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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 146, page id 1041163592:0180
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IIIII
146
PHTLOSOEHLE NATDRALIS
De Morv L superticie, proportiona-
Conrono lis; PsIY recta axi
parallela per corpus tran-
HenS, eE GF, PII recte
a punctis C SE P in p2
rallelam illam TIITF
perpendiculariter demil-
Ex. Dico jam quod arca
AOF, radio O F ab ini-
eio mocus descripta, sIC
rempori proporcionalis.
Nam vis YC (per LC.
cum C Orol. 2.) resolvitur
An ViTCS TF, FC; e vis
TI in vires TII, IIT:
Vires autem TF, T II
agendo secundum lincam
 s plano AOF per-
pendicularem mutane (0.
lummodo motum cor-
poris quatenus huic plano perpendicularem. Ideoque motus ejus
quatenus secundum politionem plani Factus, hoc est, motus pun-
eti F quo Trajectoria veltigium AZ in hoc plano delcri-
bitur, idem cA ac ( vires T F, TFY tollerentur, dc corpus tolis vi-
ribus FC, FIL agItaretUr; Hoc eA, idem ac si corpus in plano
AOP, vi centripeta ad cenerum O tendence de summam virium
S CF_ YIY aequante, describeret curram AP. Sed vi tati describi-
cur arCA AO F (PET PTOP. L.) tempori proxortionalis. d. F. D.
Corot. Fodem aroumento s corpus a viribus agitarum ad centra
duo vel plura in eadem quaris recta CO data tendentibus, deseri-
beret in spatio libero lineam quamcunque curram SP; Foret arca
AOP tempori semper provortionalis.
PROPOSTTTO LVI. PROBLEMA XXXVII.
Concessis Ficurarum curvilinearum quadraturis, datisque tum lece
Vis centripetae ad centrum datum tendentis, tum superficie cur-
va cujus axis per centrum illud transit; invenienda est Traje-
Etoria quam corpus in eadem superficie describet, de loco dato, data
cum Velocitate, versus placam in supersioie illa datam egressum.
Stanci.
WBINIIIMIBIBIIIHUIIHIININVII