Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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ad GE, altera maiori extremæ FG in proportione con
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tinua ipſius NG ad GF. </
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<
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>Quoniam enim ob centra gra
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uitatis QPR eſt vt QP ad PR, ita portio ABCD ad
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reliquum cylindri LM, erit componendo, & per conuer
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ſionem rationis, & conuertendo, vt PQ ad QR, ita por
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tio ABCD ad LM cylindrum: ſed portio ABCD ad
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LM cylindrum eſt vt prædictus exceſſus ad axim EF;
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vtigitur prædictus exceſſus ad axim EF, ita eſt PQ ad
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QR. </
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>Quod demonſtrandum erat. </
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PROPOSITIO XLI.
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<
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>Omnis conoidis parabolici centrum grauita
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tis eſt punctum illud, in quo axis ſic diuiditur vt
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pars, quæ eſt ad verticem ſit dupla reliquæ. </
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<
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>Sit conoides parabolicum ABC, cuius vertex B, axis
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autem BD ſectus in puncto E ita vt EB ſit ipſius ED
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dupla. </
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<
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>Dico E eſse centrum grauitatis conoidis ABC.
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>Nam in ſectione per
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axim parabola ABC,
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cuius diameter erit B
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D, deſcribatur rian
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gulum ABC; ſum
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ptisque ipſius BD æ
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qualibus DH, HO,
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per puncta H, O, ſe
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centur vnà parabola
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& triangulum ABC
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duabus rectis FGH
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KL, MNOPQ: & per eas rectas ſecetur conoi
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des ABC planis baſi parallelis, factæ autem ſe
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ctiones erunt circuli circa FL, MQ, & in parabola </
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