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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINCIPIA MATHEMATICA.
lemel, eE ratIOnC P Fg ad F. Pg = P g bis, e ratione densitatis, L IVEU
Medii ad densitatem Cplindri.
Corol. 3. Tisdem poliris, ex quod longitudo I. sic ad quaaru-
Dlum lonsicudinis Cplindri in ratione quae componitur ex ratione
E Fg == P 84 ad L. F g Cemel, _c ratiONC F Fg = P 8g ad F. Fg
bis: relittentia Cplindri erit ad rim qua totus ejus motus, interea
dum lonsitudinem L describit, vel tolli PONit rei generari, ut
densicas Medii ad densitatem Cylindri.
Scholium.
In hac Propolitione relistentiam investizarimus quae orieut
Tola magnitudine tranverix sectionis C Hlindri, neglecta resictentix
Darte quae ab obliquitate motuum oriri possit. Nam quemadmo-
dum in calu primo Propolitionis xxxrI, obliquitas motuum qui-
bus partes aguae in vale, undique conversebane in Foramen Lifi,
impedirie cAuxum aquae illius per Foramen: sic in hac Propolici-
onc, obliquitas mocuum quibus partes agux ab anteriore C ylindri
termino presa, cedunt prestioni ec undique diversunt, retardat co-
rum cranlicum per loca in circuieu termini illius antecedentis ver-
sus polteriores partes CHlindris efficitque ut Ruidum ad majorem
dictantiam commoreatur ex relictentiam auget, idque in ca fere
racione qua eMluxum aquae e rate diminuit, id est, in ratione du-
Plicata 25 ad22 circiter. EE quemadmodum, in Propolicionis illius
casu primos effecimus ut partes aquae perpendiculariter ee maxima
copia transirent per Foramen P. F, ponendo quod aqua omnis in
rale quae in circuitu cacaractae conselata fuerat, ec cujus motus
obliguus crat ec inutilis, maneret sinc motu: Sic in HaC PFOPOII-
tione, ut obliquitas motuum tollatur, ec partes aquae motu maxime
directo e brevissimo cedentes Facillimum praebeant transicum Cy-
lindro, e sola maneat resictentia quae oritur a magnitudine lecti-
onis transverlae, quaeque diminui non potes nili diminuendo dia-
metrum Cplincris concipiendum est quod partes Auidi quarum
motus sune obliqui ee inueiles ec relictentiam creant, quiescane in-
cer se ad utrumque Cplindri ter-
minum, ec cohaereant ec Cylindro
jungantur. Sit ABC D rectan-
bulum, ec sInE AF. ec BP. arCUS F
duo Parabolici axc AB delcripeis
acere autEMFECO Quod ACad lpa
quro
5ec020.