Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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lelas, ac (ſi ſint inclinatę, incidantque ipſis in punctis, C, N, iun-
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ganturque, CB, CD, NP, NO,) pyramides, ACDB, HNO
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P, ſimiles eſſe. </
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<
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xml:space
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">Sumatur ergo in, AD, etiam quantumuis protenſa
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vbicumq; </
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<
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<
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">accipiatur in, HO, producta, ſi opus ſit,
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HL, ęqualis, AF, & </
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<
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xml:space
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">indefinitè extenſis lineis, AC, AB, HN, H
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">Vidi dicta
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lib.7. An-
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not. Pro-
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poſ.3.</
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P, ducantur in planis, FAC, FAG, LHN, LHP, à punctis, F,
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0079-01
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L, ipſis, AF, HL, per-
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pendiculares, FE, FG,
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LI, LM, occurrentes
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ipſis, AE, AG, HI, H
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M, in punctis, E, G, I,
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M, & </
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<
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">iungantur, EG,
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IM. </
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<
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">Quoniam ergo duo
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anguli, AFG, HLM,
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recti, &</
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<
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">, FAG, LH
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M, ſunt æquales, & </
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<
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tera, AF, HL, ęqua-
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lia, erunt etiam, FG,
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Elem.</
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LM, GA, MH, ęqua-
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lia; </
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<
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">eodem modo oſten-
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demus æqualia eſſe, F
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E, LI, EA, IH, vnde cum ſint ęquales, EA, IH, AG, HM, & </
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<
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Elem.</
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anguli, EAG, IHM, pariter ęquales, etiam baſes, EG, IM, æ-
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quales erunt, & </
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<
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">ęquales
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ad inuicem exiſtent. </
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">Defin. 10.
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vndec. El.</
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tur punctum, F, in, L, demittaturque, FG, ſuper, LM, cui con-
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gruet, ſed & </
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<
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">triangulo, EFG, cadente ſuper, ILM, punctum, F,
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erit in, I, ac latus, AF, in, HL, alioquin duę eidem plano, ILM,
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<
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perpendiculares eſſent eductæ ab eodem puncto, L, quod eſt abſur-
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dum (ſunt autem, AF, HL, perpendiculares planis, EFG, ILM,
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<
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Elem.</
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hoc eſt ſolo plano, ILM, cum ſuperponuntur, ex eo, quod duabus,
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IL, IM, ſint perpendiculares in puncto, L,) ergo, FA, cadet ſu-
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per, LH, & </
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<
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">punctum, A, in, H, vnde etiam, EA, cadet in, IH,
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&</
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<
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">, AG, in, HM, punctum, B, verò eſto, quod ſit in, T, D, in,
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S, &</
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<
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&</
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<
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">quia angulus, ABD, æquatur ipſi, HPO,
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ABD, autem eſt etiam æqualis, HTS, ergo, HTS, HPO, ſunt
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æquales, &</
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<
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<
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Elem.</
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æquidiſtare ipſi, NOP, ſi .</
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ipſi, OP, poterit per, ST, duci planum ipſi, NOP, parallelum,
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ducatur, & </
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puncto, H, ipſi, OP, perpendiculari, quę ſit, HQ, ſecante, </
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