Valerio, Luca - De centro gravitatis solidorvm libri tres

Valerio, Luca, De centro gravitatis solidorvm libri tres

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1portionis circulus, cuius diameter AC, & vt EG ad GF,
ita ſit GF ad S, & S ad FM, cuius ſit pars tertia FN, &
ponatur ipſius BG, ſubſeſquialtera GL. Dico portio
nem ABC ad cylindrum KH eſse vt LN ad BF. Nam
vt FG ad GE, ſiue ad BG, ita ſit EG ad PQ, à qua
abſcindatur QR, pars tertia ipſius FG. Et plano per G
tranſeunte baſibus cylindri KH, & ABC portionis pa
rallelo ſecentur vna cylindrus KH in duos cylindros DH,
EK: & portio ABC, in portionem ECAD, & DBE
hemiſphærium. Quoniam igitur eſt conuertendo, vt PQ
ad EG, ita EG
ad GF, & eſt ip
ſius GF pars ter
tia QR, erit por
tio DACE ad
cylindrum EK,
vt PR ad Pque
Rurſus, quia eſt
vt EG ad GF:
hoc eſt vt PQ ad
EG, ita GF ad
S, & vt EG ad
GF, ita eſt S ad
FM; erit ex æqua

85[Figure 85]
li, vt PQ ad GF, ita GF ad FM. Sed vt GF ad RQ,
ita eſt MF ad FN, tertiam ipſius MF partem, ex æquali
igitur erit vt PQ ad QR, ita GF ad FN, & per conuer
ſionem rationis, & conuertendo, vt PR ad PQ, ita NG ad
GF. Sed vt PR ad PQ, ita erat portio ECAD ad cy
lindrum EK; vtigitur NG ad GF, ita erit portio EC
AD ad cylindrum EK. Sed vt GF ad FB, ita eſt cy
lindrus EK ad cylindrum KH: ex æquali igitur vt NG
ad BF, ita portio ECAD, ad cylindrum KH. Similiter
oſtenderemus eſse, vt GL ad BF, ita DBE hemiſphæ-

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