Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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bus quadratis, BF, ad omnia quadrata, AF, vt 11. </
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<
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<
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xml:space
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">ergo,
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exæquali, omnia quadrata figuræ, CBDF, demptis omnibus qua-
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dratis BF, ad omnia quadrata, BF, demptis omnibus quadratis tri-
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linei, BCF, erunt vt 11. </
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<
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<
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<
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<
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">figura, ſiproducatur
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baſis, DF, (quæ retineatur pro regula) vtcunq; </
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<
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M, & </
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<
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">per M, ipſi, BE, parallela ducatur, MH, cui occur-
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rat, AC, producta, in ipſo, H. </
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<
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xml:space
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">Omnia quadrata, AM,
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demptis omnibus quadratis, CM, ad omnia quadrata figu-
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ræ, HBDM, demptis omnibus quadratis quadrilinei, H
<
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BFM, erunt vt, AF, ad parabolam, DBF, ideſt erunt
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eorum ſexquialtera: </
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<
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xml:space
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">Quod facilè patebit, quia parabola, D
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BF, inſcripta parallegrammo, AF, eſt figura, qualem po-
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ſtulat Propoſit. </
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<
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">Vlterius autem dico omnia qua-
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drat’a, AM, ad omnia quadrata figuræ, BDMH, eſſe vt
<
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quadratum, DM, ad quadratum, ME, dimidium qua-
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drati, ED, cum rectangulo ſub ſexquitértia, DE, & </
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ſub, EM.</
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<
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<
s
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xml:space
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">In conſtructa figura igitur omnia quadrata figuræ, HBDM, per
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rectam, BE, diuiduntur in omnia quadrata ſemiparabolæ, BDC,
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in omnia quadrata, BM, & </
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<
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xml:space
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">in rectangula bis ſub ſemiparabola, B
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DE, & </
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<
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drata, AM: </
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nia igitur quadr@@-
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ta, AM, ad om-
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nia quadrata, BM,
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ſunt vt quadra-
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tum, DM, ad
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quadratum, ME,
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quod ſerua. </
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<
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omnia quadrata,
<
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AM, ad omnia quadrata, AE, ſunt vt quadratum, MD, ad qua-
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dratum, DE, omnia verò quadrata, AE, ſunt dupla omnium qua-
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dratorum ſemiparabolæ, BDE, ergo omnia quadrata, AM, ad
<
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omnia quadrata ſemiparabolæ, BDE, ſunt vt quadratum, MD,
<
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ad dimidium quadrati, DE, quod etiam ſerua. </
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<
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