Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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tam in ſemicirculo CAE, reliquus arcus AE, quam in ſemicirculo
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ACD, reliquus arcus CD, quadrans: </
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<
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AED, vel CDE, reliquus arcus DE, quadrans erit; </
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<
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tuor anguliad B, quatuor quadrantibus æqualibus inſiſtentes erunt æqua-
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les, & </
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<
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bus angulis
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tirãguli re-
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ctilinei, da-
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tus etiã erit
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tertius. Itẽ
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in triãgulo
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rectangulo,
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ſi detur vnꝰ
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angulus a-
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cutus, datus
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quoq; erit
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acutus reli-
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quus.</
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<
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">_IN_ materia porro triangulorum rectilineorum, cum dantur duo anguli noti, ter
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tius illico notus quoq; </
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<
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">erit, cum ſit complementum duorum rectorum: </
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<
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">Item cum in
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triangulo rectãgulo datur vnus acutus angulus, notus etiã erit reliquus acutus, quod
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ſit complementum vnius recti. </
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<
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</
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<
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xml:space
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tus ex grad. </
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<
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">Latera triã-
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guli rectili-
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nei ſunt ſi-
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nubus an-
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gulotũ op-
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poſitorum
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proportio-
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nalia.</
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duo eandem proportionem habent, quam ſinus
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angulorum illis oppoſitorum.</
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<
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">SIT primum triangulum rectangulum ABC, cuius angulus rectus B.
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AB, ad BC, vt eſt ſinus anguli C, ad ſinum angu-
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li A, &</
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<
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nuum oſtendimus, ſi AC, ponatur ſinus totus, latus
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AB, eſt ſinus anguli C; </
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conſtat, ita eſſe latus AB, ad latus AC, vt eſt AB, ſinus
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anguli C, ad AC, ſinum totum anguli recti B: </
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eſſe latus AC, ad latus AB, vt eſt AC, ſinus totus re-
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cti anguli B, ad AB, ſinum anguli C; </
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<
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ſint ſinus angulorum oppoſitorum, ac proinde vtro-
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biq; </
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ita AC, ſinus totus anguli recti B, ad BC, ſinum anguli A: </
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ad latus AC, ita BC, ſinus anguli A, ad AC, ſinum totum recti anguli B.
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</
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guli A: </
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num anguli C.</
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</
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<
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tus AB, ad latus AC, vt eſt ſinus anguli C, ad ſinum anguli B, &</
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</
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<
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lia, erunt quoq; </
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<
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<
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">ac proinde, vt in definitionibus ſi-
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<
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nuum docuimus, eorum ſinus æquales. </
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<
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AC, ita ſinus anguli C, ad ſinum anguli B: </
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<
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ſinus anguli B, ad ſinum anguli C; </
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<
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