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