Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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gemus ſequentes propoſitiones ad triangula quoque ſphærica rectangula ſpectantes,
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antequam triangulorum ſphæricorum non rectangulorum calculum exponamus.
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<
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<
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xml:space
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">minus confuſæ, proponemus ſemper
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triangulum ſphæricum rectangulum, cuius duo arcus circa angulum rectum, ac pro-
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inde omnes tres, minores ſint quadrante. </
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<
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xml:space
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conuenient, vt in hoc ſcbolio demonſtrauimus: </
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<
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<
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culum conſicientes, quàm duo anguli duobus rectis æquales, eandem habeant tangen
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tem, ac ſecantem, quemadmodum & </
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& </
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<
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ius omnes arcus quadrante ſint minores: </
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tus ad ſinum vtriuſuis arcuum circarectum angu-
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lum eandem habet proportionem, quam tangens
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anguli non recti dicto arcui adiacentis ad tangen-
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tem reliqui arcus circa angulum rectum huic an-
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gulo oppoſiti.</
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<
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">IN triangulo ſph ærico ABC, cuius omnes arcus quadrante minores, ſit
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angulus C, rectus. </
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gens anguli B, ad tangentem arcus AC. </
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enim arcubus BC, BA, donec fiant quadrantes BF,
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BD, ac per puncta F, D, arcu FD, circuli maximi
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deſcripto; </
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<
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drantes BF, BD: </
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B, polus ſit arcus DF. </
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<
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ximi in ſphæra BF, BD, ſecant ſeſe in B, ductiq́ue
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ſunt ex A, D, ad BF, arcus perpendiculares AC,
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DF; </
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<
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<
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xml:space
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">Theor. 6.
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ſcholij. 40.
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huius.</
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tus, ad tangentem arcus FD, hoc eſt, ad tangentem
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anguli B, ita ſinus arcus BC, ad tangentem arcus AC: </
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ſinus totus ad ſinum arcus BC, ita tangens anguli B, ad tangentem arcus AC.
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</
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<
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tangens anguli A, ad tangentem arcus BC: </
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<
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ducantur, donec fiant quadrantes AG, AE, perque G, E, arcus maximi cir-
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culi deſcribatur GE. </
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ſcholij 40.
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huius.</
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totus, ad tangentem arcus EG, ſeu anguli A, ita ſinus arcus AC, ad tangen
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tem arcus BC: </
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<
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anguli A, ad tangentem arcus BC. </
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<
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gulo, &</
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