Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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">ITAQVE primum habeat portio ad humidum in
<
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grauitate proportionem quidem maiorem, quàm qua dra
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tum x o ad quadratum b d; </
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>
<
s
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">minorem uero, quàm quadra
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tum, quod fit ab exceſſu, quo axis eſt maior, quàm ſeſquial-
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ter eius, quæ uſque ad axem, ad quadratum b d: </
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<
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">quam
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proportionem habet portio ad humidum in grauitate, eã
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habeat quadratum, quod fit à linea ψ ad quadratum b d:
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<
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">erit ψ maior quidem, quàm x o, minor uero, quàm exceſ-
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ſus, quo axis eſt maior, quàm ſeſquialter eius, quæ uſque ad
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axem. </
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<
s
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">aptetur quædam recta linea m n conicis ſectioni-
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bus a m q l,
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0085-01
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a x d interiecta,
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ac media, quæ li
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neæ ψ ſit æqua-
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lis; </
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quã coni ſectio
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nem in pun cto
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h; </
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<
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">rectam li-
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neam r g in u.
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</
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<
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">demõſtrabitur
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">D</
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m h dupla ip-
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ſius h n, ſicuti
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demonſtratum
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eſt o g ipſius g x
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duplam eſſe. </
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>
<
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xml:id
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xml:space
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">à
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puncto autẽ m
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ducatur m y contingens ſectionem a m q l in m: </
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xml:space
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<
s
xml:id
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">m c a d
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b d perpendicularis. </
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<
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">poſtea ducta a n, & </
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>
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">producta ad q li
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neæ a n, n q inter ſe æquales erunt. </
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>
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">quoniã enim in ſimi-
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note-0085-03a
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">E</
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libus portionibus a m q l, a x d ductæ ſunt à baſibus ad
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portiones lineæ a q, a n, quæ æquales angulos continent
<
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cum ipſis baſibus, eandem proportionem habebit q a ad
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an, quam la ad a d. </
s
>
<
s
xml:id
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xml:space
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">æqualis eſt ergo a n ipſi n q; </
s
>
<
s
xml:id
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xml:space
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s
>
<
s
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">a q
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