Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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quadrata, AE, EG, (quia etiam, AEG, rectus eſt) æquabuntur
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tribus quadratis, AE, EF, FG, vnde, ablato communiquadrato,
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El. Def. 6.</
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AE, quadratum, GE, ęquabitur duobus quadratis, GF, FE; </
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ratione autem probabimus quadratum, YT, æquari quadratis, Y
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Z, ZT, vnde anguli, GFE, YZT, recti erunt; </
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<
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">eodem modo
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probabimus eſſe rectos, EPG, TXY, ergo anguli, AFE, KZT,
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Vnd. El.</
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erunt anguli inclinationis primorum planorum, BG, LY, cum iu-
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biectis planis, HV, & </
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APE, KXT, erunt inclinationes ſecundorum planorum, AV, K
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Λ, cum eiſdem ſubiectis planis. </
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ſunt æquales, &</
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">, AEF, KTZ, recti, erunt triangula, AFE, K
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ZT, inter ſe ſimilia, vt etiam triangula, AFG, KZY, inter ſe,
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nam anguli, AGF, KYZ, ſunt quoque æquales, &</
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<
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Y, recti; </
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<
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">erit ergo, vt, EF, ad, FA, ſic, TZ, ad, ZK, & </
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F, ad, FG, ſic, KZ, ad, ZY, ergo ex æquali, vt, EF, ad, FG,
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itaerit, TZ, ad, ZY, & </
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Elem.</
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los, GFE, YZT, ergo triangula, GFE, YZT, pariter ſimilia
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erunt, anguli igitur, EGF, TYZ, adæquabuntur, totus autem,
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PGF, toti, XYZ, æquatur, ergo reliquus, EGP, erit ęqualis re-
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liquo, TYX, & </
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erunt, GPE, YXT, ſimilia triangula, igitur, vt, PG, ad, GE,
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ſic erit, XY, ad, YT, vt verò, GE, ad, GF, ſic eſt, YT, ad, YZ,
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& </
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">vt, GF, ad, GA, ſic, YZ, ad, YK, ergo ex æquali, PG, ad,
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GA, erit vt, XY, ad, YK, habemus ergo duo triangula, APG,
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KXY, habentia duos angulos, APG, KXY, ęquales, ſunt. </
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cti, circa verò duos, PGA, XYK, latera proportionalia, & </
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quorum vtrumq; </
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ſimilia, & </
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">anguli, PGA, XYK, ęquales, vnde reliqui, AGV, Κ
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Υ Λ, pariter æquales erunt, quod eſt vnum propoſitorum.</
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">Rurſus, quia, PE, ad, EF, eſt vt, XT, ad, TZ; </
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ad, EA, vt, TZ, ad, TK, ergo ex æquali, PE, ad, EA, erit vt,
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XT, ad; </
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proportionalia, ergo triangula, APE, KXT, ſimil a erunt, nec-
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non anguli, APE, KXT, inclinationis ſecundorum planorum, A
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V, Κ Λ, cum ſubiectis planis inter ſe æquales, & </
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quod etiam demonſtrare propoſitum fuit.</
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libus figuris rectilineis, ſequitur pro ipſis etiam defini-
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tio geneneralis, quam de omnibus ſimilibus figuris planis
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ipſe attuli.</
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