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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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IIII
252
PFITLOSOPTILLE NATDRALIS
Dr Morv dium, adeoque exdem sunE ac si a corpore intermedio mana-
LONPORVM FeNE. Q. F. D.
Fc quoniam data est ratio distantia corporis utriulvis a centro
illo communi ad diltantiam corporis ejusdem a corpore altero, da-
bicur racio cujulris porestatis distantix unius ad eandem poresta-
cem dictantix alterius; ut ec ratio quanticatis cujulvis, quae Cx una
distantia ec quantitatibus datis urcunque deriratur, ad quanritarem
aliam, guae ex altera distantia ex quantitatibus totidem daris da-
camque illam distantiarum rationem ad priores habencibus similiter
deriratur. Proinde s vis, qua corpus unum ab altero trahitur, (IE
directe vel inverse ut dictantia corporum ab invicem; vel ut quae-
libet hujus distantia porestas; vel denique uc quantitas quaeris ex
hac distantia ec quantitatibus datis quomodocunque derivata: erie
eadem ris, qua corpus idem ad commune graritaris centrum era-
hitur, directe itidem vel inverse ut corporis attracti distancia 2 cen-
tro illo communi, vel ue eadem distantix hujus pocestas, vel de-
nique ut quanticas ex hac distantia ex analogis quantitatibus da-
eis similicer derivata. Hloc est, Vis trahentis cadem erit L Cx respe-
ctu distantix ueriusque. Q. F. D.
PROPOSTTIO EXII PROBLEMA XXXVIII.
Corporum duorum quae Viribus quadrato distantiae suae reciproce
proportionalibus se mutuo trahunt, ac de locis datis demittun-
tur, determinare NTOtUS.
COrpOra (per Theorema novissimum) perinde movebuntur ac
Si a corpore certio, in communi graricatis cenero constituto, trahe-
rentur; ec centrum illud ipso motus initio quiescet per FIrpoche-
SIn; _ propterca (per Legum C Orol. 4.) Semper quiescet. Deter-
minandi sunc isitur motus corporum (per Prob. XXV,) perinde
2c sia viribus ad centrum illud tendentibus ursereneur, de habe-
buntur motus corporum se mutuo trahencium. Q. F. I.
PROPOSITIO LZIII PROBLEMA XXXIX.
Corporum duorum quae Viribus quadrato distantiae suae reciproce pro-
portionalibus se mutuo trahunt, deque locis datis, secundum datas
rectas, datis cum Velocitalibus exeunt, determinare Motus.
EX
eEAIISIA MIM