Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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quadrato AC: & quod fit ex BC, & rectangulo ACB,
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eſt quod fit ex AC, & quadrato BC; cubus igitur ex
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AB æqualis eſt duobus cubis ex AC CB, vna cum ſex
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ſolidis, quorum tria fiunt ex AC, & BC quadrato, tria
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autem ex BC, & quadrato AC, hoc eſt duobus ſolidis,
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quorum alterum fit ex tripla ipſius AC, & quadrato BC,
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alterum ex tripla ipſius BC & quadrato AC. </
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<
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monſtrandum erat. </
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PROPOSITIO XI.
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>Si recta linea vtcumque ſecta fuerit, cubus qui
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fit à tota æqualis eſt cubis partium vna cum ſoli
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do rectangulo, quod totius tripla, & partibus
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continetur. </
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>Sit recta linea AB ſecta in puncto C vtcumque. </
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co cubum ex AB æqualem eſse duobus cubis ex AC,
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CB, vna cum ſolido rectangulo ex AC CB, & tripla
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ipſius AB. </
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>Quoniam enim quod fit ex AC, & rectan
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gulo ACB, eſt id quod fit ex BC, & quadrato AC: &
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quod fit ex BC, & rectangulo ACB, eſt id, quod fit ex
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AC & quadrato BC. ſed duo ſolida ex AC CB, & re
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ctangulo ACB ſunt id, quod fit ex compoſita vtriuſque
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altitudine AB, et rectangulo ACB; duo igitur prædi
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cta ſolida, quæ ex AC CB, & earum quadratis recipro
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ce fiunt æqualia ſunt ſolido ex AB BC CA, & triplum
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triplo, videlicet duo ſolida, quæ fiunt reciproce ex triplis </
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