Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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erit axis DE, pyramidis ABCD, cuius axis ſegmentum
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DP eſt triplum ipſius PE: igitur P centrum erit pyra
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midis ABCD. </
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>Et quoniam tres rectæ FK, KH, HF,
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ſunt parallelæ tribus BD, DC, CB, pro vt inter ſe reſpon
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dent, vt KH, ipſi LG, quoniam vtraque lateri DC, ob
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latera triangulorum ſecta proportionaliter in punctis K, H,
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L, G: & ſic de reliquis; erit pyramis A
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K
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FH, ſimilis toti
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pyramidi ABCD. </
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>Similiter vnaquæque trium aliarum
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pyramidum abſciſſarum, videlicet FLBG, GHMC,
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KDLM, ſimilis erit pyramidi ABCD, atque ideo in
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ter ſe ſimiles. </
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<
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>Rurſus,
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quoniam pyramidum
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ſimilium latus AD eſt
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duplum lateris AK, ho
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mologi; pyramis AB
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CD, octupla erit py
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ramidis AKFH, ob
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triplicatam laterum ho
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mologorum proportio
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nem. </
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<
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qunæque</
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trium reliqua
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rum pyramidum abſciſ
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ſarum erit octaua pars
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pyramidis ABCD;
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quatuor igitur pyramides abſciſſæ ſimul ſumptæ dimi
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dium erit pyramidis ABCD: & reliquum igitur ſoli
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dum demptis quatuor pyramidibus, dimidium pyramidis
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ABCD. </
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>Dico reliquum ſolidum LKMGFH, eſſe
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octaedrum. </
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<
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>Nam octo triangulis ipſum contineri mani
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feſtum eſt. </
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<
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>bina autem oppoſita eſſe parallela, & æqualia,
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& ſimilia, ſic oſtendimus. </
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<
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>Quoniam enim triangulum
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FGH, eſt in plano trianguli ABC, plano trianguli KLM
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parallelo; erit triangulum FGH, parallelum triangu-</
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