Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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omnia quadrata, EG, regula, FG, ſunt in ratione compoſita ex
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ratione quadrati, BC, ad quadratum, FG, & </
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">ex ratione, DC, ad,
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HG, ſiue, BC, ad, FG, .</
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">in ratione compoſita ex tribus rationi-
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bus, BC, ad, FG, ideſt habent eandem rationem, quam, BC, ad
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Quin. El.</
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quartam propo tionalem duarum, quarum prima, BC, ſecunda eſt,
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FG, .</
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<
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">. ſunt in tripla ratione eius, quam habet, BC, ad, FG, quod
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erat oſtendendum.</
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">_H_Inc patet, quod eodem modo idem oſtendemus de omnibus quibuſ-
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uis alijs figuris ſimilibus parallelogrammorum, AC, EG vice
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quadratorum ſumptis, regulis eiſdem, ex ſuperioribus Corollarijs id de-
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ducentes.</
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ſtituta, omnes figuræ ſimiles vnius ad omnes figuras ſi-
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huius.</
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miles alterius, etiamſi ſint diffimiles primò dictis, regulis ba-
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ſibus, iuxta quas altitudo ſumitur, erunt, vt figura deſcripta
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à baſi parallelogrammi primò dicti ad figuram deſcriptam à
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baſi parallelogrammi ſecundò dicti.</
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huius.</
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ras ſimiles parallelogrammi, EC, etiamſi ſint diſſimiles prædictis,
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eſſe vt figura deſcripta à, DE, ad figuram deſcriptam ab, EF, quæ
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ſunt baſes, iuxta quas ſumitur dictorum paral-
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lelogrammorum altitudo .</
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drata, AE, ad omnes circulos, EC, eſſe vt
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quadratum, DE, ad circulum deſcriptum ab,
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EF. </
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">Ducta enim ipſa, HN, vtcunque paral-
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lela, DF, reperiemus, vt figura, DE, ad fi-
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guram, EF, ita eſſe figuram, HM, ad figu-
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ram, MN, quia quæ deſcribuntur lateribus,
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HM, DE, equalibus ſunt ęquales, veluti de
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ſcriptę à lateribus, MN, EF, pariter ſunt æquales, & </
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ad vnum, ſic omnia ad omnia .</
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huius.</
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rain deſcriptam ab, EF, ſic erunt omnes figuræ ſimiles </
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