Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO IX.
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>Si recta linea vtcumque ſecta fuerit, cubus qui
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fit à tota æqualis eſt duobus ſolidis rectangulis,
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quæ ex partibus, & totius quadrato fiunt. </
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>Sit recta linea AB ſecta in puncto C vtcumque. </
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co cubum ex AB æqualem eſse duobus ſolidis rectangu
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lis, quæ fiunt ex AC CB, & quadrato AB. </
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enim communi altitudine AB, eſt vt rectangulum BAC
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ad quadratum AB, ita ſolidum ex AB, & rectangulo
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BAC ad cubum ex AB, eademque ratione vt rectangu
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lum ABC, ad quadratum AB, ita ſolidum eſt AB, &
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rectangulo ABC ad cubum ex AB; erunt vt duo rectan
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gula BAC, ABC ad quadratum AB, ita duo ſolida
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ex AB, & rectangulis BAC, ABC ad cubum ex AB.
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<
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>Sed duo rectangula BAC, ABC ſunt æqualia quadrato
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AC; duo igitur ſolida ex AB, & rectangulis BAC, CBA,
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æqualia ſunt cubo ex AB. </
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<
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>Sed ſolidum ex AB & rectan
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gulo BAC eſt id quod fit ex AC, & AC & quadrato
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AB; duo igitur ſolida ex AC, CB, & quadrato AB ſi
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mul ſumpta æqualia ſua cubo ex AB. </
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<
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>Si igitur recta linea
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vtcumque ſecta fuerit, &c. </
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<
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>Quod demonſtrandum erat. </
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