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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 201, page id 1041163592:0235
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III
PRINOIPLA MATHEMATTCA.
t
vis qua planum quodris m II M cratiie punctum C eAt reciprOCC UE L. TVEM
CFIn- 2. In PlanO m FYM capiatur longicudo FIM ipSI C FFn - 2 re PurmUS
ciproce proportionalis, ee erie vis illa ut PI MI. Similiter in planis sin-
sulistGLn LNI, OKO, ScC. capiantur lonsicudines EFL, TNI, K(O, ecc.
IPsIS CCn- 29 C Tn2, C Rn-2, ecc. reciproce proportionales; ec vi-
res planorum corundem crunt ue lonsicudines capexe, adeoque
lumma virium uc summa longicudinum, hoc est, vis Solidi corius ut
arC2 E L. O R in intinitum versus OR producta. Sed area illa (Per
nocas quadraturarum methodos) eAt reciprOCCUt C. (Fn =3, eE PFOP-
cerea vis Solidi torius cst reciprOCC UE C(7n = 3. d. F. D.
Ca5. 2. Collocetur jam corpusculum C ex parre plani VGL. in-
era Solidum, ec capiatur distantia C. R aequalis distantix CCr. RFS0-
lidi parS L. G10KO, planis Parallelis LEF L, OKO terminata, cOr
Dulculum C. in medio sicum nullam in partem crahet, contrariis op.
Politorum punctorum actionibus se mutuo per aequalicatem tollenti
bus. Proinde corpusculum C Sola vi Solidi ulera planum OR AIFi EF2-
hitur. FlaeC autem vis (per C asum primum) CAreciprOCC UE CH n - 3
hoc cA (ob aequales CG, CR) rECIPEOCC UE CCF n - 3. D. F. D.
Corol. 1. TIinc si Solidum L CT. N planis duobus infinicis pa-
rallelis L. C, INV utrinque terminetur; innotescit ejus vis attra-
etiras subducendo de vi actractiva Solidi torius infiniti Y. C KC
vim attractiram partis ulterioris NTCO, in infinitum vertus KC
productae.
Corol. 2. Si Solidi hujus infiniei pars ulterior, quando attractio e-
jus collata cum aetractione partis citerioris nullius pene est momen-
ei rejiciatur: attractio partis illius citerioris augendo distantiam de-
crescet quam proxime in ratione potectatis C(n = 3
Corol. 3. FF hinc s corpus quodris finitum ec ex una parte pla-
num trahiac corpuiculum c regione medii illius plani, sc dictancia
inter corpusculum ec planum collata cum dimensionibus corpo
ris actratientis perexigua TC, Constet autem corpus actrahens ex
Parciculis homogeneis, quarum vires actractire decrescunt in
ratione potestatis cujusris plusquam quadruplicatae distantiarum;
vis aetractira corporis totius decrescet quamproxime in ratione
Potestatis, cujus lacus sc dictantia illa perexisua, ee Index terna-
rio minor quam Index potestatis prioris. De corpore ex particulis
constante, quarum rires acrractirae decrescune in ratione porestatis
eriplicatae distantiarum, assertio non ralet; propterea quod, in hoc
catus aecractio parris illius ulterioris corporis intiniti in Corollario
lecundo, semper est intinire major quam auractio partis citerioris.
Scholiumo
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