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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 173, page id 1041163592:0207
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PRINOIPLA MATHEMATICA.
d qualicates PhysiCaS, Ped quantitates ec proxortiones Mathema-
LTBE R
ticas in hoc Tractaru expendens, uc in Detinitionibus explicui. In s
Machesi investisandae Cune ririum quanticates ee rationes illae, que
ex conditionibus quibulcunque politis consequentur: deinde, ubi
in Pbplicam descenditur, conterenda sunt lixe rationes cum PhX-
nomenis, ue innorelcat quaenam virium condiriones lingulis cor-
Porum actractirorum generibus competant. Pt tum demum de vi-
riuns specicbus, causis ec rationibus Phylicis tutius disputare lice-
Dic. Vidcaus isitur quibus viribus corpora Sphaerica, ex parcicu-
is olo jam expolito actractiris constantia, debeane in se muruo.
sere, et Gllales morus inde consequaneuT.
DEC, TIO
XII.
De Corporum Sphaericorum Viribus attractivis.
PROPOSTTIO LXZ. THEOREMA XXX.
Si ad Sphaericae superficiei puncta sineula tendant vires aequales cen-
tripetae decrescentes in duplicata ratione distantiarum a punctis:
dico quod corpusculum intra superficiem constitutum his viri-
bus nullam in partem attrahitur.
SIE ZTLK P superticies illa Splaeri
ca ec P corpusculum intus consticu-
cum. Per F asantur ad hanc super-
ficiem lineae duxe IYK, IL arCUS
quam minimos TI R L incercipi
entes; e, ob triangula IIP L L. F
per Corol. 3. Lem. VIT) Similia, arcus
illi crune distantiis HP, L P PrO.
portionales; e superticiei Sphaericx
Particulae quaeris ad FTI _ RL, rCc-
eis per punctum P tranleuntibus un
dique terminatae, crunc in duplicata
illa ratione. Ergo vires harum particularum in corpus P exercICA
Tunc incer se aequales. Sune enim ut particulae directe ee quadrata
dictanciarum iriverse.
Ec hae dux raciones componunt racionem
aquali