Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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tis, ergo, vt vnum ad vnum, ſic omnia ad omnia .</
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<
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">i. </
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">vt quadratum,
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huius.</
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EF, ad figuram aliam quamcumq; </
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<
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">deſcriptam ab, EF, ſic erunt om-
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nia quadrata figuræ, DEF, regula, EF, ad omnes figuras ſimiles
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eiuſdem figuræ, DEF, regula eadem, EF, ſimiles inquam deſcri-
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ptæ ab, EF, vt autem quadratum, EF, ad figuram deſcriptam ab,
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EF, ita quadratum, BC, ad figuram, quę deſcribitur à, BC, ſimi-
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lis ei, quę deſcripta eſt ab, EF, ita vt deſcribentes ſint earumdem ho-
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mologę, vt autem quadratum, BC, ad figuram deſcriptam à, BC,
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ſic eſſe oſtendemus omnia quadrata figuræ, ABC, regula, BC, ad
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omnes figuras ſimiles eiuſdem figurę, ABC, ſimiles inquam deſcri-
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ptæ à, BC, vel ab, EF, eodem modo, quo id oſtendimus in figura,
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DEF, ergo omnia quadrata figurę, ABC, ad omnes figuras ſimi-
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les alias quaſcunque eiuſdem figuræ, ABC, erunt, vt omnia qua-
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drata figuræ, DEF, ad omnes figuras ſimi-
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les prædictis eiuſdem figuræ, DEF, regulis
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prædictis, BC, EF, ergo permutando, vt
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omnia quadrata figuræ, ABC, ad omnia
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quadrata figurę, DEF, ita erunt omnes fi-
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guræ ſimiles quæcumque figurę, ABC, ad
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omnes figuras ſimiles prædictis figuræ, DE
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F, quia verò omnes figuræ ſimiles alicuius
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figuræ planæ regula quadam ſumptæ, ſunt
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omnia plana ſolidi, quod dicitur ſimilare, & </
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genitum ex tali figura iuxta eandem regulam, ideò, vt omnes figurę
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">B. Diff. 8.
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huius.</
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ſimiles quæcumque ipſius figuræ, ABC, regula, BC, ad omnes fi-
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guras ſimiles ipſius figuræ, DEF, regula, EF, ſimiles inquam præ-
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2. huius.</
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dictis .</
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<
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">vt omnia quadrata figuræ, ABC, regula, BC, ad omnia
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quadrata figuræ, DEF, regula, EF, ita erunt omnia plana ſolidi
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ſimilaris cuiuſcumque geniti ex figura, ABC, iuxta regulam, BC,
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ad omnia plana ſolidi ſimilaris geniti ex figura, DEF, iuxta regu-
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lam, EF, vt au@em omnia plana duorum ſolidorum ſic & </
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<
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da, ergo etiam ſolida ſimilaria genita ex figuris, ABC, DEF, (quę
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ſunt ſimilaria ad inuicem, quia omnes figuræ ſimiles figuræ, ABC,
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ſunt etiam ſimiles omnibus figuris ſimilibus figuræ, DEF,) iuxta
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regulas, BC, EF, erunt ad inuicem, vt omnia quadrata earumdem
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figurarum eiſdem regulis ſumpta, quod erat oſtendendum.</
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">regula, BC, deſcripſerit
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duas quaſcumque figuras, quod vt vna ad aliam, ita erunt om-
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nes figuræ ipſius, ABC, ſimiles vni deſcriptarum ad omnes figuras </
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