Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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& cylindrus, vel portio cylindrica FG abſciſsa vnà cum
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portione ABC ex cylindro, vel portione cylindrica NO
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circumſcripta hemiſphærio, vel hemiſphæroidi NBO,
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cuius baſis circa diametrum NO, ſit baſi portionis ABC
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parallela: qua ratione baſis prædicti ſolidi FG, erit vel cir
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culus, vel ellipſis æqualis circulo maximo, vel ſimilis, &
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æqualis ellipſi circa NO, portionis ABC baſi paralle
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læ. </
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<
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>Dico portionem ABC ad cylindrum, vel portio
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nem cylindricam FG, eſse vt rectangulum BED, vnà
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cum duabus tertiis qua
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drati EB ad quadratum
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BD. </
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vel coni portio HDG,
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cuius fruſtum HKLG
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prædicto plano abſciſſum:
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& omnino ſint
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circulorũ
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,
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vel ellipſium ſimilium dia
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metri eiuſdem rationis
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cũ
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NO, vt ad XII huius, in
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eadẽ
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recta linea tres FM,
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AC, KL, ſectæ omnes bi
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fariam in
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cõmuni
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cẽtro
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E,
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& HBG, in eodem plano per axem. </
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<
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>Quoniam igitur ex ſu
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perioribus, reliquum ſolidi FG, dempto ABC, æquale eſt
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fruſto HKLG; erit eiuſdem ſolidi FG reliquum ABC
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æquale reliquo ſolidi FG, dempto HKLG: ſed hoc reli
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quum dempto HKLG, ſupra oſtendimus eſse ad ſolidum
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FG, vt rectangulum ex KL, & differentia HG, vnà
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cum duabus tertiis quadrati differentiæ, ad quadratum
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GH: & vt HG ad KL, ita eſt BD ad DE, propter ſimi
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litudinem triangulorum; vt igitur eſt rectangulum BED,
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vnà cum duabus tertiis quadrati BE, ad quadratum BD,
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ita erit portio ABC, ad cylindrum, vel portionem cylin
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dricam FG. </
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<
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>Quod demonſtrandum erat. </
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