Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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vt eſt HN, ad NG, ita fiat KM, ad ML, & GM, iun
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gatur: & vt eſt GO, ad ON, ita fiat GP, ad PM, & iun
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gantur MN, OP, FG, GD, GE. </
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>Quoniam igitur re
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cta KL, ſecat trapezij BCFE, latera parallela bifariam
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in punctis K,L, & eſt vt HN, ad NG, hoc eſt vt duplum
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lateris BC, vna cum latere EF, ad duplum lateris EF, vna
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cum latere BC, ita KM, ad ML; erit punctum M, cen
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trum grauitatis trapezij BCFE, & pyramidis GBCFE,
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axis GM. </
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>Et quoniam vt GO, ad ON, ita eſt GP, ad
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PM, atque ideo GP, tripla ipſius PM, erit punctum P,
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centrum grauitatis pyramidis GBCFE, atque ideo in
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linea OP. </
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>Rurſus quoniam angulus ACB; æqualis eſt
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angulo DFK: & vt AC, ad CK, ita eſt DF, ad FK:
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eſt autem DF, parallela ipſi AC, & FK, ipſi CL; erit
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reliqua DK, reliquæ AL, parallela; vnum igitur planum
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eſt, ADKL, in quo iacet triangulum GMN; cum igitur
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ſit parallela KH, ipſi GL, vtque HN, ad NG, ita
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K
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M, ad ML; erit MN, ipſi LG, parallela: ſed OP, eſt
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parallela ipſi MN; ſecant enim latera trianguli GMN,
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in eaſdem rationes; igitur OP, erit LG, parallela. </
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<
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>Simi
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liter ex puncto O, ad axes duarum pyramidum GABED,
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GACFD, duæ aliæ rectæ lineæ ducerentur, quas & cen
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tra grauitatis pyramidum habere, & parallelas rectis GQ,
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GR, alteram alteri eſse oſtenderemus, ſicut oſtendimus
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OP, habentem centrum grauitatis pyramidis GBCFE,
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ipſi GL, parallelam; ſed tres rectæ GL, GQ, GR, ſunt
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in eodem plano trianguli nimirum ABC; tres igitur præ
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dictæ parallelæ, quæ ex puncto O, atque ideo trium præ
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dictarum pyramidum centra grauitatis erunt in eodem pla
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no, per punctum O, & trianguli ABC, parallelo. </
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<
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>Quo
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niam igitur fruſti ABCDE, centrum grauitatis eſt in axe
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GH; (manifeſtum hoc autem ex duobus centris grauitatis
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pyramidis, cuius eſt prædictum fruſtum, & ablatæ, quæ
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centra grauitatis ſunt in axe, cuius ſegmentum eſt axis </
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