Archimedes
,
Archimedis De insidentibvs aqvae
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DE INSIDENTIBVS AQVAE
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ſcriptum eſt, et alia eadẽ diſponãtur, demõſtrabitur autẽ rurſum ꝙ t,
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m, æquales exiſiens ipſi, f, i, & </
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<
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xml:space
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& </
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ductæ, quæ a, q, a, Z, æquales portiones auferentes æquales faciunt an-
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gulos ad dyametros. </
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<
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">portionum igitur a, h, b, Z, a, f, q, qui apud ſignal,
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***, anguli ſunt æquales. </
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xml:space
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">quæ b, s, recta ipſi b, c, æqualis & </
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">quæ s,
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r, ipſi r, c. </
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xml:space
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">Et quæ h, a, ipſi f, h, & </
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xml:space
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xml:space
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">Et quoniam dupla
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est, quæ f, x, ipſiy, i. </
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">Manifeſtum quòd quæ h, a, eſt maior, quàm dupla
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ipſius a, t. </
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">Rurſum autem ex hijs pa
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lam quòd non manet portio ſed inclinabitur ex parte a, quoniam ſup
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ponebatur portio, ſecundum unum ſignum tangere humidum palam
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quòd ſecundum ampliorẽ locum baſis ab humido comprehendetur.</
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">HAbeat etiam rurſum portio ad humidum in grauitate propor-
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tionem minorẽ ea, quam habet tetragonum, quod ab n, o, ad id q đ
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a, b, d. </
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">Quam autem proportionem habet portio ad humidum in gra-
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uitate, hanc habeat tetragonum, quod a, x, minorem autem eſt, quæ x,
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quàm o, n. </
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">Rurſum igitur in aptetur quædam intermedia portionum
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a, m, d, apol quæ p, i, æquedistanter ipſi b, d, producta æqualis ipſi x.
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">Secet autem ipſa intermedia coniſectione penes y, ipſam autem x, r,
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rectam penes h, demonſtrabitur, autem quæ p, y, dupla ipſius y, i, ſicut
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demonſtrata eſt, quæ, g, o, ipſius g, h, ducatur autem & </
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">quæ quidem
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p, ***, contingens ſectionem apol ſecundum p, quæ autem p, e, perpen-
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dicularis ſuper b, d, & </
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