Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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b ψ dupla ſit ψ d, erit d b ipſius b ψ ſeſquialtera. </
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<
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<
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xml:space
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">quoniam e b ſeſ
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quialtera est b r, ſequitur reliquam c d ipſius ψ r, boc est eius, quæ
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uſque ad axem ſeſquialteram eſſe. </
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<
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">quare b c erit exceſſus, quo axis
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maior est, quàm ſeſquialter eius, quæ uſque ad axem.</
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<
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<
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<
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">]_ Nam cum portio ad bumi-
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dum in grauitate proportionem habeat eandem, quàm quadratum
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f q ad quadratum d b: </
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<
s
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">habeatq, minorem proportionem, quàm qua
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dratum factum ab exceſſu, quo axis maior eſt, quàm ſeſquialter eius,
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quæ uſque ad axem, ad quadratum ab axe; </
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<
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">boc eſt minorem, quàm
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quadratum c b ad quadratum b d: </
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<
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axi: </
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<
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">quadratum f q ad quadratum d b proportionem minorem ha-
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bebit, quàm quadratum c b ad idem b d quadratum. </
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<
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tum f q minus erit quadrato c b: </
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<
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minor.</
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<
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<
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">]_ Quoniam enim c b ſeſquial-
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tera eſt b r, & </
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<
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">estq; </
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ti.</
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ipſa b r minor erit.</
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<
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">_Itaque quoniam ponitur axis portionis cum ſuperficie_
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_humidi facere angulum maiorem angulo b: </
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_p y i angulo b maior.</
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<
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">]_ Nam cum linea p y ſuperficiei bumidi
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æ quidistet; </
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">angulus p y i æqualis erit angulo, qui
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diametro portionis n o, & </
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">quare & </
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b maior erit.</
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<
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">_Maiorem igitur proportionem habet quadratum p i ad_
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_quadratum i y, quàm quadratum e ψ ad ψ b quadratu.</
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Deſcribantur ſeorſum triangula p i y, e ψ b. </
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<
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maior ſit angulo e b ψ, ad lineam i y, atque ad punctum y in ea da-
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tum fiat angulus u y i æqualis angulo e b ψ. </
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<
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i rectus æqualis recto ad ψ. </
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<
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">reliquus igitur y u i reliquo b c ψ est
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æqualis. </
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<
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">quare linea u i ad lineam i y eandem proportionem ha-
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bet, quam linea e ψ ad ψ b. </
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<
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<
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xlink:label
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lineam in maiorem habet proportionem quam u i ad eandem. </
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<
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ti.</
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p i ad i y maiorem proportionem habebit, quàm e ψ ad ψ b: </
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<
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propterea quadratum p i ad quadratum i y maiorem habebit, </
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