Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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ſcidit portionem ABC, plano circuli FH parallelum.
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<
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>Quoniam igitur fruſtum FH
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K
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L æquale eſt cylindri EF
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reſiduo, dempta ABC portione, quod ex præcedenti theo
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remate perſpicuum eſse debet: erit portio ABC æqualis
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ei, quod relinquitur cylindri EF, ſi fruſtum auferatur
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FHKL: ſed hoc reliquum eſt ad cylindrum EF, vt exceſ
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ſus, quo tripla lineæ FH, ſuperat tres deinceps proportio
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nales FH, KL, & minorem extrema, ad triplam lineæ FH:
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vt FH, ad KL, ita eſt BD ad DG, & DG, ad M; vt igi
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tur exceſſus, quo tripla ipſius BD, ſuperat tres BD, DG,
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& M, ſimul, ad lineæ BD triplam, ita erit portio ABC ad
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cylindrum EF. </
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>Quod demonſtrandum erat. </
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PROPOSITIO XIV.
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>Omnis portio ſphæræ abſciſsa duobus planis
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parallelis alteroper centrum acto ad cylindrum,
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cuius baſis eſt eadem baſi portionis, ſiue circu
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lo maximo, & eadem altitudo, eam habet pro
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portionem, quam exceſſus, quo maior extrema ad
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ſphæræ ſemidiametrum, & axim portionis exce
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dit tertiam partem axis portionis; ad maiorem ex
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tremam antedictam. </
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<
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>Sit portio AB
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CD, ſphæræ, cu
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ius centrum F,
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abſciſſa duobus
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planis parallelis
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altero per
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F tranſeunte;
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axis autem por
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tionis fit FG: &
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