Full text: Archimedes: Archimedis De iis qvae vehvntvr in aqva libri dvo

FED. 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.

73.1.

0137-01
5. huius.

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
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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