Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ctæ FH, æqualis, ob parallelogrammum FI. </
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nuum FH, GI. </
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<
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<
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">Ducta enim recta BE, quæ latus hexagoni eſt, ac propterea, ex coroll propoſ. </
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15. </
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<
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<
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<
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BD, bifariã in M, iungaturq́ recta EM. </
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<
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tur latera DM, ME, lateribus BM, ME, æqualia
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ſunt, & </
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<
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">baſis DE, baſi BE, æqualis, erunt anguli ad
<
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<
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M, ęquales, atque adeo recti. </
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micirculo ABC, & </
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<
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">productis rectis GI, EM, ad
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N, O, erit arcus NO, arcui GE, hoc eſt, arcui EF,
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æqualis, ex ſcholio propoſ. </
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<
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quod rectæ GN, EO, parallelæ ſunt, ob rectos angu
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<
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los I, M. </
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<
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cus FN, arcui EO, æqualis: </
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<
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eſt arcus BE. </
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<
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">(Nam recta DB, rectam EO, ſecans ad
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angulos rectos ſecat eandem bifariam: </
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arcum EO, bifariam, ex ſcholio in definitionibus
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poſito) Igitur & </
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<
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">arcus FN, eiuſdem arcus BE, du-
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plus erit. </
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<
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">Quare ductis rectis DF, DN, erit quoque
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angulus FDN, anguli EDB, duplus: </
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<
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<
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">33. ſexti.</
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tro anguli FGN, in circunferentia duplus. </
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FGK: </
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<
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EDM,
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GK: </
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<
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">atque idcirco erit vt ED, ad DM, ita FG, ad GK. </
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<
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<
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ED, dupla ſit ipſius DM, (ſecta enim eſt DB, ipſi DE, æqualis, bifariam in
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M.) </
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<
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pla. </
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<
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">Igitur recta GK, differentia ſinuum FH, GI, æqualis eſt rectæ FL, ſi-
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nui arcus EF, vel rectæ GL, ſinui arcus EG. </
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<
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rum arcuum quadrantis, &</
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<
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duorum ar
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cuũ confi-
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cientium
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grad. 60. ſi-
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mul æqua-
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les ſunt ſi-
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nui arcus
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compoſiti
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ex arcu
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grad. 60. &
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arcu mino
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re illorum
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duorum.</
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<
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<
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<
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effici ſinum arcus cõpoſiti ex arcu grad. </
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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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cuum BF, FE, conſicientium grad. </
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<
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<
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compoſiti ex arcu BE, grad. </
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<
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">& </
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<
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">arcu EG, qui minori EF, æqualis eſt: </
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<
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vt demonſtratum eſt, differentia GK, inter ſinus FH, GI, æqualis eſt ſinui FL.</
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<
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omniũ ar-
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cuum ſinus
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recti ſuppu
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tentur.</
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ſeſe ordine ſuperantium vno Minuto, in partibus
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Sinus totius in quotcunque particulas diſſributi,
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ſupputare.</
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<
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