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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 82, page id 1041163592:0116
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MIIIIVIIHI
82
PFIILOSOPETTA NATORALIS
DEMorD Hac fgura tangentes illae duae cradene sibi inricem parallelae, a lal
honroro gens certia hec parallela rectae per
puncta duo data transcunti. Sunte
Bi, kD tangentes illae dux parallelae,
ik tangens tertia, e hl recta huic
parallela transiens per puncta illa
an b, per quae Conica sectio in hac
fgura nora transire debet, et pa-
ralleloorammum hiel complens.
Secentur rectae Bi, ik, kV in C, d, es
ita UE SIE hC ad latus quadracum
rectanguli abb, ic 2did, ec Re
ad a ut est Cumma rectarum B2
ec st ad summam crium linea-
rum quarum prima est recta ik, ee alterae duxe sune latora quadratz
rectanculorum aBb e alb: Sc crunte, d, e puncta contactuum. PF-
enim ex Conicis, sune hc quadratum ad rectangulum ahb, et
ic quadratum ad i a quadratum, et k e quadratum ad k a quadratum,
ec et quadratum ad rectangulum alb in cadem ratione; eE PFOPTEr-
ea BC ad latus quadratum ipEus aB b, 1c 2did, ke ad k d, eE et ad
Tacus quadratum ipsius alb fune in subduplicata illa ratione, ee
composite, in data ratione omnium antecedentium BI ec KV ad
omnes consequences, qua sunt lacus quadratum rectansuli ah b e
recta ik e latus quadratum rectanguli a lb. Ilabentur igieur CX
data illa ratione puncta contactuum c, d, es in Agura nOva. PCF
invertas operationes Lemmaris novissimi cransterantur haec pun-
Eta in figuram primam ec ibi, per Probl. XIV, describetur
Trajectoria. Q. F. F. Cererum perinde ue puncta a, b ja-
cent vel inter puncta B, h vel extra, debene puncta c, d, e vet
inter puncta h, 23 e, b capis vel extra. Si punctorum as b al-
cerurrum cadie inter puncta h, b, et alterum extra, Problema im.
Bomibile cA.
PROPOSTTIO ZEVI PROBLEMA XVIIT
Trajectoriam describere quae transibit per punctum datum es rectas
quatuor positione datas continget.
AB incerfectione communi duarum quarumlibet tangeneium ac
incerlectionem communem reliquarum duarum agatur recta intini-
143
WTIIHBEBIIBHHIEHISEIBGINIIBHBII