Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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ptis regulis, OS, fp, omnes ęquidiſtare: </
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<
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">Et quidem ſi plana ſecent
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figuras, oOS, sfp, hoc manifeſtum eſt, etenim productę lineę ip-
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ſis baſibus, OS, sp, erunt parallelæ, & </
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<
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">latera homologa ſimilium
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figurarum ex traiectis planis in ſolidis productarum. </
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<
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">Siverò plana
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parallela ſecent duas figuras ipſis, oOS, sfp, continuatas, vti ſa-
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ciunt plana figurarum, HMPL, VZdY, quæ etiam ſecant plana
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figurarum, oOS, sfp, producta in rectis, KN, ug, oſtendemus
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ipſas, KN, ug, eſſe regulas homologarum ſimilium figurarum, L
<
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HMP, VZdY, iunctis, PK, du. </
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<
s
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xml:space
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">Quia enim, Oo, fs, ſunt ip-
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ſorum ſimilium ſolidorum latera homologa, producta, ac terminata
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ad baſium plana, & </
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<
s
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echoid-s1688
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">oppoſitorum tangentium, in punctis, O, B; </
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<
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">f,
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">Elicitur
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ex Corol.
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Lem. 6.</
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Q, ideò, BO, Qf, ſunt ſimiliter ad eandem partem ſectæ in, o, s,
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& </
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<
s
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">nedum, Oo, fs, ſed etiam, oB, sQ, ſunt vt eorum altitudines
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ſumptæ reſpectu dictarum baſium, ſed ſic etiam ſunt ipſæ, oS, sp,
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latera homologa, ergo, Bo, ad, oS, eſt vt, Qs, ad, sp, & </
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<
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los æquales, BoS, Qsp, complectuntur latera proportionalia, er
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">6. Sex. El.</
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go triangula, BoS, Qsp, ſunt ſimilia, cum verò ſint in planis trian-
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gulorum, oOS, sfp, ſunt etiam ſimilibus figuris, LPSo, Ydps,
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ęquè ad eandem partem inclinata, quibus communia ſunt homolo-
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xlink:label
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">Ex Lem.
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1.</
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galatera, oS, sp, ergo anguli, KoL, usY, interſe, necnon, PS
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">Corollar.
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Lem. 6.</
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I, dpX, æquales erunt; </
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<
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">cum verò, BS, Qp, ſint vt dictæ altitudi-
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nes, & </
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<
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">ſic etiam, IS, Xp, necnon, PS, dp, (etenim, BS, Qp, in,
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huius.</
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I, X, &</
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<
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">ad eandem partem, in pun-
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ctis, P, d,) erit, IS, ad, SP, vt, Xp, ad, pd, & </
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<
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xml:space
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">circumſtant an-
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">6. Sex. El.</
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gulos æquales, ISP, Xpd, ergo triangula, ISP, Xpd, ſunt ſimi-
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lia. </
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<
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">Eodem modo oſtendemus ſimilia eſſe triangula, LoK, Y su.
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</
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<
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">Vlterius, quia eſt, Ko, ad, oS, vt, us, ad, sp, &</
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<
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">, oS, ad, SI,
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vt, sp, ad, pX, & </
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<
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">anguli, KoS, usp, necnon, oSI, spX, ſunt
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æquales, ideò trapezia, KoSI, uspX, erunt ſimilia, ſed etiam fi-
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guræ, LPSo, Ydps, ſunt ſimiles, eſt autem, KL, ad, Lo, vt,
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uY, ad, Ys, &</
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<
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">, oL, ad, LP, vt, sY, ad, Yd, ergo, KL, ad, L
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P, erit vt, uY, ad, Yd, eodem modo autem oſtendemus, LP, PI,
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IK, KL, binas eſte in eadem proportione cum ipſis, Yd, dX, Xu. </
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uY. </
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<
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">Manifeſtum eſt autem ſi iungeremus, AO, Tf, AS, Tp, quod
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fierent ſimiles pyramides triangulatæ ipſæ, AOoS, Tfsp, ſimili-
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bus n. </
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<
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">triangulis comprehenderentur, vt meditanti compertum fiet,
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">Ex Lem.
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4.</
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ideò plana, AoO, Tsf, ideſt triangula ſimilia, LKo, Yus, ſunt
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1.</
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æquè ad eandem partem ipſis ſimilibus figuris, LPSo, Ydps, in-
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clinata, cum quibus coincidunt in lateribus homologis, Lo, Ys,
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<
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">Ex Lem.
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2.</
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ergo anguli, KLP, uYd, erunt æquales, quibus circumſtant latera
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proportionalia, vt probatum eſt, ergo triangula, KLP, uYd, ſi-
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milia erunt, & </
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<
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">erit, KP, ad, PL, vt, ud, ad, dY, eſt verò, </
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