Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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<
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>Sit fruſtum ABCFGH, pyramidis, vel coni ABCD,
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cuius baſis triangulum, vel circulus ABC, axis autem
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DE: & vt eſt AC ad FH, ita ſit FH ad N, & fru
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ſti axis EK, nec non idem pyramidis, vel coni AB
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CK, vt ſit eadem altitudo. </
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<
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>Dico fruſtum ABCF
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GH, ad pyramidem, vel conum, ABCK, eſse vt
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tres lineas AC, FH, NO, ſimul ad ipſius AC, tri
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plam: ad priſma autem, vel cylindrum, cuius baſis ABC,
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altitudo autem eadem cum fruſto, vttres AC, FH, NO,
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ſimul, ad ipſius AC, triplam. </
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<
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>Nam vt eſt AC ad FH,
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& FH ad NO, ita ſit NO ad P: & exceſſus, quo hæ
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quatuor lineæ differunt, ſint AL, FM,
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Ergo
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vt AC ad FH, ita erit AL ad FM, & FM ad
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Quoniam igitur eſt vt AC ad P, ita pyramis, vel conus
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ABCD, ad ſimilem ipſi pyramidem, vel conum DFGH,
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ob triplicatam laterum homologorum proportionem; erit
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diuidendo, vt tres AL, FM, OQ, ſimul ad P, ita fru
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ſtum ABCFGH, ad pyramidem, vel conum DFGH:
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ſed conuertendo eſt vt P, ad AC, ita pyramis, vel conus
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DFGH, ad pyramidem, vel conum ABCD: ex æquali
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igitur, vt tres AL, FM, OQ, ſimul ad AC, ita fruſtum </
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