Valerio, Luca - De centro gravitatis solidorum

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Sit fruſtum ABCFGH, pyramidis, vel coni ABCD,
cuius baſis triangulum, vel circulus ABC, axis autem
DE: & vt eſt AC ad FH, ita ſit FH ad N, & fru
ſti axis EK, nec non idem pyramidis, vel coni AB
CK, vt ſit eadem altitudo. Dico fruſtum ABCF
GH, ad pyramidem, vel conum, ABCK, eſse vt
tres lineas AC, FH, NO, ſimul ad ipſius AC, tri
plam: ad priſma autem, vel cylindrum, cuius baſis ABC,
altitudo autem eadem cum fruſto, vttres AC, FH, NO,
ſimul, ad ipſius AC, triplam. Nam vt eſt AC ad FH,
& FH ad NO, ita ſit NO ad P: & exceſſus, quo hæ

17[Figure 17]
quatuor lineæ differunt, ſint AL, FM, Oque Ergo
vt AC ad FH, ita erit AL ad FM, & FM ad Oque
Quoniam igitur eſt vt AC ad P, ita pyramis, vel conus
ABCD, ad ſimilem ipſi pyramidem, vel conum DFGH,
ob triplicatam laterum homologorum proportionem; erit
diuidendo, vt tres AL, FM, OQ, ſimul ad P, ita fru
ſtum ABCFGH, ad pyramidem, vel conum DFGH:
ſed conuertendo eſt vt P, ad AC, ita pyramis, vel conus
DFGH, ad pyramidem, vel conum ABCD: ex æquali
igitur, vt tres AL, FM, OQ, ſimul ad AC, ita fruſtum

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