Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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15723DE CENTRO GRAVIT. SOLID. eſtſolidi g m altitudo ad o e altitudinem ſolidi m c, uel quã
axis
k q ad q l axem.
ducatur a puncto k ad idem planum per
pendicularis
k r, occurrẽs plano m n o p in s.
ſimiliter de-
mõſtrabimus
ſolidum g m ad ſoli Sed ut K q ad q l, ita k s altitudo ad altitudi-
nem
s r, nam lineæ K l, K r à planis æquidiſtantibus in eaſ-
1117. unde-
cimi
dem proportiones ſecantur.
ergo ſolidum g m ad ſolidum
m
c eandẽ proportionem habet, quam altitudo ad altitu
dinẽ
, uel quam axis ad axem.
quod demõſtrare oportebat.
Sint ſolida parallelepipeda in eadẽ baſi cõſtituta a b c d,
a
b e f:
& producatur au-
tem
planum c d adeo, utſolidum a b e f ſecet;
erũſoli
2229. unde-
cimi
da a b c d, a b g h
in
&
æquali altitu
dine
inter ſe æ-
qualia
.
Quoniã
igitur
ſolidum
a
b e f ſecatur
plano
baſibus
æquidiſtãte
, erit
ſolidum
g h e f
3318. huius adipſum a b g