Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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vterque angulus E, G, rectus erit. </
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<
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xml:space
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ſe mutuo in ſphæra ſecant in B, ſumptaq́ue ſunt in BD, duo puncta A, D, à
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quibus ad BC, ducti ſunt duo arcus AC, DF, perpendiculares, erit vt ſinus
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arcus AB, ad ſinum arcus AC, ita ſinus arcus BD, ad ſin um arcus DF: </
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mutando, vt ſinus arcus AB, trianguli ABC, ad ſinum quadrantis BD, hoc
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eſt, ad ſinum totum anguli recti C, in eodem triangulo ABC, ita ſinus arcus
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AC, eiuſdem trianguli ABC, ad ſinum arcus DF, hoc eſt, ad ſinum anguli
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B, in eodem triangulo ABC. </
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<
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<
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">ratione erit, vt ſinus arcus AB, trian
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guli ABC, ad ſinum quadrantis AE, hoc eſt, ad ſinum totum anguli recti C,
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in eodem triangulo ABC, ita finus arcus BC, eiuſdem trianguli ABC, ad
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finum arcus EG, hoc eſt, ad ſinum anguli A, in eodem triangulo ABC. </
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<
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eſt propoſitum.</
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<
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">SI denique alter angulorum A, B, recto maior eſt, & </
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ior, & </
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quadrante etiam maior, at verò BC, minor
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quadrante. </
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BD, AE, & </
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quadrans BF; </
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<
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">per puncta D, F, ducatur ar-
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cus DF, circuli maximi, necnon per E, G,
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arcus circuli maximi EG; </
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<
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polus arcus DF, & </
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tur DF, EG, arcus erunt angulorum B, A;
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anguli C, recti, ex defin. </
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drantes AE, AG, vterque angulus E, G, re-
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ctus erit. </
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mi BA, BF, in ſphæra ſe mutuo ſecant in B,
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ſumptaq́ue ſunt in BA, duo puncta A, D, à
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quibus ad BF, ducti ſunt duo arcus perpendiculares AC, DF; </
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<
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arcus AB, ad ſinum arcus AC, ita ſinus arcus BD, ad ſinum arcus DF: </
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permutando, vt ſinus arcus AB, trianguli ABC, ad ſinum quadrantis BD,
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hoc eſt, ad ſinum totum anguli recti C, in eodem triangulo ABC, ita ſinus
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arcus AC, trianguli eiuſdem ABC, ad ſinum arcus DF, hoc eſt, ad ſinum an-
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guli B, in triangulo eodem ABC. </
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trianguli ABC, ad ſinum quadrantis AE, hoc eſt, ad ſinum totum recti an-
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guli C, in eodẽ triangulo ABC, ita ſinus arcus BC, eiuſdem trianguli ABC,
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ad ſinum arcus EG, hoc eſt, ad ſinum anguli A, eiuſdem trianguli ABC,
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Quod eſt propoſitum.</
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ctum A, & </
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li maximi AD, cadatq́ue primum in latus BC, in-
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tra triangulum; </
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igitur in triangulo ABD, angulus D, rectus eſt; </
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vt iam demonſtratum eſt, vt ſinus arcus AB, ad ſi-
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num anguli ADB, ita ſinus arcus AD, ad ſinum an-
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guli B: </
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<
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arcus AD, ita ſinus anguli ADB, ad ſinum anguli
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B. </
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