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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 181, page id 1041163592:0215
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PRIMOIPTA MATTIEMATLCA.
b 0. 2
crahitur vertus cenerum S, est ue planum illud ductum in distantiam LIVEK
luam P5. Sirc uc huic aequale planum P S ductum in distantiam PRruS
illam P8; ec summa virium plani ueriusque uc planum F F duc-
cum in summam distantiarum P G. L P e, id eAt, uc planum illud
ductum in duplam centri ec corpusculi distantiam F S, hoc est, ut
duplum planum P s ductum in distanciam F S, vel ut summa xe-
qualium planorum F F + ef ducta in distantiam candem. NE A-
mili argumento, rires omnium planorum in Sphaera eoca, hinc in-
de aequaliter a cenero Sphaerae distantium, sune ut summa planorum
ducta in distantiam P S, hoc est, uc Sphaera tota ducta in distan-
tiam centri sui Sa corpusculo P. D. L. D.
Ca5. 2. Trahat jam corpusculum P Sphaeram AF BF. FF CO.
dem argumento probabitur quod vis, qua Sphara illa trahitur, crit
ut dictantia FS.
d. F. D
Ca5. 3. Componatur jam Sphaera altera ex corpusculis innume-
ris F; ex quoniam vis, qua corpuiculum unumquodque trahieur,
eA ut distantia corpusculi a centro Sphaerae primae ducta in SpHX-
ram eandem, aeque adeo eadem est ac s prodiret tota de corpul-
culo unico in centro Sphaerae; vis toca qua corpuscula omnia in
Sphaera secunda cratuntur, hoc eAt, qua Sphaera illa tota trahiturs
eadem erit ac s Sphaera illa craheretur ri prodeunte de corpusculo
unieo in centro Sphaerae primae, e propterea proportionalis cR di-
Cantixe inter cenera Sphaerarum. d. L. D
Cas. 4. Trahane Sphaerae se mutuo, et vis seminata proxortio.
nem priorem serrabit. Q. P. D.
Cas. 5. Locetur jam corpusculum p intra Sphaeram A F B F: 8t
quoniam vis plani ef in corpusculum est ut concentum sub plano
illo ex distantia pe; ec vis contraria plani F. F ut contentum sub
plano illo ex distantia pC; erit ris ex utraque composica ut diste-
rentia contentorum; hoc es, uE summa aequalium planorum ducta
in Cemilsem disserencia distanciarum, id cAt, ut summa illa ducta in
DS distantiam corpusculi a centro Sphaera. EF simili argumento,
attractio planorum omnium F F, ef in Sphaera toca, hoc CA, aF-
cractio Sphaera torius, est uc summa planorum omnium, Pcu Sphaera
tota, ducta in pS distantiam corpusculi a centro Sphaerae. . F. D
Ca5. 6. EF S ex corpusculis innumeris p componacur Sphaera
nora intra Sphaeram priorem AP B F lica; probabitur uc prius
quod accractio, sire simplex Sphaerae unius in alteram, sive mutua
ucriusque in se invicem, eric uc distancia centorum p S. R. F. ∞.
FR O.
NIIMIISMIIG IMINIIIIIIIIIIIIIIIIE