Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
tur, centrum grauitatis eſt idem, quod circuli cen
trum.
Sit primo triangulum æquilaterum a b c in circulo de-
ſcriptum:
& diuiſa a c bifariam in d, ducatur b d. erit in li-
nea b d centrum grauitatis triãguli a b c, ex tertia decima
primi libri Archimedis de centro grauitatis planorum.
Et
quoniam linea a b eſt æqualis
Figure: /permanent/library/4E7V2WGH/figures/0115-01 not scanned
[Figure 70]
lineæ b c;
& a d ipſi d c; eſtq́;
b d utrique communis: trian-
gulum a b d æquale erit trian
8. primi.gulo c b d:
& anguli angulis æ-
quales, qui æqualibus lateri-
bus ſubtenduntur.
ergo angu
13. primi.li ad d utriq;
recti ſunt. quòd
cum linea b d ſecet a c biſa-
riam, &
ad angulos rectos; in
corol. p@@
mæ tertii
ipſa b d eſt centrum circuli.
quare in eadem b d linea erit
centrum grauitatis trianguli, &
circuli centrum. Similiter
diuiſa a b bifariam in e, &
ducta c e, oſtendetur in ipſa utrũ
que centrum contineri.
ergo ea erunt in puncto, in quo li-
neæ b d, c e conueniunt.
trianguli igitur a b c centrum gra
uitatis eſt idem, quod circuli centrum.
Sit quadratum a b c d in cir-
Figure: /permanent/library/4E7V2WGH/figures/0115-02 not scanned
[Figure 71]
culo deſcriptum:
& ducantur
a c, b d, quæ conueniant in e.
er-
go punctum e eſt centrum gra
uitatis quadrati, ex decima eiuſ
dem libri Archimedis.
Sed cum
omnes anguli ad a b c d recti
ſint;
erit a b c femicirculus:
51. tortil.itemq́; b c d: & propterea li-
neæ a c, b d diametri circuli:

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