Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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Theorematis, nam, vt alibi oſtendimus, ſi ſupponamus ipſi, BE, adiun-
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girectam, EM, æqualem ipſi, DE, & </
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">BE, eſſe æqualem ipſi, EF, om-
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nes lineæ trapezij, ADEC, erunt æquales omnibus abſciſſis ipſius, BE,
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(quæ ſit propoſita linea) adiuncta tamen, EM, & </
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<
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li, CEF, (intellige ſemper regulam, DF,) erunt æquales reſiduis om-
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nium abſciſſarum prop@ſitæ lineæ, BE, item omnes lineæ, AE, erunt
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æquales ijs, quæ adiunguntur maximis abſciſſarum, BE, nam earum ſin-
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gulæ ſunt æquales ipſi, DE, vel, EM, & </
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<
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">omnes lineæ, EC, maximis
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abſciſſarum, BE, pariter æquales erunt, vnde patet propoſitum. </
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cunda verò parte conſimili ratione colligemus rectangula ſub maximis
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abſciſſ rum propoſitæ lineæ, vt, BE, adiuncta quadam, vt, EM, & </
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ſub maximis abſciſſarum eiuſdem propoſitæ, BE, ad rectangula ſub om-
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nibus abſciſſis, ſumptis verſus, E, eiuſdem propoſitæ, BE, adiuncta,
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EM, & </
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<
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">ſub eiuſdem omnibus abſciſſis propoſitæ, BE, eſſe vt compoſita
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ex propoſita, & </
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eſt, ME, & </
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">{1/3}, propoſitæ, quæ eſt, BE.</
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">intra parallelas,
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AC, DF, eiſdem æquidiſtanter ducta recta linea, H
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O, quæ ſecet, BE, in, M, &</
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">, CE, in, N, oſtendemus, re-
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gula eadem, DF, rectangula ſub parallelogrammis, AO, O
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B, ad rectangula ſub trapezijs, HACN, MBCN, eſſe vt
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rectangulum, HOM, ad rectangulum ſub, HO, MN, cum
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rectangulo ſub compoſita ex, {1/2}, HM, &</
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">Rectangula enim ſub parallelogram-
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mis, AO, OB, ad rectangula ſub paral-
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lelogrammis, AM, MC, ſunt vt re-
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ctangulum, HOM, ad rectangulum,
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26. huius.</
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HMO, rectangula verò ſub, AM, M
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C, ad rectangula ſub parallelogrammo,
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AM, & </
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O, ad trapezium, BMNC, .</
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ad, MN, cum, {1/2}, NO, vel vt rectan-
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gulum, HMO, ad rectangulum ſub, H
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M, & </
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O, ergo, ex æquali, rectangula ſub, AO, OB, ad rectangula ſub,
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AM, & </
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gulum ſub, HM, & </
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