Archimedes
,
Archimedis De insidentibvs aqvae
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DE IN SIDENTIBVS AQV AE
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guram in r. </
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<
s
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xml:space
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mis comprendens figuram r, ſecundum quod & </
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<
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xml:space
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gnum K. </
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<
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xml:space
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preserve
">Secentur autem ipſius plana aſuperficie plani a, b, g, ſecundum a,
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K, K, b. </
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<
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">Accipiatur autem, & </
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<
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">aliqua alia pyramis æqualis, & </
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</
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<
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xml:space
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">Secentur autem ipſius plana a plano a, b, g, ſecundum K, b, K, g, deſcribatur
<
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autem & </
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>
<
s
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xml:space
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">quædam alterius ſphæræ ſuperficies in humido circa centrum K. </
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<
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Sub ſolida autem magnitudine ſecetur ipſa ab eodem plano ſecundũ x, o, p. </
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Intelligatur autem, & </
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">magnitudo abſumpta ab humido quæ ſecundumh,
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in poſteriori pyramide æqualis ſolidæ quæ ſecundum r, partes aũt humidi,
<
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quòd in prima pyramide quæ ſub ſuperficiebus, quæ ſecundum ſuperficiem
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x, o, & </
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<
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">quod in ſecunda quæ ſub ſuperficiebus quę ſuperficie o p, ex quo ſunt
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poſitæ, & </
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<
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">continuæ inuicem non ſimiliter autem premuntur quæ quidẽ in
<
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prima pyramide premitur a ſolida magnitudine, quæ ſecundumr, & </
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<
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xml:space
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">ab hu
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mido continente ipſas, & </
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<
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xml:space
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">exiſtente in loco pyramidis, quæ ſecundum a, b, o,
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x. </
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<
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xml:space
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">Quæ autem in altera pyramide præmittitur ab humido continent ipſam
<
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exiſtente in loco pyramidis qui ſecundum p, o, b, g, eſt autem, & </
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<
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">grauitas
<
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quæ ſccundum r, minor grauitate humidi, quod ſecundum h, quoniam ma-
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gnitudinem quidem eſt æqualis. </
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<
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xml:space
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">Solida autem magnitudo ſupponitur eß le
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uior humido humidi continentis magnitudines r, b, eritq́ pyramidum æ-
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qualis. </
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<
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">Magis igitur premitur pars humidi quòd ſub ſuperficiebus, quæſe-
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cundum periferiam o, p, expellet ergo quod minus premitur, & </
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<
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humidum non motum. </
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<
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">Supponebatur autem non motum n n ergo demerge
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tur tota, ſed erit aliquid ipſius extra ſuperficiem humidi.</
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<
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">Theorema v. Propoſitio v.</
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<
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">Solidarum magnitudinum quæcunque fuerit leuior dimiſſa
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in humidũ in tanto demergetur ut tanta moles humidi quan-
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ta eſt moles demerſæ habeat æ qualem grauitatem cumtota ma
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gnitudine.</
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<
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</
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<
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<
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">Siigitur humidum eſt
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non motum ſimiliter prementur partes ipſius ex æquo poſitæ, ſimi-
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liter ergo premetur humidum quodſub ſuperficiebus, quæ ſecundum perife
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rias x, o, & </
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<
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<
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bumidi grauitas, quod in prima pyramide ſine b, h, t, g, ſolido æqualis graui
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tati bumidi, quod in altera pyramide ſiue r, s, c, y, humido palam igitur, ꝙ
<
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grauitas magnitudinis e, Z, h, t, eſt æqualis grauitati humidir, s, c, y. </
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<
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feſtum igitur quòd tanta moles humidi quanta eſt demerſa pars ſolidæ ma
<
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gnitudinis habet grauitatem æqualem toti magnitudini.</
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