Valerio, Luca, De centro gravitatis solidorvm libri tres

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1
PROPOSITIO X.
Si recta linea vtcumque ſecta fuerit, cubus qui
fit à tota æqualis eſt cubis partium, & duobus ſo­
lidis rectangulis, quæ partium triplis, & earun­
dem quadratis reciproce continentur.
Sit recta linea AB ſecta vtcumque in puncto C. Dico
cubum ex AB æqualem eſse duobus cubis ex AC, CB,
& duobus ſolidis rectangulis, quorum alterum fit ex tripla
75[Figure 75]
ipſius AC, & quadrato BC; alterum autem ex tripla ip­
ſius BC, & quadrato AC. Quoniam enim quadratum
ex AB æquale eſt duobus quadratis ex AC, CB, & ei
quod bis fit ex AC CB: & parallelepipeda eluſdem al­
titudinis inter ſe ſunt vt baſes; erit rectangulorum folido­
rum id quod fit ex AC, & quadrato AB æquale cubo ex
AC, & ei, quod fit ex AC, & rectangulo ACB bis, &
ei, quod ex AC, & quadrato BC. Eadem ratione erit
quod fit ex BC, & quadrato AB æquale cubo ex BC, &
ei, quod fit ex BC, & rectangulo ACB, bis & ei, quod ex
BC, & quadrato AC. Sed cubus ex AB æqualis eſt
duobus ſolidis ex AC CB. & quadrato AB; cubus igi­
tur ex AB æqualis eſt duobus cubis ex AC CB, & ſex
ſolidis, quorum tres fiunt ex AC, & duobus rectangulis
ex AC CB, & quadrato BC: tria vero ex BC, & duo­
bus rectangulis ex AC CB, & quadrato AC. Sed quod
fit ex AC, & rectangulo ACB, eſt quod fit ex BC, &

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