Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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ABCDFGH, ad pyramidem, vel conum ABCD.
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>Rurſus quoniam axis DE, & latera pyramidis, vel coni
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ABCD, ſecantur plano trianguli, vel circuli FGH, baſi
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ABC, parallelo; erit componendo, vt AD, ad DF, hoc
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eſt, vt AC ad FH, propter ſimilitudinem triangulorum,
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hoc eſt vt AC, ad CL, ita ED, ad DK; & per conuer
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ſionem rationis, vt AC, ad AL, ita DE, ad EK: ſed vt
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DE ad EK, ita eſt pyramis, vel conus ABCD, ad py
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ramidem, vel conum ABCK; vt igitur AC, ad AL,
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ita eſt pyramis, vel conus ABCD, ad pyramidem, vel
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conum ABCK; ſed vt tres lineæ AL, FM, OQ ſimul
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ad AC, ita erat fruſtum ABCFGH, ad pyramidem,
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vel conum ABCD; ex æquali igitur, erit vt tres lineæ
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AL, FM, OQ, ſimul ad AL, ita fruſtum ABCFGH,
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ad pyramidem, vel conum ABCK. Rurſus, quoniam
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tres exceſſus AL, FM, OQ, ſunt deinceps proportio
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nales in proportione totidem terminorum AC, FH, NO,
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erunt vt AL, FM, OQ, ſimul ad AL, ita AC, FH,
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NO, ſimul ad AC: ſed vt AL, FM, OQ, ſim ul ad
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AL, ita erat fruſtum ABCFGH, ad pyamidem, vel
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conum ABCK; vt igitur tres lineæ AC, FH, NO, ſi
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mul, ad AC, ita erit fruſtum ABCFGH, ad pyrami
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dem, vel conum ABCK. </
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<
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>Sed vt AC, ad ſui triplam, ita
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eſt pyramis, vel conus ABCK ad priſma, vel cylindrum,
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cuius eſt eadem baſis ABC, & eadem altitudo cum py
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ramide, vel cono ABCK; ex æquali igitur, erit vt tres
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lineæ AC, FH, NO, ſimul ad ipſius AC, triplam, ita
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fruſtum ABCFGH, ad priſma, vel cylindrum, cu
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ius baſis ABC, & eadem altitudo pyramidi, vel cono
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ABCK: ideſt eadem, fruſto ABCFGH. </
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eſt igitur propoſitum. </
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