Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
"/>
ſeſquialter eius, quæ uſque ad axem, quanta eſt linea m o.
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<
s
xml:id
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xml:space
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">Ponebatur autem portio ad humidum æqualis molis non
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minorem in grauitate proportionem habere, quam qua-
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/>
dratum, quod fit ab exceſſu, quo axis eſt maior, quam ſeſ-
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quialter eius, quæ uſque ad axem, ad quadratum, quod ab
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axe. </
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<
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xml:space
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">quare conſtat portionem ad humidum in grauitate
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non minorem proportionem habere, quàm quadratum li
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neæ m o ad quadratum ipſius n o. </
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<
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xml:space
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">Sed quam proportio-
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nem habet portio ad humidum in grauitate, eandem por-
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tio ipſius demerla habet ad totam portionem: </
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<
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xml:space
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ſupra demonſtratum eſt: </
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<
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xml:space
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<
s
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xml:space
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">quam proportionem habet de
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merſa portio ad totam, eam quadratum p f habet ad n o
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quadratum: </
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<
s
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xml:space
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">cum demonſtratum ſit in iis, quæ de conoidi
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bus, & </
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<
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">ſphæroidibus, ſi à rectangulo conoide duæ portio-
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nes planis quomodocunque ductis abſcindantur, portio-
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/>
nes inter ſe eandem habere proportionem, qnàm quadra-
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ta, quæ ab ipſorum axibus conſtituuntur. </
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<
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">non minorem
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ergo proportionẽ habet quadratum pf ad quadratũ n o,
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quàm quadratum m o ad idem n o quadratum. </
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<
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">quare
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xlink:label
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">E</
note
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p f non eſt minor ipſa m o; </
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xml:space
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igitur ab h ducatur linea ad rectos angulos ipſi n o, coi-
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bit cum b p, atque inter b, & </
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niam p f quidem æquidiſtans eſt diametro, h t autem ad
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diametrum perpendicularis; </
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<
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xml:space
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">& </
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>
<
s
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xml:space
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">r h æqualis ei, quæ uſque
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ad axem: </
s
>
<
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xml:id
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xml:space
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">ducta linea ab r ad t & </
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<
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xml:space
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faciet cum linea ſectionem in puncto p contingente. </
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re & </
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xml:space
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">cum humidi ſuperficie, quæ per is tran-
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ſit. </
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">Itaque ſi per b g puncta lineæ ipſi r t æquidiſtantes du
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cantur, angulos rectos facient cum ſuperficie humidi: </
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quod quidem in humido eſt ſolidum conoidis feretur ſur-
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ſum ſecundum eam, quæ per b ducta fuerit ipſi r t æquidi
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ſtans: </
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<
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">quod autem extra humidum, ſecundum eam, quæ
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per g deorſum feretur. </
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noides rectum conſtituatur.</
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