Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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æquale erit cono KBL. </
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<
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>Rurſus quia eſt vt EB ad BD, ita
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quadratum GD ad quadratum DK, hoc eſt circulus cir
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ca GH ad circulum circa KL, hoc eſt conus GBH ſi
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deſcribatur ad conum KBL: ſed vt FB ad BE ita eſt co
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noides GBH ad conum GBH; ex æquali igitur erit vt
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FB ad BD, ita conoides GBH ad conum KBL, hoc
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eſt ad ſolidum AGBHC. </
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<
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>Manifeſtum eſt igitur
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. </
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COROLLARIVM.
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<
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>Ex huius Theorematis demonſtratione manife
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ſtum eſt, ijſdem poſitis cylindros deficientes, ex
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quibus conſtat exceſſus, quo figura conoidi hyper
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bolico circumſcripta ſuperat circumſcriptam co
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noidi parabolico, ita ſe habere, vt quorumlibet
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trium inter ſe proximorum minor proportio ſit
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minimi ad medium, quam medij ad maximum:
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æquales enim ſunt ſinguli ſingulis cylindris, ex
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quibus conſtat figura cono BKL circumſcripta,
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qui ſunt inter eadem plana parallela. </
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<
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>Quod ſi
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ita eſt, ſimul illud manifeſtum erit, & ex hoc, &
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ex ijs, quæ in ſecundo libro demonſtrauimus; præ
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dictum exceſſum ex tot cylindris deficientibus
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eiuſdem altitudinis, quos diximus componi poſſe,
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vt ipſius centrum grauitatis in axe BD diſtet à
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centro grauitatis coni KBL, hoc eſt à puncto in
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quo axis BD ſic diuiditur, vt pars, quæ ad ver
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ticem ſit reliquæ tripla, ea diſtantia, quæ minor
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ſit quantacum que longitudine propoſita. </
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