Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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DE CENTRO GRAVIT. SOLID.
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ad punctum ω. </
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<
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">Sed quoniam π circum ſcripta itidem alia
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figura æquali interuallo ad portionis centrum accedit, ubi
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primum φ applieuerit ſe ad ω, & </
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<
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portionis centrum ſe applicabit. </
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<
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poſſe perſpicuum eſt. </
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<
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ſi ponamus centrum portionis recedere à medio ad par-
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tes ω; </
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<
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quod portionis centrũ. </
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uitatis portionis a b c. </
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<
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libri Ar-
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chimedis</
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decimi.</
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cimi.</
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conicorũ</
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<
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">Quod autem ſupra demõſtratum eſt in portione conoi-
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dis recta per figuras, quæ ex cylindris æqualem altitudi-
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dinem habentibus conſtant, idem ſimiliter demonſtrabi-
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mus per figuras ex cylindri portionibus conſtantes in ea
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portione, quæ plano non ad axem recto abſcinditur. </
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<
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enim tradidimus in commentariis in undecimam propoſi
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tionem libri Archimedis de conoidibus & </
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<
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</
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<
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">portiones cylindri, quæ æquali ſunt altitudine eam inter ſe
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ſe proportionem habent, quam ipſarum baſes; </
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<
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quæ ſunt ellipſes ſimiles eandem proportionem habere,
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quam quadrata diametrorum eiuſdem rationis, ex corol-
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lario ſeptimæ propoſitionis libri de conoidibus, & </
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roidibus, manifeſte apparet.</
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deconoi-
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dibus &
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ſphæroi-
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dibus.</
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<
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">THEOREMA XXIIII. PROPOSITIO XXX.</
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<
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abſcindatur, plano baſi æquidiſtante; </
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<
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portio tota ad eam, quæ abſciſſa eſt, duplam pro
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portio nem eius, quæ eſt baſis maioris portionis
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ad baſi m minoris, uel quæ axis maioris ad axem
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minoris.</
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