Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO XXXIV.
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<
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>Omnis priſmatis baſim pluſquam trilateram
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habentis centrum grauitatis eſt in medio axis. </
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<
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>Sit priſma ABCDEFGH, baſim habens quadrila
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teram ABCD: axis autem
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K
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L, bifariam ſectus in pun
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cto M. </
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<
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>Dico punctum M, eſse centrum grauitatis priſ
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matis ABCDEFGH. </
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>Iungantur enim rectæ BD, FH,
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vt parallelogrammum ſit BH, ſectumque totum priſma
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in duo priſmata, quorum ba
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ſes ſunt triangula, in quæ ſecta
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ſunt quadrilatera AC, EG,
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ſint autem axes duorum priſ
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matum triangulas baſes ha
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bentium NO,
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Erunt
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igitur centra grauitatis O, tri
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anguli ABD, & L, quadri
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lateri AC, & Q, trianguli
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BCD, itemque N, trianguli
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EFH, & K, quadrilateri EG,
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& P, trianguli FGH: iun
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ctæ igitur OQ, NP, per pun
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cta L, K, tranſibunt: cumque tres prædicti axes ſint
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lateribus priſmatis, atque ideo inter ſe quoque paralleli;
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parallelogramma erunt OP, NL, LP. ducta igitur per
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punctum M, ipſi OQ, vel NP, parallela RS, erit vt
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NK, ad KP, ita RM, ad MS: & vt KM, ad ML, ita
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NR, ad RO, & PS, ad SQ: ſed KM, eſt æqualis ML;
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igitur & KR, ipſi RO, & PS, ipſi SQ, æqualis erit: ſunt
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autem hæ ſegmenta axium NO,
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punctum igitur
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R, eſt centrum grauitatis priſmatis ABDEFH: & per </
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