Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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bunt & </
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laſingulis, quæ æquales angulos ſubrendunt.</
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<
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">HABEANT duo triangula ſphærica ABC, DEF, tres angulos A,
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B, C, tribus angulis D, E, F, ſingulos ſingulis, æquales. </
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<
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AB, AC, BC, tribus lateribus DE, DF, EF, eſſe æqualia, ſingula ſingulis,
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quæ angulos æquales ſubtendunt. </
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<
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tera BC, EF, (vt ab his lateribus exordiamur.)
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<
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& </
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lis. </
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<
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">Aut ergo arcus BA, æqualis eſt arcui ED,
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aut maior, aut minor. </
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<
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catur, ſequetur abſurdũ ex eo, quòd inæqua-
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lia dicuntur eſſe latera BC, EF, nempe BC,
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maius, quàm E F. </
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<
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arcui ED, æqualis; </
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A, G, arcus maximi circuli AG. </
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teribus ED, EF, angulosq́ue contineãt æquales B,E, ex hypotheſi; </
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<
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guli BAG, & </
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Angulus igitur BAG, æqualis erit quoque angulo BAC, pars toti. </
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eſt abſurdum.</
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<
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<
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<
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lis ipſi ED; </
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<
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">ac per puncta G,I, arcus circuli maximi ducatur GI, conueniens
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cum arcu CA, protracto in H. </
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<
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lateribus ED, EF, angulosq́ue continent æquales B, E; </
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BGI, angulis D, F, hoc eſt, angulis BAC, BCA, æquales; </
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æquales ſint poſiti D, & </
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HAK, ad verticem æquales. </
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tur cum & </
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<
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">angulus BGH, externus æqualis ſit interno BCH, & </
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HAK, interno HIK, vt oſtendimus: </
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<
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CH, HG, ſemicirculo æquales; </
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HG, æquales erunt, pars toti. </
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<
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abſcindatur arcus BK, æqualis arcui ED; </
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<
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culi maximi ducatur GK, ſecans arcum AC, in L. </
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BG, lateribus ED, EF, æqualia ſunt, anguloſque continent æquales B, E,
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erunt & </
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<
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">anguli BKG, BGK, angulis D, F, hoc eſt, angulis BAC, BCA,
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(quòd his duobus æquales ſint poſiti anguli D, F.) </
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angulus BAL, externus æqualis ſit interno BKL, & </
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no BCL, vt oſtendimus, erunt tam arcus AL, LK, quàm arcus CL, LG,
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ſemicirculo æquales; </
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les erunt. </
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minor. </
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<
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do oſtendemus, latera AC, DF, nec non AB, DE, æqualia eſſe. </
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<
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latera trianguli ABC, tribus lateribus trianguli DEF, æqualia ſunt. </
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ſi duo triangula ſphærica, &</
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