Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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194FED. COMMANDINI tionem cadet: Itaque cum à portione conoidis, cuius gra-
uitatis centrum e auferatur inſcripta figura, centrum ha-
bens p:
& ſit l e ad e p, ut figura inſcripta ad portiones reli
quas:
erit magnitudinis, quæ ex reliquis portionibus con
ſtat, centrum grauitatis punctum l, extra portionem ca-
dens.
quod fieri nequit. ergo linea p e minor eſt ip ſa g li-
nea propoſita.
Ex quibus perſpicuum eſt centrum grauitatis
figuræ inſcriptæ, &
circumſcriptæ eo magis acce
dere ad portionis centrum, quo pluribus cylin-
dris, uel cylindri portionibus conſtet:
fiatq́ figu
ra inſcripta maior, &
circumſcripta minor. &
quanquam continenter ad portionis centrū pro-
pius admoueatur nunquam tamen ad ipſum per
ueniet.
ſequeretur enim figuram inſcriptam, nó
ſolum portioni, ſed etiam circumſcriptæ figuræ
æqualem eſſe.
quod eſt abſurdum.
THE OREMA XXIII. PROPOSITIO XXIX.
Cvivslibet portionis conoidis rectangu-
li axis à cẽtro grauitatis ita diuiditur, ut pars quæ
terminatur ad uerticem, reliquæ partis, quæ ad ba
ſim ſit dupla.
SIT portio conoidis rectanguli uel abſciſſa plano ad
axem recto, uel non recto:
& ſecta ipſa altero plano per axé
ſit ſuperſiciei ſe ctio a b c r ectanguli coni ſectio, uel parabo
le;
plani abſcindentis portionem ſectio ſit recta linea a c:
axis portionis, & ſectionis diameter b d. Sumatur autem
in linea b d punctum e, ita ut b e ſit ipſius e d dupla.

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