Archimedes, Archimedis De insidentibvs aqvae

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[14] Explicit de Inſidentibus Aquæ Liber Primus.
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12DE IN SIDENTIBVS AQV AE guram in r. Centrum autem terræ ſit K. Intelligatur autem quædam pyra-
mis
comprendens figuram r, ſecundum quod &
prius uerticem habens ſi-
gnum
K.
Secentur autem ipſius plana aſuperficie plani a, b, g, ſecundum a,
K
, K, b.
Accipiatur autem, & aliqua alia pyramis æqualis, & ſimilis huic.
Secentur autem ipſius plana a plano a, b, g, ſecundum K, b, K, g, deſcribatur
autem
&
quædam alterius ſphæræ ſuperficies in humido circa centrum K.
Sub
ſolida autem magnitudine ſecetur ipſa ab eodem plano ſecundũ x, o, p.

Intelligatur
autem, &
magnitudo abſumpta ab humido quæ ſecundumh,
in
poſteriori pyramide æqualis ſolidæ quæ ſecundum r, partes aũt humidi,
quòd
in prima pyramide quæ ſub ſuperficiebus, quæ ſecundum ſuperficiem
x
, o, &
quod in ſecunda quæ ſub ſuperficiebus quę ſuperficie o p, ex quo ſunt
poſitæ
, &
continuæ inuicem non ſimiliter autem premuntur quæ quidẽ in
prima
pyramide premitur a ſolida magnitudine, quæ ſecundumr, &
ab hu
mido
continente ipſas, &
exiſtente in loco pyramidis, quæ ſecundum a, b, o,
x
.
Quæ autem in altera pyramide præmittitur ab humido continent ipſam
exiſtente
in loco pyramidis qui ſecundum p, o, b, g, eſt autem, &
grauitas
quæ
ſccundum r, minor grauitate humidi, quod ſecundum h, quoniam ma-
gnitudinem
quidem eſt æqualis.
Solida autem magnitudo ſupponitur le
uior
humido humidi continentis magnitudines r, b, eritq́ pyramidum æ-
qualis
.
Magis igitur premitur pars humidi quòd ſub ſuperficiebus, quæſe-
cundum
periferiam o, p, expellet ergo quod minus premitur, &
non manet
humidum
non motum.
Supponebatur autem non motum n n ergo demerge
tur
tota, ſed erit aliquid ipſius extra ſuperficiem humidi.

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