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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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DRINCIPTA MATHEMATICA.
nihili sic; nimirum Orbes eranescentes ex quibus Sphaera uleimo LrVKn
constat, ubi Orbium illorum numerus augetur ee crassitudo minui- Pxiuve
cur in intinitum. Similiter per Puncta, ex quibus lineae, superticies
ec Colida componi dicuneur, intelligendae sune particula sequales
magnitudinis contemnendae.
EROPOSITIO LXXIV. THEOREMA XXXIV.
Tisdem positis, dico quod corpusculum extra Sphaeram constitutum
attrabitur vi reciproce proportionali quadrato distantia suae ab
Epsius centro.
Nam distinguatur Sphaera in superficies Sphaericas innumeras
concentricas, et actractiones corpusculi a lingulis superticiebus
oriunda crunt reciproce proportionales quadrato dictantix cor-
Dusculi a CeNErO, PeF PFOD. LXXI. Et componendo, hicc Cum-
maattractionum, hoc est accractio corpusculi in Sphaeram totam, in
eadem rarionc. 9. F. D
Corol. 2. Tlinc in xequalibus distantiis a centris homogenearum
Sphaerarum, aetractiones Pune ut SphXER. NTaM PET PFOD. LXXIL,
si distantiae lune proxortionales diametris Sphaerarum, vires crune
uc diametri. Mlinuatur distantia major in illa ratione; ec, dittan-
tiis jam Factis aequalibus, ausebitur accractio in duplicaca illa ratio-
ne, adeoque erit ad actractionem alteram in criplicata illa rationen
hoc est, in ratione Sphaerarum.
Corol. 2. In dictanciis quibusvis aEcraCtiOneS TUNE UE SphXrX LD-
plicacae ad quadraca distantiarum.
Corol. 3. Si corpusculum, extra Sphaeram homogencam policum,
trahicur vi reciproce proportionali quadraco distantix luae ab iplius
centro, conster autem Sphaera ex particulis aetractiris; decrelcet vio
partieulae cujusque in duplicara ratione distantix a particula.
PROPOSITIO LXXV. THEOREMA XXXV.
Si ad Sphaerae datae puncta sinsula tendant vires aequales centripe-
cae decrescentes in duplicata ratione distantiarum a punctis; dico
quod Sphaera quaevis alia similaris ab eadem attrabitur vi reci-
proce proportionali quadrato distantiae centrorum.
Nam particulae cujulris aetractio est reciproce ut quadratum di-
Cancixe suxe a cenero Sphaerae trahentis, (DEF PFOP. LXXIV) dc prOP
TCrCa