Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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convexa erit verſus cataractam, & propterea major Cono cujus ba­
ſis eſt circellus ille PQ& altitudo GH,id eſt, major tertia parte
Cylindri eadem baſe & altitudine deſcripti. Suſtinet autem cir­
cellus ille pondus hujus columnæ, id eſt, pondus quod pondere
Coni ſeu tertiæ partis Cylindri illius majus eſt.
LIBER
SECUNDUS.
Corol.8. Pondus aquæ quam circellus valde parvus PQſuſtinet,
minor eſt pondere duarum tertiarum partium Cylindri aquæ cujus
baſis eſt circellus ille & altitudo eſt HG.Nam ſtantibus jam po­
ſitis, deſcribi intelligatur dimidium Sphæroidis cujus baſis eſt cir­
cellus ille & ſemiaxis ſive altitudo eſt HG.Et hæc figura æqualis
erit duabus tertiis partibus Cylindri illius & comprehendet colum­
nam aquæ congelatæ PHQcujus pondus circellus ille ſuſtinet.
Nam ut motus aquæ ſit maxime directus, columnæ illius ſuper­
ficies externa concurret cum baſi PQin angulo nonnihil acuto,
propterea quod aqua cadendo perpetuo acceleratur & propter ac­
celerationem fit tenuior; & cum angulus ille ſit recto minor, hæc
columna ad inferiores ejus partes jacebit intra dimidium Sphæroi­
dis. Eadem vero ſurſum acuta erit ſeu cuſpidata, ne horizontalis
motus aquæ ad verticem Sphæroidis ſit infinite velocior quam ejus
motus horizontem verſus. Et quo minor eſt circellus PQeo
acutior erit vertex columnæ; & circello in infinitum diminuto, an­
gulus PHQin infinitum diminuetur, & propterea columna ja­
cebit intra dimidium Sphæroidis. Eſt igitur columna illa minor
dimidio Sphæroidis, ſeu duabus tertiis partibus Cylindri cujus baſis
eſt circellus ille & altitudo GH.Suſtinet autem circellus vim aquæ
ponderi hujus columnæ æqualem, cum pondus aquæ ambientis in
defluxum ejus impendatur.
Corol.9. Pondus aquæ quam circellus valde parvus PQſuſti­
net, æquale ſet ponderi Cylindri aquæ cujus baſis eſt circellus ille
& altitudo eſt 1/2GHquamproxime. Nam pondus hocce eſt me­
dium Arithmeticum inter pondera Coni & Hemiſphæroidis præ­
dictæ. At ſi circellus ille non ſit valde parvus, ſed augeatur donec
æquet foramen EF; hic ſuſtinebit pondus aquæ totius ſibi per­
pendiculariter imminentis, id eſt, pondus Cylindri aquæ cujus ba­
ſis eſt circellus ille & altitudo eſt GH.
Corol.10. Et (quantum ſentio) pondus quod circellus ſuſtinet,
eſt ſemper ad pondus Cylindri aquæ cujus baſis eſt circellus ille &
altitudo eſt 1/2GH,ut EFqad EFq-1/2PQq,ſive ut circulus
EFad exceſſum circuli hujus ſupra ſemiſſem circelli PQquam­
proxime.

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