Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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GH, vel quadratum, EC, ad quadratum, IM, vel ad quadratum,
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">Ex 38. &
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Schol. 40.
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lib. 1.</
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CN, vt, GC, ad, CI,.</
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">. vt, ON, ad, NM, eſt autem, CH, pa-
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rallelogrammum in eadem baſi, & </
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<
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">altitudine cum trilineo, CMH
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E, & </
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">ſumptum, per quod acta eſt ipſi, CG,
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parallela, NO, repertumque eſt, vt quadratum, EC, ad quadra.
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</
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<
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">tum, CN, itaeſſe, ON, ad, NM; </
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<
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">ergo horum quatuor ordinum
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26. lib. 2.</
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magnitudines erunt proportionales ſcilicet omnia quadrata maxi-
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marum abſciſſarum, EC, magnitudines primi ordinis collectæ iuxta
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quadratum, CE, ad quadrata omnium abſciſſarum ipſius, CE, ſiue
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ambo ſint recti, vel eiuſdem obliqui tranſitus, quæ ſunt magnitudi-
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nes ſecundi ordinis collectæ, iuxta quadratum, CN, erunt vt om-
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0306-01
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nes lineæ parallelogrammi, CH, ma-
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gnitudines tertij ordinis collectæ, iux-
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ta, NO, ad omnes lineas trilinei, CM
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HE, magnitudines quarti ordinis col.
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</
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<
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">lectas, iuxta, NM, regula pro his om-
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nibus lineis exiſtenteipſa, EH; </
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tem ſunt omnes lineæ parallelogram-
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mi, CH, ad omnes lineas trilinei, CM
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HE, ita eſt parallelogrammum, CH,
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ad trilineum, CMHE, ergo paralle-
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logrammum, CH, ad trilineum, CMHE, eſt vt quadrata maxi-
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marum abſciſſarum ipſius, CE, ad quadrata omnium abſciſſarum ip-
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ſius, CE, verum illa quadrata ſuntiſtorum tripla, ergo erit paralle-
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lib. 2.</
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logrammum, CH, triplum ipſius trilinei, CMHE, ergo idem pa-
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rallelogrammum, CH, erit ſexquialterum ſemiparabolæ, GCM
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H, ideò etiam parallelogrammum, AH, erit parabole, FCH, ſex-
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quialterum. </
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">Quoniam verò triangulum, CFH, eſt dimidium pa-
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rallelogrammi, AH, ideò quarum partium parallelogrammum, A
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H, erit ſex, & </
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triangulum, CFH, erit tria, & </
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tria ad quatuor, & </
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">idcircò erit eiuſdem ſubſexquitertium, quæ oſten-
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dere oportebat.</
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">HInc patet ductas in trilineo, CMHE, æquidiſtantes axi, bel dia-
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metro, CG, eſſe inter ſe, bt quadrata abſciſſarumper eaſdem d
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tangente, CE, berſus berticem parabolæ, quieſt punctum, C; </
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<
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ſum eſt, ON, ſiue, HE, ad, NM, eſſe bt quadratum, EC, ad quadra-
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tum, CN, & </
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