Valerio, Luca - De centro gravitatis solidorvm libri tres

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1KLMN abſciſſum ijſdem planis, quibus por
tio, & ſphæræ ſemidiameter ſit EHGS: & po
ſita T tripla ipſius ES, & V ipſius EG tri
pla, eſto vt V ad T ita T ad XZ: & vt GE
ad EH ita EH ad ω, & ſit ZY, ipſius XZ,
æqualis tribus GE, EH, ω, vt ſit exceſſus
XY: & ſecto axe GH bifariam in puncto I, in
linea GI, ſumatur O, centrum grauitatis fru
ſti KLMN: Et vt ΥX ad XZ, ita fiat IO
ad OIP. Dico portionis ABCD centrum
grauitatis eſſe P. Nam circa axim GH pla
nis baſium portionis interceptus ſtet cylin
drus QR, cuius baſis ſit æqualis circulo ma
ximo. Quoniam igitur eſt vt YX ad XZ,
hoc eſt vt IO ad OP, ita portio ABCD
ad cylindrum QR, & diuidendo vt OI ad
IP, ita portio ABCD ad reliquum cylindri
QR: & I eſt cylindri QR, & O prædicti
reſidui centrum grauitatis; erit reliquæ por

115[Figure 115]
tionis ABCD centrum grauitatis P. Quod demon
ſtrandum erat.

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