Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. 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-
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
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.
Dico