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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 63, page id 1041163592:0097
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PRINOIPTA MATHEMATICA.
63
2 sh aleopsq aescateo, cclansula 5vh, spg erune similian es PFOP. PuIMVS.
cerea vh erie ad pq uc eAt sh ad 59, id est (ob similia criansula
2d 59, quaeque constituat ansulum v sp ansulo hsq ee angulum LIven
VSF, B59) uc est VS ad SF seu ab ad pg: AE quanEuE ergO
vB e ab. Porro ob similia criangula VSFF. VsB, CA VII 2d
SFF ut Vh ad sh, id est, axis Conieae sectionis jam descripex ad
illius umbilicorum interrallum, ut axis ab ad umbilicorum inter-
vallum sh; e propterea Figura jam deseripea similis eA Pigurx
apb. Transit aurem haec Figura per punctum P, eo quod trian-
culum PSFI simile sic criangulo p sB; ec quia V FI aequatur ipsius
axi ex VS bisecatur perpendiculariter a recta FR, tangit eadem
rectam TR. 9. F. F.
L F MM A ZVI.
a datis tribus punctis ad quartum non datum inftectere tres rectas
quarum differentiae vel dantur vel nullae sunt.
Cas. L. Sunco puncta illa data A, B, C ee punctum quartum Z.
quod invenire oportet; Ob daram differentiam lincarum AZ, BZ
locabitur punctum Z in Elyperbola cujus umbilici sunE A ec B, ec
Crincipalis axis differentin illa data. Sit axis ille M LVI. C apC P M.
ac