Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
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Comment. in I. Cap. Sphæræ
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5. </
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<
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<
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<
s
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">in quadrilateris autem figuris omnia latcra habentibus æqualiæ
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(quoniam neceſſario ſunt parallelogramma, vt in ſcholio propoſ. </
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<
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ſtendimus) ſinguli oppoſiti inter ſe ſint æquales: </
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in triangulis, & </
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A B C, inter ſibi Iſoperimetra triangula maximum. </
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34
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132-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/132-01
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æquiangulum. </
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<
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eſt æqui
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laterum, ſed latera
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A B, B C, ſunt inæqualia:
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</
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">ſi ſuper baſem A C, conſti-
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tuatur, per propoſ. </
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ius triangulum Iſoſceles
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A D C, ita ut latera A D,
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D C, ſimul æqualia ſint la-
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teribus A B, B C, ſimul,
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erunt triangula A B C,
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A D C, Iſoperimetra, atque adeo per propoſ. </
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<
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eſt contra hypotheſim. </
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. </
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ratio eſt de cæteris. </
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">A E quilaterum ergo eſt triangulum A B C. </
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5. </
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">& </
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">æquiangulum eſt. </
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<
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<
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ſit quadrilaterum A B C D, inter omnia ſibi Iſoperimetra maximum.
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">Si enim non eſt æquilaterum, ſint late-
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ra A B, B C, ſi fieri poteſt, inæqualia, ducaturq́ue recta A C. </
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huius, ſuper A C, conſtituatur triangulum A E C, iſoperimetrum triangulo A B C,
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erit, per propo
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ſ. </
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<
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">huius, triangulum A E C, maius triangulo A B C, Addito, ergo con
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muni triangulo A C D, erit quadrilaterum A E C D, maius quadrilatero A B C D. </
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quod eſt contra hypotheſim cum A B C D, maximum ponatur. </
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<
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latera A B, B C, ſed ę
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qualia. </
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<
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">Eademq́. </
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<
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">ratio eſt de cæteris. </
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gura A B C D.</
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<
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iam quadrilatera figura A B C D, omnium iſoperimetrarum maxima, æqui-
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latera, vt oſtenſum eſt, at non æquiangula, ſed anguli B A D, C D A, inæquales ſint.
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</
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<
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ſcholio propoſ. </
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<
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<
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<
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<
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. </
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<
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<
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<
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perpendiculares A H, D G, occurrentes lateri B C, in H, & </
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,
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parallelogrammum. </
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<
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<
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producantur hæc, ut fiant rectæ A E, D F, lateribus A B, D C, æquales, iungaturq́;
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</
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<
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<
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">Quo facto, erit figura A E F D, iſoperimetra parallelogrammo A B C D,
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cum latera A E, DF, lateribus A B, D C, ęqualia ſint, latus uero A D, commune,
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<
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& </
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<
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<
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ſit parallelogrammo A B C D; </
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<
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<
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A B C D. </
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<
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">Quare cum eidem ſit iſoperimetra, non erit A B C D, figura quadrilateræ
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inter ſibi Iſoperimetras maximam. </
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<
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ſunt anguli B A D, C D A. </
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<
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<
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">atque adeo cum A B C D, ſit parallelogram-
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mum, erunt anguli oppoſiti B, C, angulis D, A, æquales, proptereaq́; </
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<
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-
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quiangula erit. </
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