Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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rectis AB, GL, LK, triangulum ANB, quod erit Iſoſceles, cadetque punctum N,
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extra triangulum AEB, cum AE, EB, ſimul dimidium conſtituant rectæ G, H; </
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verò A N, N@B, ſimul maius efficiant, quam dimidium rectæ G H. </
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<
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"> Rurſus
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tribus rectis CD, KM, MH, conſtituatur quoque triangulum C O D, quod Iſo-
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ſceles erit, cadetque punctum O, intra triangulum CFD, eo quod CF, FD, ſimul
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æquales ſint dimidio rectæ GH; </
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<
s
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">at CO, OD, ſimul minores ſint dimidio rectæ
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GH. </
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<
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">Et quoniam quatuor latera AE, EB, CF, FD, ſimul; </
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">Item AN, NB, C O,
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O D, ſimul æqualia ſunt rectæ G H, erunt priora quatuor ſimul, poſterioribus
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quatuor ſimul æqualia; </
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<
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">additis ergo communibus AB, CD, fient ſex latera AE,
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EB, BA, CF, FD, DC, ſimul ęqualia ſex lateribus AN, NB, BA, CO, OD, DC, ſi-
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mul; </
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<
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">ideo que triangula ANB, COD, ſimul Iſoperimetra erunt triangulis AEB,
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CFD, ſimul. </
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<
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<
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">Nam
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quoniam eſt, vt AB, ad CD, ita GK, ad KH, hoc eſt, ita GL, ad KM, hoc eſt
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A N, ad C O, & </
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">erit permutando, vt A B, ad AN,
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ita C D, ad C O; </
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">& </
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">vt A N, ad N B, ita C O, ad O D. </
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">Proportionalia ergo
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ſunt latera triangulorum ANB, COD; </
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idcirco ſimilia. </
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">Quare datis duobus triangulis Iſoſcelibus, quorum baſes inæ-
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quales exiſtant &</
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duo Iſoſcelia
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ſimilia maio-
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ra ſunt duo-
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bus Iſoſcelib{us}
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non ſi milib{us},
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quæillis ſint
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Iſoperimetr@,
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baſeſque ha-
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beant eaſdem.</
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">DVO triangula Iſoſcelia ſimilia ſuper inæqualibus baſibus conſtituta,
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vtraque ſimul maiora ſunt duobus triangulis Iſoſcelibus, vtriſque ſi-
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mul, quæ habeant eaſdem baſes cum prioribus, ſintq; </
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dem inter ſe, at Iſoperimetra prioribus duobus, nec non quatuor la-
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tera inter ſe habeant æqualia.</
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baſibus inæqualibus A C, C E, ſint duo triangula Iſoſcelia inter ſe
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nonſimilia ABC, CDE, ita vt quatuor latera AB, BC, C D, D E, inter ſe ſint æ-
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qualia. </
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la Iſoſcelia AFC, CGE, ſimilia inter ſe, & </
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ſimul. </
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">Dico duo triãgula AFC, CGE, ſimul maiora eſſe duobus triangulis ABC,
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CDE, ſimul. </
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