Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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154FED. COMMANDINI
THE OREMA XII. PROPOSITIO XVI.
In ſphæra, & ſphæroide idem eſt grauitatis, &
figuræ centrum.
Secetur ſphæra, uel ſphæroidno per axem ducto;
quod ſectionem faciat circulum, ellipſim a b c d, cuius
diameter, &
ſphæræ, uelſphæroidis axis d b; & centrume.
Dico e grauitatis etiam centrum eſſe.
ſecetur enim altero
plano per e, ad planum ſecans recto, cuius fectio ſit circu-
lus circa diametrum a c.
erunt a d c, a b c dimidiæ portio-
nes ſphæræ, uel fphæroidis.
& quoniam portionis a d c gra
uitatis centrum eſt in linea d, &
centrum portionis a b c in
ipſa b e;
totius ſphæræ, uel ſphæroidis grauitatis centrum
in axe d b conſiſtet.
Quòd ſi portionis a d c centrum graui
tatis ponatur eſſe f.
& fiat ipſi f e æqualis e g: punctũ g por
tionis a b c centrum erit.
ſolidis enim figuris ſimilibus &
11per 2. pe-
titionem
æqualibus inter ſe aptatis, &
centra grauitatis ipſarum in-
ter fe aptentur neceſſe eſt.
ex quo fit, ut magnitudinis, quæ
224 Arch-
medis.
ex utriſque cõſtat, hoc eſt ipſius ſphæræ, uel ſphæroidis gra
uitatis centrum ſitin medio lineæ f g, uidelicet in e.
Sphæ-
ræ igitur, uel ſphæroidis grauitatis centrum eſtidem, quod
centrum figuræ.