Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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circulo ſunt ſexcupla rectangulorum ſub portione, RFV, & </
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<
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drilineo, RTHYV, .</
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<
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<
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xml:space
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ſextam partem. </
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<
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xml:space
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la ſub portione, RFV, & </
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<
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xml:space
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<
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RV, vel parallelepipedum ſub altitudine, RV, baſi rhombo, RZ,
<
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ad ſui ipſius eam partem, ad quam ſexta pars eiuſdem cubi, vel pa-
<
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rallelepipedi ſit, vt quadratum, CE, primæ diametri, ad quadra-
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tum, FH, ſecundæ; </
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<
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xml:space
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">ergo ex æqualiin circulo omnia quadrata, K
<
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G, adrectangula ſub portione, RFV, & </
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<
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">ſub quadrilineo, RTH
<
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YV, erunt vt parallelepipedum ſub altitudine, BK, baſi quadra-
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to, KL, vel (quodidem eſt) vt parallelepipedum ſub, LK, & </
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<
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ctangulo, KG, ad, {1/6}, cubi, RV. </
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<
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xml:space
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parallelepipedum ſub altitudine, LK, baſi parallelogrammo, KG,
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ad eam partem cubi, RV, vel dicti parallelepipedi ſub, RV, & </
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rhombo, RZ, ad quam eiuſdem cubi,
<
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vel parallelepipedi ſexta pars ſit, vt
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quad. </
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<
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</
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<
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<
s
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xml:space
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">Sunt autem omnia quadrata, KG, ad
<
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omnia quadrata figurarum, RCLT,
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VEGY, demptis, omnibus quadratis
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trilineorum, CLT, EGY, vna cum
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omnibus quadratis, RY, & </
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<
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δtangulis ſub portione, RFV, & </
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<
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RY, ſemel, vt, KG, ad portionem,
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TCFEY, vt oſtendimus .</
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<
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<
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L, communi altitudine, vt parallelepi-
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pedum ſub altitudine, KL, baſi paral
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xml:space
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<
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4. Gen.
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34. l. 2.</
note
>
lelogrammo, KG, ad cylindricum ſub
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eadem altitudine, KL, & </
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<
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tione, TCFEY, ergo, colligendo,
<
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omnia quadrata, KG, ad omnia qua
<
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drata portionum, RCT, VEY, cum
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rectangulis bis ſub ijſdem, & </
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<
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neis, CLT, EGY, inſuper ad omnia
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quadrata, RY, cum rectangulis ſub, R
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Y, & </
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<
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ne, RFV, & </
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<
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portionis, RFV, cum rectangulis iterum ſub eadem, & </
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<
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quia rectangula ſub portione, RFV, & </
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<
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ſeparantur per lineam, TY, inrectangula ſub, RY, & </
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<
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RFV, & </
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nia quadrata portionis, RFV, .</
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