Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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eſſe vt, BR, ad compoſitam ex, {1/2}, BR, &</
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<
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quadrata trianguli, DEP, cum ſint, {1/3}, omnium quadratorum pa-
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<
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note-0219-01
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rallelogrammi, FP, erunt ad omnia quadrata portionis, DEP, vt,
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{1/3}, RB, ad compoſitam ex, {1/2}, RB, &</
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<
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xml:space
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">, {1/6}, BE, ideſt vt tota, RB,
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ad compoſitam ex, {3/2}, RB, &</
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<
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<
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xml:space
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">{3/6}, RB, cum,
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{3/6}, BE, conſtituunt, {3/6}, integrę, ER, ſcilicet, {1/2}, eiuſdem, ER, quę
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ideò cum, {2/2}, ipſius, BR, .</
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<
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<
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xml:space
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">cum, BR, ad ipſam, BR, erit, vt om-
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nia quadrata (conuertendo) portionis, DEP, ad omnia quadrata
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trianguli, DEP.</
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<
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">Quoniam verò, ſi in parallelogrammi, vel trianguli dicti, baſi, D
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note-0219-02
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P, ſit parallelogrammum, vel triangulum, & </
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roll. 22.
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lib. 2.</
note
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omnia quadrata dictorum parallelogrammorum inter ſe æquantur,
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ficut etiam omnia quadrata triangulorum, regula eorundem baſi,
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ideò oſtenſum eſt omnia quadrata portionis, DEP, ad omnia qua-
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drata parallelogrammi in eadem baſi, & </
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tuti eſſe, vt compoſita ex, {1/6}, BE, &</
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<
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">, {1/2}, BR, ad eandem, BR, ad
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omnia verò quadrata trianguli in ijſdem poſiti, vt compoſita ex, B
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R, & </
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<
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">_H_INC patet in figura, in qua baſis portionis conſtitutæ per cen-
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trum circuli, vel ellipſis tranſeat, quoniam omnia quadrata pa-
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rallelogrammi, FP, ad omnia quadrata portionis, DEP, ſunt vt,
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A R, ad compoſitam ex, {1/2}, AR, &</
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<
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E A, eſt æqualis ipſi, AR, {1/2}, AR, autem, &</
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">, {1/6}, AR, conſtituunt,
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{4/6}, vel, {2/3}, ipſius, AR, ideò omnia quadrata parallelogrammi, FP, eſ-
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ſe ad omnia quadrata portionis, DEP, vt, AR, ad, {2/3}, AR, ideſt eſſe
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eorundem ſexquialtera; </
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ſunt, {1/3}, omnium quadratorum parallelogrammi, FP, ideò omnia qua-
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drata trianguli, DEP, ad omnia quadrata portionis, DEP, ſunt vt 1.
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uium quadratorum trianguli, DEP, & </
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dratorum parallelogrammi, FP, dummodo in eadem baſi, & </
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cum portione ſint conſtituti parallelogrammum, & </
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lò ſupr a in fine demonſtrationis ſubiunximus.</
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