorum dictanciam SII,
quam habet Prajectorix describendae axis principalis ad ipsius um-
bilicorum distantiam, ec propterea ejuldem eMt specici. Insuper cum
VHI, VHI aequentur axi principali, ex VS, V5 2 rectis TR +p
Derpendiculariter bisecentur, liguet, ex Lemmate XV, rectas illas
Prajectoriam descripEaM TANGCFC. O. F. F.
Ca5. 3. Dato umbilico S describenda sc Trajectoria quae rect.
am P R tanget in puncto dato R. In rectam F R demitte perpen.
dicularem SF, de produe eandem ad V, uE SIETV aqualis SF. Junsc
VR, ec rectam VS intinite productam seca in R ec R, ita ut RE
VK ad SK X V R ad St ut tillipscos describendae axis principalis
ad distantiam umbilicorum; circuloque super diametro RK de-
seriDEO, seCeTUE producta reCtA V R in YY, et umbilicis S, F, 2XC
principali rectam VII aequante, describatur Prajcetoria. Dico ta-
ctum. NTamque VFY ese ad
SFPUEVK ad SK, acque adeo
uc axis principalis Trajectorix
describendae ad distanciam um-
bilicorum ejus, patet ex demon-
Aratis in Casu secundo, eE PrOD
terea Trajcctoriam delcriptan
ejusdem esse speciei cum delcri-
Benda; reCFAM VeTO TR qua an-
1E
DuluS V RS bisecatuT, tangere Frajectoriam in punCto R, PATCE Cx
Conicis. 9. F. F.
Cas. 4. C irca umbilicum sdescribenda jam siE FTrajectoria APB,
quae eangat rectam TR, transcatque per punctum quodris P extra
tansentem dacum, quaeque similis sc Figura apb, 2xc principali
ab ec umbilicis s, h descripeae. In tangentem T R demitte per-
Dendiculum SF, et produe idem ad V, uE sit YV aequalis SF. AN-
sulis autem VSP, SVP Fac ansulos Bsq, shg aequales; cen-
eroque q ec interrallo quod sic ad a b ut SP adS delcribe circu-
lum secantem Figuram apb in p. Junsc sp ec agC SFY quae sic 2d
SB ut CA SP ad sp, quaeque angulum P SFansulop sh ec angulum
SII angulo psq aequales constituat. Denique umbilicis 5, (7,
de axc principali AB distantiam VI aequante, delcribatur sectio
Conica. Dico Factum. Nam si agatur s2 quae sit ad sp ut cAt sI
nonoononaiamon
ac
NH.NNI IHAIAMGIHMHAI SINHESESHEIL NPHBEBIN EMMMEMGIMMEMM