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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 117, page id 1041163592:0151
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PRINOIPLA MATHEMATICA.
PROPOSITIO ZLI. PROBLEMA XZVTII.
Posita cujuscunque generis Vi centripeta s concessis Firurarum
curvilinearum quadraturis, requiruntur tum Trajectoriae in qui-
bus corpora movebuntur, tum Tempora motuum in Trajectoriis
inventis.
Tendat vis quaelibee ad centrum C et invenienda sit Trajectoria
VTTRK. Detur CirculuS V XY centro C interrallo quovis CY
delcriptus, centroque eodem describantur alii quiris circuli YD
RF. Trajectoriam secantes in l ec R rectamque CV in D eE F.
Rectum rectam C NTX sccantem circulOS IL F, VY in N Sc X,
tum rectam CKY occurrentem circulo V XY in Y. Sint autem
puncta Ie RE sibi invicem vicinissima, ec pergat corpus ab V per
B3T_ K ad k; Scque punctum A locus ille de quo corpus aliud
cadere debet ut in loco D relocitatem acquirat aequalem reloci-
tati corporis prioris in P; ee Cantibus quae in PropOsitionC XXXIX,
lincola TK, daco tempore quam minimo descripta, crit ut ve-
locitas acque adeo ut lacus quadrarum arcae AB F D, ee triangu-
lum TC R tempori proportionale dabitur, adeoque R N erit reci-
Proce uc alcicudo TC, id est, si detur quantitas aliqua O de alci-
cudo TC nOminetur A, uc =. Flanc quantitarem = nominemus Z
ec ponamus cam esse magnicudinem ipsius  ut sit in aliquo
catu V ABF D ad Z AE CR P K ad X N, Se crit in omni caTu
VABFD adZ UETK ad K NV, _E ABF D 1dZZ UE TK 9. 2dK Ng.
ec dirisim ABF D - ZZ adZZ uE IN quad ad K N quad, 2d-
eoque r ABFD = Z Z ad (Z (CU) = UE PN ad R N, _E PrODECrCA
AXK N aequale
CTW
ABFD - Z7. Onde cUm YX X XC SIL ad
A Z R N NE C X g 2d A A, erit rectangulum Y PX NC aequale
DXINXC X quad.
A A Y ABFD - L.T
Temper Db, DC ip(IS
Isitur si in perpendiculo D S CapIaNEUE
X C X quad.
2VABFD - ZZ  EAA YABL D -2. 2
equales respectire, et describantur currae linex ab, cd quas
DuACta
L IBEK
PRIMDS