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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRIMCIPTA MATHEMATICA
PROPOSITIO LXXXVI THEOREMA XLII.
Si particularum, ex quibus corpus altractivum componitur, vires
in recessu corporis altracti decrescunt in triplicata vel plusquam
triplicata ratione distantiarum a particulis: attractio lonre for-
rior erit in contactu, quam cum attrahens e altractum inter-
vallo vel minimo separantur ab invicem.
Nam accractionem in accessu attracti corpusculi ad hujusmodi
Sphaeram crahentem augeri in infinitum, constac per Colutionem Pro-
blematis XL. L, in Exemplo secundo ac terrio extribitam. Idem, per
Lxempla illa _ ThCOremA XLL inter SC collata, Facile colligieuF
de actractionibus corporum versus OrDCS COnCAVO- CONVEKOS, Live
corpora attracta collocentur extra Orbes, live intra in corum cavi-
tatibus. Sed ex addendo vel auferendo his Sphaeris et Orbibus ubi-
vis extra locum contactus mareriam quamlibet atcractiram, eo ut
corpora actractira induane figuram quamris assignacar, conltabie
Propositio de corporibus univer(IS. . F. D.
PROPOSITIOLZXZMI. TIEOREMA XLIV.
Si corpora duo sibi invicem similia, es ex materia aequaliter atra-
Etiva constantia, seorsim attrabant corpuscula sibi ipsis proporii.
onalia e ad se similiter posita: attractiones acceleratrices cor-
pusculorum in corpora tota erunt ut attractiones acceleratrices
corpusculorum in eorum particulas totis proportionales  in to-
eis similiter positas.
Nam s corpora distinguantur in partieulas, quae sinc coris pro-
portionales ex in toris similiter licxe; crie, ut aetractio in particulam
quamlibet unius corporis ad actractionem in particulam correspon-
dentem in corpore altero, ita attractiones in particulas fingulas
primi corporis ad actractiones in alterius particulas singulas corres-
pondentes; e componendo, ita attractio in totum primum corpus
ad aetractionem in torum secundum. 8. L. D.
Corol. T. Ergo si vires actractirae particularum, augendo distan-
cias corpusculorum accractorum, decrescant in ratione dignitatis
Cujutris
L. 1
EX IMVS.
UIsuviTuMMIIIIIII