Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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10143DEIIS QVAE VEH. IN AQVA. ad quadratum bd: & quam habet portio ad humidum in
grauitate, eandem quadratum nt habet ad bd quadratũ,
ex iis, quæ dicta ſunt:
conſtat n t lineæ ψ æqualem eſſe,
quare &
portio-
67[Figure 67] nes a n z, a g q
ſunt æquales.
Et
quoniam in por
tionibus æquali
bus, &
ſimilibus
a g q l, a n z l, ab
extremitatibus
baſiũ ductæ ſunt
a q, a z, quæ æ-
quales portiões
abſcindunt:
per
ſpicuum eſt an-
gulos facere æ-
quales cum por
tionum diame-
tris:
& triangu-
lorum n fs, g ω c, angulos, qui ad f ω æquales eſſe:
itemque
æquales inter ſe, s b, c b;
& s r, c r, quare & n χ, g y æquales:
& χ t y i. cũq; g h dupla ſit ipſius h i, erit n χ minor, quàm
duplaipſius χ t.
Sit igitur n m ipſius m t dupla: & iuncta
m K protrahatur ad e.
Itaque centrum grauitatis totius
erit punctum K:
partis eius, quæ eſt in humido, punctũ m:
eius autem, quæ extra humidum in linea protracta, quod
ſit e.
ergo ex proxime demonſtratis patet, nõ manere por
tionem, ſed inclinari adeo, ut baſis nullo modo ſuperficiẽ
humidi contingat.
At uero portionem conſiſtere ita, uta-
xis cum ſuperficie humidi faciat angulum angulo φ mino-
rem, ſic demonſtrabitur.
conſiſtat enim, ſi fieri poteſt, ut
non faciat angulum minorem angulo φ:
& alia eadem diſ-
ponantur;
ut in ſubiecta figura. eodem modo

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