Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
metrum habens e d. Quoniam igitur circuli uel ellipſis
a e c b grauitatis centrum eſt in diametro b e, &
portio-
nis a e c centrum in linea e d:
reliquæ portionis, uidelicet
a b c centrum grauitatis in ipſa b d conſiſtat neceſſe eſt, ex
octaua propoſitione eiuſdem.

THEOREMA V. PROPOSITIO V.

SI priſma ſecetur plano oppoſitis planis æqui
diſtante, ſectio erit figura æqualis &
ſimilis ei,
quæ eſt oppoſitorum planorum, centrum graui
tatis in axe habens.
Sit priſma, in quo plana oppoſita ſint triangula a b c,
d e f;
axis g h: & ſecetur plano iam dictis planis æquidiſtã
te;
quod faciat ſectionem K l m; & axi in pũcto n occurrat.
Dico _k_ l m triangulum æquale eſſe, & ſimile triangulis a b c
d e f;
atque eius grauitatis centrum eſſe punctum n. Quo-
niam enim plana a b c
Figure: /permanent/library/4E7V2WGH/figures/0125-01 not scanned
[Figure 82]
K l m æquidiſtantia ſecã
16. unde-
cimi.
tur a plano a e;
rectæ li-
neæ a b, K l, quæ ſunt ip
ſorum cõmunes ſectio-
nes inter ſe ſe æquidi-
ſtant.
Sed æquidiſtant
a d, b e;
cum a e ſit para
lelogrammum, ex priſ-
matis diffinitione.
ergo
&
al parallelogrammũ
erit;
& propterea linea
34. prim@_k_l, ipſi a b æqualis.
Si-
militer demonſtrabitur
l m æquidiſtans, &
æqua
lis b c;
& m K ipſi c a.

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