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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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DEILLOSOPITE NATDRALIS
DE MOxDFerea eadem eA aC Si vis tota accrahens manaret de corpusculo uni-
Conronum co sico in cenero hujus Sphaerae. Haec autem actractio tanta est
quanta Foret vicissim actractio corpusculi ejusdem, si modo illud a
lingulis Sphaerae attractae particulis eadem vi traheretur qua ipsaS
actrahit. Foret autem illa corpusculi atrractio (peF PFOD. LXXLV)
reciproce proportionalis quadrato dictantix lux a centro Sphxe-
rae; adcoque huic aequalis acrractio Sphaera est in eadem ratio-
BC. Q. F. D.
Corol. T. Aerractiones Sphaerarum, versus alias Sphaeras homore.
neaSs LUINE uE SphaerE trahentes applicacae ad quadrata diltanciarum
centrorum luorum a ceneris carum quas aetrahunt.
Corol. 2. Idem valet ubi Sphaera aerracta etiam aecrahit. Nam-
que hujus puncta singula erahene singula alterius, cadem vi qua ab
ipsis vicissim crahuntur, adeoque cum in omni aetractione ursea-
cur (per Legem LTL) tam punctum accrahens, quam punctum ac-
tractum, seminabitur vis accractionis MUTUEe, COn(CEVAEIS PFOPOr-
Tionibus.
Corol. Z. Fadem omnia, quae superius de moeu corporum circa
umbilicum Conicarum Sectionum demonstrata sunes obcinene ubi
Sphaera aecrahens locacur in umbilico eE COrPOTA MOVENEUE exETA
Sphaeram.
Corob. 4. Fa vero quxe de motu corporum circa centrum Co.
nicarum Sectionum demOnATANEUT, ObEINCHNE UbI MOEUS PETABUNEUE
inera Sphaeram.
PROPOSITIOLZXVI TMEOREMA AXXVI
Si Sphaerae in proeressu a centro ad circumferentiam (quoad mate-
riae densitatem e vim attractivam) utcunque dissimilares, in
progressu vero per circuitum ad datam omnem a centro distan-
tiam sunt undique similares, e vis attractiva puncti cujusque
decrescit in duplicata ratione distantiae corporis attracti: dico
quod vis tota qua hujusmodi Sphara una attrabit aliam sit reci-
proce proportionalis quadrato distantiae centrorum.
Sunto Sphaerx quoccunque concentricxe similares AB, C D, P P,
ec. quarum interiores additae exterioribus componant materiam
densiorem