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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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L82
PHTLOSOPMLE NATDRALIS
CORFORVI PROPOSITIO EXXVIII TTEOREMA ZXXVII
Si Sphaerae in proeressu a centro ad circumferentiam sint utcunque
dissimilares e inaequabiles, in proeressu vero per circuitum ad
datam omnem a centro distantiam sint undique similares; es
vis attractiva puncti cujusque sit ut distantia corporis attracti:
dico quod vis tota qua hujusmodi Sphaerae duae se mutuo trabunt
sit proportionalis distantiae inter centra Sphaerarum.
Demonstratur ex Propositione praecedente, eodem modo quo
PFOPOSItIO LXXVE ex Propolitione LxeV demonstrata Fuit.
Corol. Ouxe superius in Proposicionibus X e LXIV de motu
corporum circa centra Conicarum sectionum demonstrata lunt,
valene ubi actractiones omnes tiunt vi Corporum Sphaericorum
conditionis jam descriptae, luntque corpora accracta SphXrX COn-
dirionis ejusdem.
Scholium.
Aetractionum Casus duos insigniores jam dedi expostos; nimi-
rum ubi Vires centripetae decrescune in duplicata diltantiarum ra-
tione, vel crescunt in distantiarum ratione simplici; eficientes
in utroque Casu ut corpora grrentur in Conicis Sectionibus, et
componentes corporum Sphaericorum Vires centripetas cadem Lege,
in recestu a centro, decrescentes vel crescentes cum scipsis: Quod
CA notatu dignum. Calus caeteros, qui conclusiones minus ele-
santes exhribene, sigillatim percurrere longum esset. Malim
cunctos methodo generali simul comprehendere ac determinare,
uE sequitur.
L E NI M A XXIX.
Si describantur centro S circulus quilibet AE B,  centro P cir-
culi duo FF, et, secantes priorem in F, C, lineamque PS in
F, F;  ad PS demittantur perpendicula F. D, C d: dico quod
si distantia arcuum F. F, CE in infinitum minui intellieatur, ra-
tio ultima lineae evanescentis Dd ad lineam evanescentem F F
ea sit, quae lineae PF. ad lineam PS.
Nam
DE MOTV