Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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CF, minor. </
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<
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tanget in C, ducantur rectæ AG, AH, AI, per puncta D, E, F. </
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<
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AC, perpendicularis. </
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<
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<
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<
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CE; </
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<
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<
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<
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">at DK, ſinus rectus
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<
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arcus CD, & </
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<
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<
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lem eſſe ſinui toti AC; </
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<
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">at CH, maiorem, & </
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<
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norem. </
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">27. tertij.</
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enim anguli CAG, GAB, æquales ſunt, ob arcus
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æquales CD, DB; </
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vterq; </
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<
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">illorum ſemirectus. </
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">32. primi.</
note
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lus CGA, in triangulo ACG, ſemirectus erit;
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</
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<
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CG, tangens arcus CD, qui ſemiſsis eſt quadran-
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tis, ſinui toti AC, æqualis erit. </
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<
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tur, CH, tangentem arcus CE, qui ſemiſſe quadrantis maior eſt, ſinu toto
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AC, maiorem eſſe; </
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<
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<
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">CI, tangentem arcus CF, qui ſemiſſe quadrantis mi-
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nor eſt, minorem: </
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<
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infra.</
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<
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gentis CG, cuius arcus eſt ſemiſsis quadrantis. </
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<
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quadrantis maior eſt, erit arcus BE, ſemiſſe quadrantis minor. </
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<
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CAH, angulo HAB, maior eſt, ac proinde maior ſemirecto. </
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<
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gulus C, rectus ſit, erit reliquus AHC, in triangulo ACH, ſemirecto minor.
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</
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Quare recta CH, tangens arcus CE, qui ſemiſſe quadrantis maior eſt, ma-
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ior eſt ſinu toto AC.</
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<
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maior, erit angulus CAI, angulo IAB, minor; </
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<
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</
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Cum ergo angulus C, ſit rectus, erit reliquus AIC, in triangulo ACI, maior
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<
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ſemirecto: </
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<
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minor eſt, minor erit ſinu toto AC.</
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<
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oſtenſum eſt; </
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<
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<
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<
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erit. </
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<
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<
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ita AD, hoc eſt, AC, ad AK; </
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totus, & </
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ergo erit quadratum ex AG, ad quadratum ex AC, vt recta AG, ad rectam
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<
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AK. </
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<
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æquale eſt quadratis ex AC, CG, æqualibus. </
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quadrátis dupla eſt ſinus AK, vel DK, eiuſdem dimidij. </
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<
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midij quadrantis ſinui toti æqualis eſt, &</
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<
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gentes in ta
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bula tágen-
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tiũ mino -
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res
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ſint ſinu
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toto, & quę
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maiores.
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Ité cur ſe-
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cás gt. 45.
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dupla ſit ſi-
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nus gt. 45.</
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<
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<
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tes arcuum minorum, quàm grad. </
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<
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<
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ſinu toto maiores. </
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<
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<
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arcus eiuſdem grad. </
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