Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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<
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Def. Sex-
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ti Elem.</
note
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ſimiles iuxta definitionem E@clidis, ideſt ſingulos habentes angulos
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æquales, A, M; </
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<
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<
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xml:space
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los latera proportionalia. </
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finitionem: </
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quæ cum duobus ex lateribus homologis earumdem angulos æqua-
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les ab eadem parte contineant, ſint autem ex vna parte tangentes
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ipſæ, AH, MN, quæ cum ipſis, HE, NP, lateribus homologis
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angulos continent ęquales, AHG, MNO, & </
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<
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gentes ipſæ, DF, RQ, quæ cum ipſis, HE, NP, productis con-
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currant in punctis, F, Q, ducantur deinde à
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punctis angulorum, qui ſunt, B, E; </
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<
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ctis tangentibus parallelæ, BG, CE, TO, S
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P, & </
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<
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ergo anguli, MNQ, AHF, ſunt æquales,
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etiam anguli, NQR, HFD, erunt ęquales,
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& </
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<
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xml:space
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æquales, etiam anguli, RPQ, DEF, erunt
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æquales, & </
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<
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PQ, DEF, erunt æquianguli, & </
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<
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Elem.</
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ad, PR, erit vt, FE, ad, ED, eſt autem, R
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P, ad, PN, vt, DE, ad, EH, ergo, ex ęquali,
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Eucl.</
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QP, ad, PN, erit vt, FE, ad, EH, igitur,
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NQ, HF, ſunt ſimiliter ad eandem partem
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diuiſæ in punctis, E, P, quia verò angulus, NPS, æquatur angu-
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lo, NQR.</
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<
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quus, SPR, æquabitur reliquo, CED, eſt autem angulus, TR
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P, ęqualis angulo, BDE, ergo trianguli, PSR, ECD, erunt æ-
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quianguli, & </
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<
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<
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xml:space
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ad, EF, erit vt, RP, ad, PQ; </
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E, ad, SP, erit vt, EF, ad, PQ .</
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<
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Elem.</
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quia anguli, BDE, TRP, ſunt æquales, & </
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proportionalia, ideò trianguli, BDE, TRP, erunt æquianguli,
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vnde anguli, DBE, RTP, &</
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autem ęquales ipſi, CED, SPR, ergo reliqui, BEC, TPS, erunt
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æquales, & </
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<
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<
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angulus, BEF, eſt ęqualis ipſi, TPQ, reliquns, BEH, erit ęqua-
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lis reliquo, TPN, eſt autem, BGE, ęqual sipſi, TOP, ergo trian-
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guli, BGE, TOP, erunt ęquianguli, ergo, BG, ad, TO, erit vt,
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BE, ad, TP, ideſt vt, CE, ad, SP, ideſt vt, HF, ad, NQ, per-
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mucando, & </
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<
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</
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<
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<
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