Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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T CFEY, regula, TY, ſunt vt rectangulum ſub, FN, & </
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N H, .</
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xml:space
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">i. </
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xml:id
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xml:space
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H N, .</
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<
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xml:space
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">vt totum quadratum, FH, ad rectangulum ſub, FI, & </
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ſub ſexquitertia ipſarum, IHN, .</
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<
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xml:space
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<
s
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xml:space
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">in circulo, vt quadratum, AP,
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165
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0268-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0268-01
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(quod æquatur quadrato, FH, ) ad
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idem rectangulum ideſt ſumpta, FI,
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communi altitudine, vt parallelepipe-
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dum ſub, FI, & </
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<
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xml:space
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<
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</
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<
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<
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G, & </
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<
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ſub, FI, ſiue, AL, &</
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<
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rallelepipedum ſub, FI, & </
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<
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rectangulo ſub, FI, & </
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">ſub ſexquiter-
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tia, IHN, ergo ex æquali omnia
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quadrata figuræ, LCFE G, dem-
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ptis omnibus quadratis trilineorum,
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CLT, YGE, regula, FI, ad omnia
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quadrata portionis, TCFE Y, regu-
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la, TY, erunt vt cylindricus ſub, M
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I, & </
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<
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cum, {1/6}, cubi, TY, ad parallelepipe-
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dum ſub, FI, & </
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<
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F I, & </
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circulo.</
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<
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">In ellipſi autem eadem habebunt
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rationem compoſitam exiam dicta ratione .</
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<
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ſub, MI, & </
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<
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">ſub portione, TGFE Y, vna cum ea parte cubi, vel
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parallelepipedi ſub, RV, & </
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<
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vt quadratum, CE, ad quadratum, FH, ad parallelepipedum,
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ſub, LG, & </
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<
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ad rectangulum ſub, FI, & </
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<
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">quas
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duas rationes in circulo in vna reſoluimus, quia in eo quadratum,
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F H, æquatur quadrato, AP, quod cum in ellipſi non verificetur,
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ideò has duas rationes componentes pro ipſa ellipſi retinuimus;
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</
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tum in ellipſi, omnia quadrata figuræ, LCFEG, dem-
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ptis omnibus quadratis trilineorum, CLT, YGE, </
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