Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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planumper, VK, XN, ductum in recta, KN, rurſus diuidatur, H
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P, vtcumq; </
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<
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">in puncto, G, à quo ducatur ipſi, SP, parallela, GD,
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ſecans baſis ambitum in punctis, F, E, C, D, deinde extendatur
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planum per, A, verticem, & </
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<
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">rectam, DG, quod per conici latera
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tranſibit, & </
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<
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">producet triangula ſiueintus, ſiue extra conicum, quæ
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ſint, ADC, ACE, AEF, AFG, ſecabitque figuram, VBO, ſe-
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cet eius productum planum in recta, BM, quæ ambitum eiuſdem,
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VBO, diuidat in punctis, B, R, I, O, habebimus etiam triangula,
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ABR, ARI, AIO, AOM, quorum latera erunt portiones late-
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rum inferiorum triangulorum, per planum autem, ADG, ſiue per
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rectam, AG, ſit ſecta, KN, in puncto, M. </
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<
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">Quia ergo plana, quę
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per rectas, VK, XN, & </
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per, TH, SP, tranſeunt
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ſunt parallela, & </
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<
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tur à plano, APH, com-
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cimi El.</
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munes eorum ſectionese-
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runt parallelę.</
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">KN, ipſi,
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HP, igitur triangulus, A
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MN, æquiangulus erit
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triangulo, AGP, & </
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<
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circa æquales angulos e-
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">4. Sexti
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Elem.</
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runt latera proportiona-
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lia, ergo vt, PG, ad, G
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A, ſic erit, NM, ad, M
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A, eodem modo oſtende-
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mus, vt, AG, ad, GH, ita eſſe, AM, ad, MK, ergo ex æquali
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PG, ad, GH, erit vt, NM, ad, MK, ſunt igitur, PH, NK, ſi-
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militer ad eandem partem diuiſæ in punctis, M, G: </
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<
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oſtendemus triangulum, AMO, eſſe ęquiangulum ipſi, AGF, &</
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AMI, ipſi, AGE, &</
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<
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">, AMR, ipſi, AGC, & </
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<
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">tandem, AMB,
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ipſi, AGD, igitur, vt, GA, ad, AM, ſic erit, permutando, FG,
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ad, OM, vt verò, GA, ad, AM, ſic permutando eſt, PG, ad,
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NM, ideſt, PH, ad, NK, ergo, FG, ad, OM, eſt vt, PH, ad,
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NK, ſimiliter oſtendemus, EG, ad, IM, &</
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<
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tandem, DG, ad, BM, eſſe vt, PH, ad, NK, & </
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<
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xml:space
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">quia, KN, eſt
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parallela ipſi, HP, &</
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<
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">, NX, ipſi, PS, ideò angulus, KNX, eſt
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<
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">10. Vnde-
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Fimi El.</
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æqualis angulo, HPS; </
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<
s
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">habemus igitur duas figuras planas, VBO,
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TDF, quarum ductæ ſunt oppoſitæ tangentes, VK, XN, vnius,
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&</
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<
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">, TH, SP, alterius, inuenimus autem rectas, KN, HP, inter
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eaſdem poſitas, cum eis ad eandem partem angulos æquales conti-
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nentes, ita ſe habere, vt ductis duabus vtcumque ipſis tangentibus
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parallelis, quæ diuidant ipſas ſimiliter ad eandem partem, </
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