Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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138FED. COMMANDINI ad priſma a b c e f g. quare linea s y ad y t eandem propor-
tionem habet, quam priſma a d c e h g ad priſma a b c e f g.
Sed priſmatis a b c e f g centrum grauitatis eſts: & priſma-
tis a d c e h g centrum t.
magnitudinis igitur ex his compo
ſitæ, hoc eſt totius priſmatis a g centrum grauitatis eſt pun
ctum y;
medium ſcilicet axis u x, qui oppoſitorum plano-
rum centra coniungit.
Rurſus ſit priſma baſim habens pentagonum a b c d e:
& quod ei opponitur ſit f g h _K_ l: ſec enturq; a f, b g, c h,
d _k_, el bifariam:
& per diuiſiones ducto plano, ſectio ſit pẽ
tagonũ m n o p q.
deinde iuncta e b per lineas le, e b aliud
planum ducatur, diuidẽs priſ
93[Figure 93] ma a k in duo priſmata, in priſ
ma ſcilicet al, cuius plana op-
poſita ſint triangula a b e f g l:
& in prima b _k_ cuius plana op
poſita ſint quadrilatera b c d e
g h _k_ l.
Sint autem triangulo-
rum a b e, f g l centra grauita
tis puncta r ſ:
& b c d e, g h _k_ l
quadrilaterorum centra tu:

iunganturq;
r s, t u o ccurren-
tes plano m n o p q in punctis
x y.
& itidem iungãtur r t, ſu,
x y.
erit in linea r t cẽtrum gra
uitatis pentagoni a b c d e;

quod ſit z:
& in linea ſu cen-
trum pentagoni f g h k l:
ſit au
tem χ:
& ducatur z χ, quæ di-
cto plano in χ occurrat.
Itaq;
punctum x eſt centrum graui
tatis trianguli m n q, ac priſ-
matis al:
& y grauitatis centrum quadrilateri n o p q, ac
priſmatis b k.
quare y centrum erit pentagoni m n o p q. &

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