Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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collectis) ad omnia quadrata figuræ, LCFEG, demptis omnibus
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quadratis trilineorum, CLT, EGY, erunt vt parallelepipedum ſub
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altitudine, KL, baſi parallelogrammo, KG, ad cylindricum ſub
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altitudine, KL, baſi portione, TCFEY, vna cum, {1/6}, cubi, RV,
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xml:space
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in circulo. </
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lindricum, vna cum ea parte cubi, RV, vel parallelepipedi ſub, R
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V, & </
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">rhombo, RZ, ad quam eiuſdem cubi, vel parallelepipedis ſex-
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ta pars ſit, vt quadratum, CE, ad quadratum, FH: </
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<
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quadrata, AG, ad omnia quadrata, KG, ſunt vt parallelepipedum
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ſub altitudine, AL, baſi parallelogrammo, AG, ad parallelepipe-
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dum ſub altitudine, LK, baſi parallelogrammo, KG, ergo ex ęqua-
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li pariter omnia quadrata, AG, ad omnia quadrata figurę, LCFE
<
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G, demptis omnibus quadratis trilineorum, CLT, EGY, erunt in
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circulo, vt parallelepipedum ſub altitudine, AL, vel, FI, baſi au-
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tem parallelogrammo, AG, ad cylindricum ſub altitudine, LK, vel,
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MI, baſi autem portione, TCFEY, vna cum, {1/6}, cubi, RV, vel,
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TY. </
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<
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">In ellipſi verò erunt, vt parallelepipedum ſub altitudine, FI,
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baſi autem parallelogrammo, AG, ad cylindricum ſub altitudine,
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MI, baſi autem ipſa portione, TCFEY, vna cum ea parte cubi,
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RV, vel, TY, ſiue parallelepipedi ſub altitudine, TY, & </
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bo, RZ, ad quam eiuſdem cubi, vel parallelepipedi ſexta pars ſit, vt
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quadra@um, CE, ad quadratum, FH; </
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<
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ſumpta vtcunq;</
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ſtant, ſuppoſitis. </
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drata portionis, RFV, eſſe, vt ſexquialtera, FM, ad reli-
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quum diametri, MH, maioris portionis, ab eodem dempta
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recta linea, ad quam tripla, MN, ſit, vt parallelogrammum,
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Δ V, ad portionem, RFV.</
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<
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vnum ad vnum. </
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">vt rectangulum, FMI, ad quadratum, VZ, vel
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ad quadratum, RV, omnia item quadrata, RZ, ſunt ſexcupla re-
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huius.</
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ctangulorum ſub portione, RFV, & </
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ſunt ad illa, vt quadratum, RV, ad ſui, {1/6}, ergo ex æquali rectan-
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gula ſub, Δ V, VT, ad rectangula ſub portione, RFV, & </
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lineo, RTHYV, erunt vt rectang. </
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