Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
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Ioan. de Sacro Boſco.
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tuor ſimul, poſterioribus quatuor ſimul æqualia: </
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A B, C D, fient ſex alte@a A E, E B, B A, C F, F D, D C, ſimul æqualia ſex late-
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ribus A N, N B B A, C O, O D, D C, ſimul; </
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ſimul iſoperimetra erunt triangulis A E B, C F D, ſimul. </
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milia inter ſe ſunt triangula A N B, C O D. </
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<
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">Nam quoniam eſt, ut A B, ad O D,
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ita G K, ad K H, hoc eſt, ita G L, ad K M, hoc eſt, ita A N, ad C O, & </
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ad O D, erit permutando, vt A B, ad A N, ita C D, ad C O; </
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<
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ita C O; </
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triangulis Iſoſcelibus, quorum baſes inæquales exiſtant. </
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faciendum erat.</
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<
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triangula Iſoſcelia ſimilia ſuper inæqualibus baſibus conſtitu-
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">Triangulæ
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duo Iſoſce-
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lia ſimilia
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maiora sũt
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duobus Iſo
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ſcelibus nõ
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ſimilibus,
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quæ illis
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ſint Iſope-
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rimetta, ba-
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ſesque ha-
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beant eaſ-
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dem.</
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ta, utraque ſimul maiora ſunt duobus triangulis Iſoſcelibus, utriuſque ſi-
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mul, quę habeant eaſdem baſes cum prioribus, ſintq; </
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inter ſe. </
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habeant æqualia.</
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baſibus inæqualibus A C, C E, ſint duo triangula Iſoſcelia in-
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ter ſe non ſimilia A B C, C D E, ita vt quatuor latera A B, B C, C D, D E,
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inter ſe ſint æqualia. </
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que ſuper eiſdem baſibus
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A C, C E, (per præceden-
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tem propoſ.) </
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tur alia duo triãgula Iſo-
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ſcelia A F C, C G E; </
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lia inter ſe, & </
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tra ſimul prioribus trian-
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gulis ſimul. </
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">Dico duo triã
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gula A F C, C G E, ſimul
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maiora eſſe duobus trian
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gulis A B C, C D E, ſi-
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mul. </
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">Ponantur enim A C,
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C E, ſecundum lineam re
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ctam vnam; </
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ſis maior baſe C E. </
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de ex F, per B, ducatur
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recta F B K, ſecans rectam
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A C, in puncto K; </
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D, per G, punctum duca
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tur recta D C H, ſecans rectam C E, in H. </
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">Et quia latera A F, F B, triangu-
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li A F B, æqualia ſunt lateribus C F, F B, trianguli C F B, & </
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B C, æqualis, erit angulus A F B, angulo C F B, æqualis. </
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<
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@a A F, F K, trianguli A F K, æqualia ſunt lateribus C F, F K, trianguli,
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<
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