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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRTMCIPLA MATHEMATIOA.
Corol. 4. Globus in Duido compresso quiescente ejusdem secum EIVEn
densicaris movendo, dimidiam motus sui Partem prius aMIItCE SECURDOS.
quam longicudinem duarum iplius diametrorum descripserit, per
idem C= OrOl. 7.
DRODOSETTOZZHIZ. TTTEOREMA ZXXI.
Clobi, per Fluidum in canali Cxlindrico clausum e compressum uni.
formiter prorredientis, resistentia est ad vim qua totus ejus motus,
interea dum octo tertias partes diametri suae describit, vel ge-
nerari possit vel tolli, in ratione quae componitur ex ratione ori
ficii canalis ad excessum hujus orificii supra dimidium circuli
maximi Clobi, et ratione duplicata orificii canalis ad excessum
hujus orificii supra circulum maximum Globi, e ratione den-
sitatis Fluidi ad densitatem Globi quamproxime.
Patet per Corol. 2. PrOp. XXXVIT; procedit vero demonstratio
uemadmodum in Propolitione praecedente.
eROPOSITIO XI. PROBLEMA IX.
Elobi, in Medio fuidissimo compresso propredienis, invenire resi-
stentiam per Phaenomena.
Sit A Pondus Globi in vacuo, B pondus ejus in Medio res
Renre. D diamerer CIobi, F Spatium quod sic ad = D ut densitas
Globi 2d densitatem Medii, id est, uE R ad A = B, G tempus quo
Globus pondere B absque resistentia cadendo deseribit spatium F.
ec HI velocitas quam Cilobus hocce casu suo acquirit. RC erit II
velocitas maxima quacum Clobus, pondere suo B, in Medio resi-
ente Porest descendere, per Corol. 2, PrOP. XRRVITL; ec reH-
tentia quam Globus ea cum velocitate descendens patitur, aequa
lis erit ejus ponderi B: resistentia vero quam patitur in alia qua-
cunque relocitate, erit ad pondus B in duplicata rarione velo-
citatis hujus ad relocitatem illam maximam. Cr, per. Corol. 13
CrOD. XXXVILL.
LLXC