Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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tera proportionalia, ideòtriang. </
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<
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xml:space
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">HAB, NMT, ſuntæquiangun,
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Elem.</
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& </
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<
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">anguli, AHB, MNT; </
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<
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echoid-s1321
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xml:space
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">ABH, MTN, interſe ęquales, ergo
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cum anguli, AHG, MNO, ſint æquales, reliqui, BHG, TN
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O, erunt æquales, ſunt etiam æquales anguli, HGB, NOT, ergo
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trianguli, HBG, NTO, ſunt æquianguli, ergo, BG, ad, GH,
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erit vt, TO, ad, ON, erat autem, FH, ad, GB, vt, QN, ad, O
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T, ergo ex ęquali, FH, ad, HG, erit vt, QN, ad, NO, ſunt@gi-
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tur ipiæ, HF, NQ, ſimiliter diuiſæ, & </
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<
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">ad eandem partem in pun-
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ctis, G, O, & </
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<
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">ipſæ diuidentes, BG, TO, ſunt vt ipſæ, HF, NQ.</
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<
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<
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<
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">Ducantur nunc inter dictas oppoſitas tangentes elſdem parallelæ
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duæ v@cumque, VK, XY, inter circuitum figurarum iam propoſi-
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tarum, & </
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<
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">rectas, HF, NQ, comprehenſę, ſimiliter ad eandem par-
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tem diu@dentes ipſas, HF, NQ, in punctis, K, Y, ſecanteſque ip-
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ſas, BE, TP, in punctis, 3, 4, eſt ergo, FK, ad, QY, permutan-
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do, vt, HF, ad, QN, ideſt vt, FE, ad, QP, ergo, FK, ad, Q
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Y, erit vt, FE, ad, QP, & </
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<
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">reliqua, EK, ad reliquam, PY, vt, F
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K, ad, QY, ideſt vt, FH, ad, QN; </
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<
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">Similiter oſtendenius, vt, F
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H, ad, QN, ſic eſſe, GK, ad, OY, ergo, GK, ad, OY, erit vt,
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KE, ad, YP, &</
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<
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">, permutando, GK, ad, KE, erit vt, OY, ad, Y
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P, componendoque, GE, ad, FK, erit vt, OP, ad, PY, eſt verò,
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vt, GE, ad, EK, ita, BG, ad, 3K, & </
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<
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">vt, OP, ad, PY, ita, T
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O, ad, Y4, ergo, BG, ad, 3K, erit vt, TO, ad, Y4, & </
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<
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tando, BG, ad, TO, erit vt, 3K, ad, 4Y, eſt verò vt, BG, ad, T
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O, ita, HF, ad, NQ, ergo, 3K, ad, 4Y, erit vt, HF, ad, NQ,
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ſimiliter, quia ipſæ, VK, XY, diuidunt ſimiliter ad eandem partem
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ipſas, BC, TS, in punctis, V, X, ac diuiduntur ipſę, GE, OP, in
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punctis, K, Y, ideò eodem modo oſtendemus ipſas, V3, X4, eſſe
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vt ipſas, CE, SP, ideſt vt ipſas, HF, NQ, erant autem, 3K, 4
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X, vt ipſæ, HF, NQ, ergo totæ, VK, XY, erunt vt ipiæ, HF,
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NQ, habemus igitur figuras, ADE, MRP, in quibus ductę ſunt
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oppoſitæ tangentes, AH, DF, MN, RQ, quibus inciderunt ip-
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ſæ, HF, NQ, ad eundem angulum ex eadem parte, inuentum eſt
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autem eas, quæ inter dictas, HF, NQ, & </
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<
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ſdem tangentibus vtcumq; </
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<
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<
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HF, NQ, ſimiliter ad eandem partem, eodem ordine ſumptas, eſſe
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vt ipſas, HF, NQ, ergo figuræ, ADE, MRP, quæ erant ſimi-
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les iuxta definitionem Euclidis, erunt etiam ſimiles iuxta definitio-
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nem meam, & </
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<
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">erunt dictæ tangentes regulæ homologarum earum-
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huius.</
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dem, & </
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<
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F, NQ, quod erat oſtendendum.</
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