Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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tes A deficiens, cuius baſis BC. </
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<
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>Dico fieri poſse quod
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proponitur: ducta enim per verticem figuræ A, baſi BC,
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parallela, atque ideo figuram ipſam contingente, abſol
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uatur parallelogrammum BL, ſectaque diametro AD,
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bifariam, & ſingulis eius partibus ſemper bifariam, du
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cantur per puncta ſectionum rectæ lineæ baſi BC, & in
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ter ſe parallelæ, atque ita multiplicatæ ſint ſectiones,
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vt ſecti parallelogrammi in parallelogramma æqua
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lia, & eiuſdem altitudinis quælibet pars, vt paralle
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logrammum BF, ſit minus ſuperficie propoſita, cu
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ius parallelogram
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mi latus EF, ſe
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cet figuræ termi
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num BAC, in
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punctis GH, &
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diametrum AD, in
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puncto K. erit igi
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tur GK, æqualis
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KH: per omnia
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igitur puncta ſe
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ctionum termini
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BAC, quæ à prædictis fiunt lineis parallelis, ſi ducan
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tur diametro AD parallelæ, figura quædam ipſi ABC,
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inſcribetur, & altera circumſcribetur ex parallelogram
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mis æqualium altitudinum. </
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<
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>Dico harum figurarum
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inſcriptam ſuperari à circumſcripta minori ſpacio ſuper
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ficie propoſita. </
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<
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>Quoniam enim omnia parallelogramma,
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quibus figura circumſcripta ſuperat inſcriptam ſimul ſum
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pta ſunt æqualia BF parallelogrammo: ſed parallelo
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grammum BF, eſt minus ſuperficie propoſita: exceſſus
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igitur quo figura circumſcripta inſcriptam ſuperat, minor
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erit ſuperficie propoſita. </
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<
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>Fieri igitur poteſt, quod propo
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nebatur. </
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