Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. COMMANDINI
in linea e b punctũ g, it aut ſit g e æqualis e f. erit g por-
tionis a b c centrum.
nam ſi hæ portiones, quæ æquales
&
ſimiles ſunt, inter ſe ſe aptentur, ita ut b e cadat in d e,
&
punctum b in d cadet, & g in f: figuris autem æquali-
bus, &
ſimilibus inter ſe aptatis, centra quoque grauitatis
ipſarum inter ſe aptata erunt, ex quinta petitione Archi-
medis in libro de centro grauitatis planorum.
Quare cum
portionis a d c centrum grauitatis ſit ſ:
& portionis
a b c centrum g:
magnitudinis; quæ ex utriſque efficitur:
hoc eſt circuli uel ellipſis grauitatis centrum in medio li-
neæ f g, quod eſt e, conſiſtet, ex quarta propoſitione eiuſ-
dem libri Archimedis.
ergo circuli, uel ellipſis centrum
grauitatis eſt idem, quod figuræ centrum.
atque illud eſt,
quod demonſtrare oportebat.
Ex quibus ſequitur portionis circuli, uel ellip-
ſis, quæ dimidia maior ſit, centrum grauitatis in
diametro quoque ipſius conſiſtere.

[Figure 80]
Sit enim maior portio a b c, cu_i_us diameter b d, & com-
pleatur circulus, uel ellipſis, ut portio reliqua ſit a e c, dia