Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRI Æ
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pezium, FCMO, eſſe vt compoſita ex, RC, &</
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compoſitam ex, MD, &</
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<
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<
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xml:space
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">Nam trapezium, CRGF, ad, GD, eſt vt compoſita ex, RC,
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&</
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<
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">, {1/2}, CD, ad, RD, inſuper, GD, ad, AM, eſt vt, RD, ad, C
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M, & </
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<
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xml:space
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">tandem, AM, ad trapezium, FCMO, eſt vt, CM, ad, M
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D, cum, {1/2}, CD, ergo ex æquali trapezium, FGRC, ad trape-
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zium, FCMO, erit vt, RC, cum, {1/2}, CD, ad, MD, cum, {1/2}, D
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C, quod erat demonſtrandum.</
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<
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">_H_Inc patet omnes lineas trapezij, FGRC, regula, RM, ad omnes
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lineas trapezij, FCMO, regula eadem eſſe, vt, RC, cum, {1/2},
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CD, ad, MD, cum, {1/2}, DC, veluti autem in antecedenti oſtendimus,
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ſi, CD, ſit æqualis ipſi, DF, omnes lineas trapezij, FGMO, regula,
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CM, æquari omnibus abſciſſis ipſius, FD, adiuncta, DM, ita in præ-
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ſenti oſtendemus omnes lineas trapezij, FGRC, regula, RD, æquari re-
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ſiduis omnium abſciſſarum ipſius, AC, vel, FD, adiuucta, RC; </
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<
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patebit reſiduas abſciſſarum propoſitæ lineæ, vt, FD, adiuncta, RC, ad
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omnes abſciſſas eiuſdem, adiuncta alia linea, vt, DM, eſſe vt compoſi-
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tum ex prima adiuncta, &</
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<
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">, {1/2}, propoſitæ, CD, ſiue, FD, illi æqualis,
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ad compoſitum ex ſecunda adiuncta, &</
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">, {1/2}, propoſitæ lineæ, ideſt vt, R
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C, cum, {1/2}, CD, vel, DF, ad, MD, cum, {1/2}, CD, vel, DF.</
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<
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que ductis diametris, & </
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regula ſumptis, nempè in vnoquoq; </
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drata cuiuſuis dictorum parallelogrãmorum ad omnia qua-
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drata cuiuſuis triangulorum per diametrum in ipſo conſtitu-
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torum, erunt vt omnia quadrata reliqui parallelogrammi ad
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omnia quadrata cuiuſuis triangulorum per diametrum in
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iſto ductam pariter conſtitutorum.</
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<
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ctæ diametri, EO, Z &</
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<
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quadrata, AS, ad omnia quadrata trianguli, OES, eſſe vt omnia
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quadrata, Τ β, ad omnia quadrata, & </
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