Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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<
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xml:space
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cas, quod etiam vniuerſalius oſtenditur Vndecimo Elementorum
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Propoſ. </
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poſſibile eſt ipſam ad alteram eiuſdem partium ita
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producere, vt cubus compoſitæ ex propoſita linea, & </
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<
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cta, ſit æqualis cubo propoſitæ lineæ, ſimul cum cubo com-
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poſitæ ex adiecta, & </
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<
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">illi conterminante portione ſectæ lineę.</
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</
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<
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<
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xml:space
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">Sit data recta linea, AC, terminata, diuiſaq; </
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<
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xml:space
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">vtcumque in pun-
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cto, B, oftendendum eſt poſſibile eſſe ipſam ita producere ad alteram
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illius partium, vt ad, C, vt cubus compoſitę ex, AC, & </
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<
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æqualis cubo, AC, cum cubo compoſitæ ex eadem adiecta, & </
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xml:space
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BC, portione, AC, adiectæ conterminante. </
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<
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A, ad partes, A, vt in, N, ita quod, NB, ſit tripla, BA, ſiat dein-
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de, vt, NB, ad, BC, ita quadratum, BC, ad quadratum rectæ li-
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neę, M, ſeorſim poſitæ: </
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poſitæ ex, AC, CB, cui applicetur rectangulum æquale quadrato,
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0213-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0213-01
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M, excedens figura quadrata,
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lem,</
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cuius latus ſit, FH, producatur
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autem, AC, verſus, C, vt in,
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D, ita nempè, vt, CD, ſit
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æqualis, FH. </
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tius, AD, æquari duobus cubis,
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AC, BD. </
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<
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B, ad, BC, ita quadratum, BC,
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ad quadratum, M, ideò parallelepipedum ſub altitudine, AB, (qu
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eſt, {1/3}, prædictę altitudinis, NB,) & </
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<
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tiæ parti cubi, BC. </
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<
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Gen. 34.
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huius.</
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gulo, EHF, ideſt rectangulo ſub compoſita ex, AD, BC, & </
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CD, ideò parallelepipedum ſub altitudine, AB, & </
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ſub compoſita ex, AD, BC, & </
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cubi, BC, addatur commune parallelepipedum ſub, BC, & </
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<
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ctangulo, BDC, erit ex vna parte hoc parallelepipedum cum, {1/3}, cu-
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bi, BC, ex alia verò hæcſumma; </
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& </
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cum parallelepipedo ſub, BC, & </
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ſumma efficit parallelepipedum ſub, AC, & </
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