Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
trianguli g h K, & ipſius ρ τ axis medium.
Sit priſma a g, cuius oppoſita plana ſint quadrilatera
a b c d, e f g h:
ſecenturq; a e, b f, c g, d h bifariam: & per di-
uiſiones planum ducatur;
quod ſectionem faciat quadrila-
terum _K_ l m n.
Deinde iuncta a c per lineas a c, a e ducatur
planum ſecãs priſma, quod ipſum diuidet in duo priſmata
triangulares baſes habentia a b c e f g, a d c e h g.
Sint autẽ
triangulorum a b c, e f g gra-
Figure: /permanent/library/4E7V2WGH/figures/0137-01 not scanned
[Figure 89]
uitatis centra o p:
& triangu-
lorum a d c, e h g centra q r:
iunganturq; o p, q r; quæ pla-
no _k_ l m n occurrant in pun-
ctis s t.
erit ex iis, quæ demon
ſtrauimus, punctum s grauita
tis centrum trianguli k l m;
&
ipſius priſmatis a b c e f g:
pun
ctum uero t centrum grauita
tis trianguli _K_ n m, &
priſma-
tis a d c, e h g.
iunctis igitur
o q, p r, s t, erit in linea o q cẽ
trum grauitatis quadrilateri
a b c d, quod ſit u:
& in linea
p r cẽtrum quadrilateri e f g h
ſit autem x.
deniqueiungatur
u x, quæ ſecet lineam ſ t in y.
ſe
cabit enim cum ſint in eodem
5. huius.plano:
atq; erit y grauitatis centrum quadril ateri _K_ lm n.
Dico idem punctum y centrum quoque gra uitatis eſſe to-
tius priſmatis.
Quoniam enim quadri lateri k lm n graui-
tatis centrum eſt y:
linea s y ad y t eandem proportionem
habebit, quam triangulum k n m ad triangulum k lm, ex 8
Archimedis de centro grauitatis planorum.
Vtautem triã
gulum k n m ad ipſum k l m, hoc eſt ut triangulum a d c ad
triangulum a b c, æqualia enim ſunt, ita priſina a d c e h g

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