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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 307, page id 1041163592:0341
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IIIIIII.
PRTNOTDLA HATHIEMAETOA.
30
mergatur, d altitudo aquae stagnantis supra Fundum vasis sIEG R: LINEn
velocitas quacum aqua quxe in rase est, cAAUCE per FOTAMEN L. AISECVNvOS.
in aquam stagnancem, ca eric quam aqua cadendo et casu suo de-
Ecribendo alticudinem TR acquirere porest. Nam pondus aquae
omnis in rase quae inferior cst suverticie aguae Ragnantis, suctine-
bitur in aequilibrio per pondus aquae Cagnantis, ideoque motum
aquae descendentis in rase minime accelerabit. Patebic eriam 8
hic CasuS per Experimenta, mensurando scilicet tempora qui-
bus aqua cAuit.
Corol. Y. Flinc ( 2qu_ altiendo C  producatur ad KE, UIE CIE A R
ad CK in duplicata ratione arex Foraminis in quaris tundi varce
Facti, ad aream circuli AB: velocicas aguae eAuentis xgualis crie
veloeitati quam aqua cadendo et casu uo describendo alcitudinem
RCi acquirere porett.
Corot. 2. Ft vis qua cotus aqua exilientis motus generari pot est,
aequalis est ponderi CHlindricae columnae aquae cujus basIS CIE FOrZ-
Men F F, ex alcicudo 2GY vel 2CK. Nam aqua exitiens quo
tempore hanc columnam aequat, pondere Tuo ab alcicudinc GP ca-
dendo, relocitarem suam qua exilie, acquirere porest.
Corol. 3. Pondus aquae eorius in rase B D C, est ad ponderis
Parrem quae in delluxum aquae impenditur, ut summa circulorum
AB ec F F, ad duplum circulum P. F. Sic enim YO media pro-
Portionalis inter YFY e TC; e aqua per Foramen F Scorediens,
quo tempore gueta cadendo ab P describere ponet alcitudinem YCF,
aequalis erit Crlindro cujus basis est circulus L. Fec alcitudo est 2I(,
id eA, Cplindeo cujus BaRS es circulus AB ec alcieudo clt 2FO,
nam circulus F F est ad circulum AB in Cubduplicata ratione
altitudinis PFT ad alcicudinem PC, hoc cst, in simplici ratione me-
dix proporcionalis IO ad alcicudinem PC: ec quo tempore sutta
cadendo ab Y describere porest alcicudinem PH, aqua corediens
aequalis erie Cplindro cujus basis eA circulus B ec alcitudo cAt
2THI: ex quo tempore gutra cadendo ab Y Per VY ad C describie
alcicudinum differentiam FYC, aqua cgrediens, id cA, aqua tota in
solido AB NV F F M aequalis erie differentia Cflindrorum, id est,
Cylindro cujus basis est AB e altitudo 2HIO. EE PrOPECrCA
aqua EOca in vase AB DC. es ad aquam totam cadencem in
solido AB N F F M uE HIG ad 2HIO, id cA, ut HIO +OO
ad 2FIO, Scu TFT+ 1O ad 2TTI. Sed pondus aquxe torius in
olido ABNFP M in aguae detuxum impenditur: aC PFO.
inde
l  s . s s st f . f s  sistel