Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ad ſinum complementi arcus recto angulo oppo-
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ſiti eandem proportionem habet, quam tangens
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vtriusvis angulorum non rectorum ad tangentem
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complementi reliqui anguli.</
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<
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">IN triangulo ABC, cuius omnes arcus quadrante minores, ſit angulus
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B, rectus. </
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<
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">Dico, ita eſſe ſinum totum ad ſinum complementi arcus AC, vt
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eſt tangens anguli C, ad tangentem complementi anguli A. </
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<
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ctione, vt in propoſ. </
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<
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">arcu CE, ad G, vt CG, ſit quadrans,
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deſcribatur ex polo C, ad interual lum quadran
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tis CG, arcus circuli maximi GH, ſecans ar-
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cus CF, EF, productos in I, H: </
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drans quoque; </
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">cum circulus GH, à polo C, ab-
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1. Theod.
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25. huius.</
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ſit quadrante. </
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">Arcus item GH, EH, quadran-
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tes erunt, propter rectos angulos G, E. </
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<
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angulus E, rectus, vt propoſ. </
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<
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</
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<
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">at G, rectus eſt, propterea quòd circulus CG,
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ad circulum GH, rectus eſt. </
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cus eſt anguli C; </
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">Quoniam igitur duo cir-
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culi maximi CG, CI, in ſphæra ſe interſecant in C, ductiq́; </
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punctis F, I, ad arcum CG, arcus perpendiculares FE, IG; </
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">Theor. 6.
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ſcholij 40.
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huius.</
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tus quadrantis CG, ad tangentem arcus IG, hoc eſt, anguli C, ita ſinus ar-
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cus CE, hoc eſt, complementiarcus AC, ad tangentem arcus FE, hoc eſt,
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complementi anguli A: </
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<
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mentiarcus AC, recto angulo oppoſiti, ita tangens anguli C, ad tangentem
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complementi anguli A. </
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<
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">Similimodo, aliter conſtructa figura, demonſtrabi-
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mus, ita eſſe ſinum totum ad ſinum complementi arcus AC vt eſt tangens
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anguli A, ad tangentem complementi anguli C. </
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ſphærico rectangulo, &</
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<
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">IN triangulo ſphærico rectangulo, dato arcu, qui recto angulo
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opponitur, cum alterutro angulorum non rectorum, inuenire alte-
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rum angulum non rectum, & </
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<
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">IN triangulo
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, cuius angulus C, rectus, datus
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ſit arcus
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, cum angulo
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. </
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<
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angulum
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, & </
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<
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. </
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ſinus totus ad ſinum complementi arcus
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, ita tangens
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anguli
<
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, ad tangentem complementi anguli
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:</
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<
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<
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arcus recto angulo oppoſiti, & </
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anguli dati ad aliud, reperietur tangens </
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