Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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deinde inter eadem plana tangentia eiſdem æquidiſtantia
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vtcumque plana ducta fuerint, altitudines ſolidorum, re-
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ſpectu dictorum tangentium ſumptas, ſimiliter ad eandem
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partem diuidentia, reperiamus figuras exhis planis in di-
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ctis ſolidis conceptas eſſe ſimiles, vel ſi plures producan-
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tur, tot numero in vno, quot in alio ſolido produci, quæ
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fint binæ ſimiles, & </
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">quæ ſunt vnius ſolidi ſimiliter inter ſe
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diſpoſitę, ac quę ſunt alterius, & </
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<
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bus quibuſdam rectis lineis communiter, tamquam earum-
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dem regulis, æquidiſtare. </
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<
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<
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<
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">earum homologæ cum
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quibuſuis alijs duabus regulis angulos æquales cum præ-
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dictis facientibus, vt infra Prop. </
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<
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<
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">huius oſtendetur, e-
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tiam haberi poterunt) Vnde ſiregulæ homologarum acci-
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piantur cum incidentibus planis concurrentes, & </
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ptarum in ſolidis ſimilium figurarum ductæ in ſingulis op-
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poſitæ tangentes præfatis regulis Parallelę producantur, ſt
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opus ſit, quouſq; </
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<
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& </
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cta occurſuum iungantur rectis lineis, etiam has iungentes
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reperiamus ſingulas eſſe incidentes ſuarum ſimilium figu-
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rarum, & </
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<
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dentes concipi in figuris ſimilibus, quarum, & </
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dentes ſint homologæ, & </
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ctiones planorum incidentium, & </
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tangentium. </
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lida in vniuerſum habere ſuppono.</
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ctas incidentes, vocentur. </
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ſimilium ſolidorum, & </
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ctorum.</
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<
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">FIguræ verò ex planis dictis tangentibus Parallelis in
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eiſdem ſolidis conceptæ, quotcumque ſint, altitudi-
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nes eorumdem reſpectu dictorum tangentium ſumptas ſi-
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militer ad eandem partem diuidentes, quæ ſimiles eſſe </
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