Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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<
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xml:space
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">SI fiat, vt ſinus totus ad ſinum arcus angulo recto oppoſiti, ita ſecans
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complementi arcus circa rectum angulum dati ad aliud, producetur ſe-
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cans complementi anguli quæſiti, qui dicto arcui opponitur. </
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<
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tis duobus arcubus tertium inueniemus, vt in problemate propoſ. </
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<
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in problemate propoſ. </
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<
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opponitur, & </
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<
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">hoc arcu inuento, reperiemus reliquum angulum huic inuen
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to arcui oppoſitum, vt dictum eſt in hoc problemate, vel certe, vt in pro-
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blemate 1. </
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<
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, acutus ſit, an obtuſus, docebit arcus
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, circa an-
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gulum rectum datus, vt in problemate 1. </
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ius arcus ſint omnes quadrante minores: </
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tus ad ſinum complementi vtriuſlibet arcuum cir
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ca rectum angulum eandem proportionem ha-
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bet, quam ſecans anguli huic arcui oppoſiti ad ſe-
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cantem complementi reliqui anguli non recti.</
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cus quadrante minores. </
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cus BC, vt eſt ſecans anguli non recti A, ad ſecantem complementi anguli
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C. </
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cti, & </
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tes, & </
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C, vt ex demõſtratis in propoſ. </
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ſcholij 40.
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huius.</
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CI, ſe in C, interſecant, ductiq́; </
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ctis F, I, arcus CI, ad arcum CG, arcus perpen-
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diculares FE, IG; </
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tis CI, ad ſecantem complementi arcus FE, hoc
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eſt, ad ſecantem arcus DE, anguli A, ita ſinus
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arcus CF, qui complementum eſt arcus BC, ad ſecantem complementi arcus
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GI, anguli C: </
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<
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">Et permutando, vt ſinus totus ad ſinum complementi arcus
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BC, ita ſecans anguli A, ad ſecantem complementi anguli C. </
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ſtendemus, ſi aliter conſtruatur figura, ita eſſe ſinum totum ad ſinum comple
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menti arcus AB, vt eſt ſecans anguli C, ad ſecantem complementi anguli A.
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dum erat.</
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