Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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PROPOSITIO XXIV.
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<
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>Si duarum pyramidum triangul as baſes haben
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tium æqualium, & ſimilium inter ſe, tria latera
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tribus lateribus homologis fuerint in directum
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conſtituta, in vertice communi erit vtriuſque ſi
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mul centrum grauitatis. </
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>Sint duæ pyramides ſimiles, & æquales, quarum ver
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tex communis G, baſes autem triangula ABC, DEF.
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<
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>Et ſint latera homologa pyramidum in directum inter ſe
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conſtituta: vt AG, GF: & BG, GD, & CG, GE.
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<
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>Dico compoſiti ex duabus pyramidibus ABCG, GDEF,
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ita conſtitut is centrum gra
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uitatis eſse in puncto G.
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<
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>Eſto enim H, centrum gra
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uitatis pyramidis ABCG,
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& ducta HGK, ponatur
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G
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K
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, æqualis GH, & iun
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gantur EK, KD, BH,
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CH. </
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>Quoniam igitur eſt
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vt HG, ad GK, ita CG,
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ad GE, & proportio eſt
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æqualitatis: & angulus
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HGC, æqualis angulo EG
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K
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, erit triangulum CGH,
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ſimile, & æquale triangulo EGK. </
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>Similiter triangulum
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BGH, trian gulo DGK; & triangulum BGC, triangu
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lo DGE: quare & triangulum BCH, triangulo DEK.
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pyramis igitur BCGH, ſimilis, & æqualis eſt pyramidi
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EDGK. </
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