Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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_humidi ſuperficiem.</
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">]_ Est enim t ω æqualis κ r, hoc eſt ei, quæ
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uſque ad axem. </
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<
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">quare ex ijs, quæ ſuperius demonſtrata ſunt, linea
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t h ducta erit ad humidi ſuperficiem perpendicularis.</
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<
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">_Minorem igitur proportionem habet quadratum p i_
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_ad quadratum i y, quàm quadratum e ψ ad ψ b quadratũ]_
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Hæc & </
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">alia, quæ ſequuntur, tum in hac, tum in ſequenti propoſitio-
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ne non alio, quàm quo ſupra modo demonstrabimus.</
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<
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">_Itaque per z g ductis perpendicularibus ad humidi ſu-_
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_perficiem, quæ i pſi t h æ quidiftent; </
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<
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_ſam non manere, ſed reuolui adeo, ut axis cum ſuperſicie_
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_humidi angulum faciat maiorem eo, quem nunc facit.</
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<
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Nam cum perpendicularis, quæ per g, ducitur ad eas partes cadat,
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in quibus eſt l; </
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">neceſſarium eſt
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centrum g deorſum ferri, & </
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<
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">quare partes ſolidi, quæ
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ſunt ad l deorſum; </
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<
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">quæ uero ad a ſurſum ferentur, ut axis cum ſu-
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perficie humidi maiorem angulum contineat.</
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<
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<
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">Sic enim erit i o æ qualis ψ b, itẽq; </
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ipſi f.</
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<
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">] _Hoc in tertia figura, quam nos addidimus, perſpicue apparet_.</
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">PROPOSITIO IX.</
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<
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portio conoidis rectanguli, quando
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axem habuerit maiorem quidem, quàm ſeſquial-
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terum eius, quæ uſque ad axem; </
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<
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">minorem uero,
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quàm ut ad eam, quæ uſque ad axem proportio-
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nem habeat, quam quindecim ad quatuor; </
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">& </
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<
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grauitate ad humidum proportionem habeat ma
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iorem, quàm exceſſus, quo quadratum, quod fit
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ab axe maius eſt quadrato, quod ab exceſſu, quo
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axis eſt maior, quàm ſeſquialter eius, quæ uſq; </
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axem, habet ad quadratum, quod ab axe: </
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