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.
Si uero axis k l non ſit perpendicularis
ad planum baſis;
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 m c ita eſſe, ut axis k q
ad axem q l.
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.
THEOREMA XV. PROPOSITIO XIX.
Solida parallelepipedain eadem baſi, uel in
æqualibus baſibus conſtituta eam inter ſe propor
tionem habent, quam altitudines:
& ſi axes ipſo-
rum cum baſibus æquales angulos contineant,
eam quoque, quam axes proportionem habebũt.
Sint ſolida parallelepipeda in eadẽ baſi cõſtituta a b c d,
a b e f:
& ſit ſolidi a b c d altitudo minor: producatur au-
tem planum c d adeo, utſolidum a b e f ſecet;
cuius ſectio
ſit g h.
erũſoli
111[Figure 111]2229. unde-
cimi
da a b c d, a b g h
in eadem baſi,
&
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

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