Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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ad, PI, vt, dY, ad, dX, ergo ex æquali, KP, ad, PI, erit vt, u
<
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d, ad, dX, eſt autem, PI, ad, IK, vt, dX, ad, Xu, ergo trian-
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gula quoque, PKI, duX, pariter ſimilia erunt, vnde anguli, LP
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I, YdX; </
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<
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xml:space
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">PIK, dXu, &</
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echoid-s1707
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xml:space
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">, IKL, XuY, æquales erunt. </
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<
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">Ducantur
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nunc in planis figurarum, LHMP, YVZd, à punctis, L, Y, pa-
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0086-01
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rallelæ, KN, ug, ipſæ, L3,
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Y4. </
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<
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">Cum igitur anguli, LK
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I, YuX, ſint ęquales, etiam,
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KL3, uY4, æquales erunt,
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huius.</
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ſed &</
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">, KLP, uYd, ſuntæ-
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quales, ergo reſidui quoque, 3
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LP, 4Yd, erunt ęquales, vn-
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de cum ipſæ, L3, Y4, con-
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tineant cum lateribus homo-
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logis, LP, Yd, ad eandem
<
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partem angulos æquales, e-
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runt regulę homologarum ſi-
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milium figurarum, LHMP,
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YVZd, vnde etiam ipſæ, K
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N, ug, velipſæ OS, fp, e-
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runt regulæ homologarum
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earundem, ſunt. </
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<
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">n. </
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<
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">OS, KN,
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parallelæ, vt etiam, ug, fp,
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vnde omnes homologæ ſimi-
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lium figurarum, LHMP, Y
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VZd, ipſis regulis, OS, fp,
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æquidiſtabunt, quod & </
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<
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">de cę-
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teris eodem modo oſtende-
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tur, dumſectio fiet in figuris,
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AESo, Tlps. </
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<
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xml:space
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">Quod ſi fi-
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guris, AESO, Tlps, aliæ
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figuræ planæ continuarentur
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citra cõtactum planorum ba-
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ſibus oppoſitorum, cum his
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in lateribus homologis, AE,
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Tl, conuenientes, quibus eſ-
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ſent inclinatę, parum diſſimili
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methodo, producentes, OB,
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fQ, vſq; </
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<
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">occurſuum puncta cum ipſis, S, p,
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iungentes, necnon extrema laterum homologorum, qualia fuerunt,
<
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LP, Yd, cum extremis rectarum in triangulis (qualia fuerunt, BO
<
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S, Qfp,) productarum, panter iungentes, vt fecimus cum ipſis, </
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