Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS

PROPOSITIO VI.

Solidae magnitudines humido leuiores, in
humidum impulſæ ſurſum feruntur tanta ui, quã
to humidum molem habens magnitudini æqua-
lem, grauius eſt ipſa magnitudine.
SIT enim magnitudo aleuior humido: & ſit magnitu
dinis quidem a grauitas b:
humidi uero molem habentis
æqualem ipſi a, grauitas ſit b c.
demonſtrandum eſt magni
tudinem a in humidum impulſam tanta ui ſurſum ferri,
quanta eſt grauitas c.
accipiatur enim quædam magnitu-
do, in qua d habens grauitatem ipſi c æqualem.
Itaque
magnitudo ex utriſque magnitudinibus conſtans, in qui-
bus a d, leuior eſt humido:
nam magnitudinis quidem quæ
ex utriſque conſtat grauitas eſt b c;
humidi uero habentis
molem ipſis æ qualem grauitas maior eſt, quàm b c:
quo-
niam b c grauitas eſt humidi
Figure: /permanent/library/4E7V2WGH/figures/0020-01 not scanned
[Figure 9]
molẽ habentis æqualem ipſia.
Si ergo demittatur in humidũ
magnitudo ex utriſque a d con
ſtans;
uſque eò demergetur, ut
tanta moles humidi, quanta eſt
pars magnitudinis demerſa eã
dem, quam tota magnitudo
grauitatem habeat.
hoc enim
iam demonſtratum eſt.
ſit autẽ
ſuperſicies humidi alicuius a b
c d circunferentia.
Quoniam igitur tanta moles humidi,
quanta eſt magnitudo a grauitatem habet eandem, quam
magnitudines a d:
perſpicuum eſt partem ipſius demer-
ſam eſſe magnitudinem a;
reliquam uero d totam ex hu-

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