Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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ad portionem, RCT, ergo ex æquali omnia quadrata, KG, adom-
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huius.</
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nia quadrata figuræ, LCRT, demptis omnibus quadratis trilinei,
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CLT, erunt vt, KG, ad portionem, RCT. </
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demus omnia quadrata, KG, ad omnia quadrata figuræ, VEGY,
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demptis omnibus quadratis trilinei, EGY, eſſe vt, KG, ad portio-
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nem, VEY, quæ conſerua.</
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26. l. 2.</
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probauimus, ſunt vt, KG, ad, RY, item omnia quadrata, RY,
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ad rectangula ſub, RY, R Φ, ſunt vt, RY, ad R Φ, & </
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26. l. 2.</
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ctangula ſub, R Φ, RY, adrectangula ſub portione, RFV, & </
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ſub, RY, ſunt vt, R Φ, ad portionem, RFV, ergo ex æquali
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omnia quadrata, KG, adrectangula ſub portione, RFV, & </
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RY, erunt vt, KG, ad portionem, RFV, ergo, colligendo, om-
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nia quadrata, KG, ad omnia quadrata figurarum, LCRT, VE
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GY, demptis omnibus quadratis trilineorum, CLT, EGY, & </
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omnia quadrata, RY, & </
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& </
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& </
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quadrata portionis, RFV, & </
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quia autem, RV, æquatur ipſi, TY, portio, RFV, æquatur por-
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tioni, THY, etiam in ellipſi, quia, RV, TY, ſunt parallelæ,
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ideò omnia quadrata portionis, RFV, ſunt rectangula ſub portio-
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ne, RFV, & </
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ſub eadem portione, RFV, & </
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la ſub eadem portione, RFV, & </
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ſiue rhombus, vel, RV, non eſt æqualis ipſi, VY, & </
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VY, producta, ſi opus ſit ſumatur, VZ, æqualis, ipſi, VR, & </
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cta per, Z, Z Π, ipſi, RV, parallela, ſit conſtitutum, RZ, qua-
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dratum, vel rhombus ipſius, RV: </
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omnia quadrata, RZ, habent rationem compoſitam ex ratione
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l. 1.</
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quadrati, KL, ad quadratum, R Π, vel ad quadratum, RV, & </
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ex ratione ipſius, KB, ad, RV, quæ duæ rationes componunt ra-
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tionem parallelepipedi rectanguli ſub altitudine, BK, baſi autem
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quadrato, KL, ad cubum, RV. </
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l. 2.</
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diametri, ſic dicemus, nempè, Omnia quadrata, KG, ad omnia
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quadrata, RZ, rhombi habent rationem compoſitam ex ratione,
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KL, ad, R Π, bis ſumpta, & </
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rationes componunt rationem parallelepiped ſub altitudine, KL,
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baſi parallelogrammo, KG, ad parallelepipedum ſub altitudine,
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RV, baſi autem rhombo, RZ: </
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