Cavalieri, Buonaventura
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Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBERI.
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xml:space
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">SI ſphæroides, vel conoides parabolicum, ſeu hyperboli-
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cum ſecentur quomodocumq; </
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<
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rectis, ſiue inclinatis, communes ſectiones ſimiles erunt, & </
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diametri eiuſdem rationis erunt omnes in eadem figura per
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axem tranſeunte, rectè eaſdem ſecante.</
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<
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<
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">de Conoidibus,
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& </
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<
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Arch. </
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<
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">demonſtrantur. </
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guras verificari pariter manifeſtum eſt, hoc autem dico, vtor enim
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ijſdem ſectionum nominibus tamquam figuras ſub ipſis comprehen-
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fas ſignificantibus.</
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xml:space
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">THEOREMA XLIII. PROPOS. XLVI.</
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<
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">EXpoſitis prædictis coni ſectionibus, circulo nempè, El-
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lipſi, Parabola, & </
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">Hyperbola, ſi, quę ad earundem axes
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ordinatim applicantur, diametri eſſe intelligantur circulo-
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rum ab ipſis deſcriptorum, qui ſint erecti pianis ipſarum figu-
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rarum, periphærię deſcriptorum circulorum in ſectione, quę
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eſt circulus, erunt omnes in ſuperficie ſphęrę, in Ellipſi verò
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in ſuperficie ſphæroidis, in Parab. </
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rabolici, & </
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<
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ſcilicet, ipſæ, ABCD, earum
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axes, AC, vna ex ordinatim ad
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axim applicatis, BD, quæ in-
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telligatur eſſe diameter ab ea
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deſcripti circuli, BNDE. </
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co circumferentiam, BNDE,
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eſſe in dicta ſuperficie. </
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<
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xml:space
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gantur dictę figuræ reuolui circa
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ſuos axes, vt ex circulo fiat ſphę-
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ra, ex ellipſi ſphæroides, ex pa-
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rabola conoides parabolicum,
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& </
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<
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xml:space
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">ex hyperbola hyperbolicum,
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ſecentur autem planis ad axem
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rectis, eundem axem ſecantibus in eodem puncto, in quo </
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