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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 129, page id 1041163592:0163
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PRINOTPTA MATHEMATTOA.
129
ec collatis numeratorum cerminis, ACE R C C = RFF + T F F LIBEK
2d b F  + CT, UE = FF ad = m B F m = .
+ Mm- M,  n - 2, nB - n
LXY
n
NC Xn = , PRIXVS
_C. EF sumendo rationes ulti-
mas quae prodeune ubi Orbes ad Formam circularem accedune, tc
CC 2d B F m.
F cFn.
vicistim C C+ ad F F UF B F m. 2 L C 7 n. 1
ad mb F m. 1 = nc F n. 2
Oux proxortio, exxonendo altitudinem maximam CV seu Y Arich-
meticeper Onitatem, scC C 2d F F ut b = c ad m b = nc, adeoque VF
T 20mb + nC
hs Onde cA C ad F, id est angulus VCP ad angulum
VCF, UE F 2d mb +nc
hLc. EF propterea cum angulus VCP inter
Apsidem summam et Apsidem imam in F llipsi immobili sIC X8O er
erie angulus VCD inter caIdem APSides, in Orbe quem corpuS vi
Centripeta quantitati  Am F C A2
Acub. proportionali describit, aequa-
lis angulo graduum 160 V  +
ErIDCTA SIEUL A = CA
180V
mb = nC
Et eodem argumento si viscen-
A cub. angulus inter APSides invenietur gractUUM
mb =ne NeC SecuS resolvetur Problema in casibus diffi-
cilioribus. Ouantitas cui vis centripeta proportionalis est, re-
Solvi semper debet in Scries convergentes denominatorem ha-
bentes A cub. Dein pars data numeratoris qui ex illa opcratione
provenic ad ipsius partem alteram non dacam, ec pars data nu-
meratoris Bujus R C+ C -R E F F T E E = E F Z ad ipSIUS PaFFCM
alteram non datam in eadem ratione ponendae TUnE: EE GuantitaLes
cupertuas delendo, cribendoque Vnitatem Pro T, obrinebitur
provortio (r ad F.
Corol. L. Tlinc s vis centripeta sit ue aliqua alcicudinis digni-
tas, inveniri potest dignitas illa ex motu Aplidum; ee COntra.
Nimirum s mocus totus angularis, quo corpus redit ad Apsidem
eandem, sic ad motum angularem revolutionis unius, Peu graduum
360, ut numcrus aliquis n ad numerum alium n, e alcirudo no-
minetur A: erie vis uc alcicudinis dignitas illa Amm 3, cujus In.
dex