Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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quadrantes ſunt, ob angulos rectos B, BAE. </
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<
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<
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">arcum AC, minorem eſ-
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ſe quadrante, ita oſtendemus. </
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<
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xml:space
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cus BD; </
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<
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xml:space
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">(oſtendemus enim E, eſſe polum arcus AB,
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vt ſupra, cum BE, quadrans ſit, rectusq́ue ad arcum
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AB.) </
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<
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xml:space
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">erit punctum C, intra peripheriam circuli ar-
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cus BD, in ſuperficie ſphæræ, & </
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<
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lum. </
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">Schol. 21.</
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oſtenſus eſt eſſe quadrans. </
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nor erit. </
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">Omnes ergo arcus trianguli ABC, qua-
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drante ſunt minores. </
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<
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ſpherico rectangulo, &</
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<
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">_PRIMA_ pars buius propoſitionis vera quoque eſt, ſi ſolum vterque arcus circa
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angulum rectum ponatur quadrante miner, etiamſi ignoretur, reliquum arcum,
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qui rectum angulum ſubtendit, minorem eſſe quadrante. </
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<
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demonſtratione prioris partis. </
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">Oſtenſum eſt enim, angulos _BAC, BCA,_ eſſe acu-
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tos, ex eo ſolum, quòd vterque arcus _BA, BC,_ quadrante minor ponatur, nulla
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facta mentione arcus _AC._ </
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<
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quadrante minor, ſi duo arcus rectum angulum continentes quadrante minores ſint,
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vt ex demonſtratione manife ſtum eſt. </
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<
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xml:space
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">Nam cum ex eo, quòd arcus _BA, BC,_ mino-
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res ſint quadrante, anguli A, C, acuti ſint, vt in priore parte demonſtratum eſt, ſit,
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vt & </
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<
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">arcus AC, minor ſit quadrante, vtin parte poſteriori eſt oſtenſum. </
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proponi poterit etiam buiuſmodi Theorema.</
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<
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xml:space
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">IN omni ttiangulo ſphærico rectangulo, cuius duo arcus rectum
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angulum comprehendentes quadrante ſint minores, erit & </
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<
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angulum rectum ſubtendens quadrante minor.</
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guli ſint acuti, arcus ſinguli quadrante ſunt mi-
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nores.</
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<
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<
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xml:space
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">IN triangulo ſphærico ABC, ſint omnes an-
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guli acuti. </
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<
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res eſſe. </
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<
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æquales. </
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25. huius.</
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drante minores, vt ſupra demonſtratum eſt.</
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<
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quales B, C; </
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igitur vterque arcus AB, AC, minor quadrante.</
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