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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 282, page id 1041163592:0316
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232
PHILOSOPMLAE NATOKCALIO
DN MOrD Nam A uniformis sIE resCentia D R, Figura a B RRF reCtanGU-
lum erit sub Ba 8c DR; e inde rectangulum (uD ZB a e Aa
erie equale rectangulo sub B a SE D K, e D K aequalis erit : Aa.
Ouarc cum D R sic exponens resiltentix, ex longitudo penduli ex-
ponens gravitaris, erie relistentia ad gravicarem ut Z Aa ad longi-
cudinem Penduli; ommino uE in PxOP. ZZ VrrI demonstratum cA.
Si relctentia sic ut velocitas, Figura a B RR T FIlipsis erit quam
proxime. Nam si corpus, in Medio non resistente, oscillatione
incegra describeret longitudinem B A, relocitas in loco quovis D
Foret ut Circuli diamerro B descripei ordinacim applicata D F.
Proinde cum B a in Medio resiltence, ee B A in Mledio non resi-
sente, aequalibus circiter temporibus describantur; adeoque velo-
citates in lingulis ipsius
Ba punctis, sint quam
prexime ad velocitates
in punctis correspon-
dencibus longicudinis
BA uC es Ba 2d BA;
erit relocitas DK in
Medio resistente ut Cir-
culi vel Ellipseos SupCF
diametro Ba delcripei
ordinatim applicata; adeoque Figura B RV T a FIlipIS, quam pro-
xime. Cum resistentia relocitati proportionalis supponatur, siEOV
exponens resistentia in puncto Medio O; _ EIlipsiS a BRV S,
centro O, semiaxibus OB, OV descripta, Figuram aBKVT,
eique aequale rectangulum LaXBO, aequabie quamproxime. EA
ioitur La XBO ad OV ZBO uc area F IlipeoS hujuS ad OV YBO:
id est, Aa 2d OV ue area Cemicirculi ad quadratum radii, sive ut
IF ad7 circiter: FE propterea F. Aa ad longicudinem penduli uE
corvoris oscillaneis resistentia in O ad ejuldem gravitatem.
Ouod A relictentia D R sic in duplicata ratione velocitatis, Fi-
Gura BKV T a Parabola crit verticem habens V ee axem OV, id.
eoque egnalis erie rectangulo (ub Z Ba eEOV quam proxime. FK
isicur rectangulum sub EB a ec Aa aequale rectangulo (ub ZBa
sc OF, adeoque OV aequalis + Aa: ex propterea corporis oscillan-
ris resistentia in O ad ipsius gravitarem ut 2A a ad longicudi
nem Penduli.
AEque has conclusiones in rebus practicis abunde Paris accuratAS
esse censeo. Nam cum EIlipsis vel Parabola BRV Sa congrUAE
Cum
CoxPBRDI