Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER V.
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pipedo ſub, SO, & </
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<
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</
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<
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">pipedum ſub, ΛΩ, & </
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">quadrato, Ω4, vna cum parallelepipedo ſub,
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Λ4, & </
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<
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xml:space
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">quadrati, Λ4, ab his dẽ-
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pto parallelepipedo ſub, SO, & </
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<
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<
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quod oſtendere opus erat.</
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">_H_Inc patet, quod eadem methodo oſtendemus omnia quadrátá fi-
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guræ parallelogrammi, TV, nibil ab eis dempto, ad omnia
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quadrata figuræ parallelogrammi βΩ, nibil pariter ab eis dempto, eſſe
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Vt parallelepipeda primò dicta ad parallelepipeda ſecundò dicta.</
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duarum quarumcunq; </
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">figurarum notificata fuit ratio
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omn ium quadratorum, iuxta regulas in eiſdem aſſumptas,
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nota etiam euadit ratio ſimiliarium ſolidorum, quæ exillis
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gignuntur figuris, iuxta eaſdem regulas.</
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drata duarum figurarum inter ſe ſumpta cum datis regulis, ita eſſe
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ſolida ſimilaria genita ex ijſdem figuris iuxta eaſdem regulas, ideò
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cum in huius Libri Propoſitionibus inuẽta eſt ratio omnium qua-
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dratorum duarum figurarum cum talibus regulis, colligemus etiã
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nunc eandem eſſe rationem duorum ſimilarium ſolidorum, quæ
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ex illis figuris iuxta eaſdem regulas genita dicuntur, quæ amplius
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in ſequentibus dilucidabimus ſingulas Propoſitiones, quæ oppor-
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tunæ fuerint, denuò aſſumentes.</
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<
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ſpecta denuò eiuſdem figura) omnia quadrata hyperbolæ, DBF,
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regula, DF, ad omnia quadrata, AF, eſſe vt compoſitam ex, NB,
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& </
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">{1/3}, BE, ad, OE, eandem comperiemus habere rationem ſolidum
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ſimilare genitum ex hyperbola, DBF, ad ſolidum ſimilare genitũ
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ex, AF, iuxta communem regulam, DF; </
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<
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mus, veluti omnia quadrata hyperbolæ, DBF, ad omnia quadra-
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ta trianguli, DBF, ſunt vt compoſita ex ſexquialtera, OB, & </
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BE, ad, OE, ita eſſe ſolidum ſimilare genitum ex hyperbola, </
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