Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER V.
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OVX, ſimilia rectangulo, XOP, regula, OX, habebunt rationem
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compoſitam ex ea, quam habetrectangulum ſub, MB, HI, adre-
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ctangulum ſub, RI, FB, & </
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">ex ea, quam habet parallelepipedum
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ſub altitudine hyperbole, ADC, baſi quadrato, AC, ad parallele-
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bipedum ſub altitudine hyperbole, OVX, baſi rectangulo, XOP,
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quod erat demonſtrandum.</
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">ASſumptis quibuſcunq; </
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">hyperbolis, in vnaquaq; </
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<
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">re-
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gula baſi, oſtendemus omnia quadrata vnius ad om-
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nia quadrata alterius, habere rationem compoſitam ex ra-
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tione rectanguli ſub compoſita ex ſexquialtera tranſuerſi
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lateris, & </
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">axi, vel diametro hyperbolæ primò dictæ, & </
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compoſita ex tranſuerſo latere, & </
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">axi, vel diametro hyper-
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bolæ ſecundò dictæ ad re ctangulum ſub compoſita ex trã-
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ſuerſi lateris ſexquialtera, & </
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ſecundò dictæ, & </
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vel diametro hyperbolæ primò dictæ, & </
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">ex ratione paral-
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lelepipediſub altitudine hyperbolæ primò dictæ, baſiau-
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tem quadrato baſis eiuſdem, ad parallelepipedum ſub al-
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t tudine hyp rbolæ ſecundò dictæ, baſi pariter quadrato
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b ſis eiuſdem. </
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">Velſi comparentur omnia quadrata hy-
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perbolæ primò dictæ, ad omnia rectangula hyperbolæ fe-
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cundò dictæ ſimilia cuidam rectangulo, illa ad hæchabe-
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buntrationem compoſitam exratione prædictorum rectã-
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gulorum, & </
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">exratione parallelepipedi primò dictiad pa-
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rallelepipedum ſub altitudine hyperbolæ ſecundò, dictæ
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baſirectangulo, cuiomnia dicta rectangula ſunt ſimilia.
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">Vel tandem ſi comparentur omnia rectangula primæ hy-
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perbolæ ſimilia cuidam rectangulo ad omnia rectangula
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ſecundæ hyperbolæ ſimilia pariter cuidam rectangulo, il-
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la ad hæchabebunt rationem compoſitam ex ratione pa-
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rallelepipedi ſub altitudine hyperbolæ primò dictæ baſi
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rectangulo, cuiomnia eiuſdem rectangula ſunt ſimilia, ad
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parallelepipedum ſub altitudine ecundæ hyperbolæ baſi
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rectangulo, cuiomnia eiuſdem rectangula iam dicta </
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