Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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igitur M, N, ſint centra grauitatis propoſiti priſmatis par
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tium priſmatum AFG, AGH, atque obid O, totius priſ
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matis AFGH, in linea MN, centrum grauitatis; per pun
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ctum O, recta MN, tranſibit. </
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<
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>Et quoniam planum tra
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pezij PV, ſecatur duobus planis parallelis, erunt TV, PQ,
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fectiones parallelæ. </
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>His demonſtratis, fiat rurſus vt AB,
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bis vna cum EF, ad EF, bis vna cum AB, ita TY, ad
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YP: & ſumatur T
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, pars quarta ipſius TP, & YZ, pars
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quarta ipſius PY, & ad axim KL, ducantur ipſis TV,
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PQ, parallelæ
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S, YR, ZX,
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quæ rectas TP,
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KL, ſecabunt in
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rationes:
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vt igitur TY, ad
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P, hoc eſt vt
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AB, bis vna cum
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EF, ad EF bis
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vna cum AB, ita
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erit
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K
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R, ad RL,
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eritque KS, pars
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quarta ipſius K
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L, qualis & R
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X, ipſius RL. </
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<
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>Et quoniam M, eſt centrum grauitatis fru
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ſti AFG; manifeſtum eſt ex tribus prædictis axis TP, ſe
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ctionibus
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, Z, eſse MZ, ad Z
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, hoc eſt OX, ad XS,
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vt eſt 6 ad compoſitam ex tribus deinceps proportionalibus
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AB, EF, 6; Fruſti igitur ABCDEFGH, centrum gra
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uitatis O, axim KL, ita diuidit, vt propoſuimus. </
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<
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>Quod
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ſi fruſtum propoſitum ſit pyramidis baſim habentis quin
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quelateram, & quotcumque plurium deinceps fuerit la
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terum, eadem demonſtratione ſemper deinceps, vt in priſ
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mate monuimus, propoſitum concluderemus. </
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