Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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complementi arcus AB, ad tangentem complementi arcus AC. </
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conſtructione, vt in pręcedẽti propoſ. </
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BF, DF, ſe mutuo ſecãt in F, productiq́; </
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ex pũctis B, C, arcus BF, ad arcum DF, arcus
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perpendiculares BD, CE; </
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<
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quadrantis DF, ad rangentem arcus BD, ita
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ſinus arcus EF, ad tangentem arcus CE: </
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ſcholij 40.
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huius.</
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permutando, vt ſinus totus ad ſinũ arcus EF,
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hoc eſt, ad ſinum complementi anguli A, ita
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tangens arcus BD, hoc eſt, ita tangens com-
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plementi arcus AB, ad tangentem arcus CE,
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hoc eſt, ad tangentẽ complementi arcus AC.
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<
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tum ad ſinum complementi anguli C, vt eſt
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tangens complementi arcus BC, ad tangentem complementi arcus AC, ſi ni-
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mirum arcus CB, CA, angulum C, continentes producantur, &</
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igitur triangulo ſphærico rectangulo, &</
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antecedentis propoſ. </
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<
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">demonſtratum quoque ſit, facilius tamen hic abſoluitur, cùm in
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aurea regula primum locum ſortiatur ſinus totus.</
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<
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">IN triangulo ſphærico rectangulo, dato alterutto arcuum cir-
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ca angulum rectum, cum angulo non recto adiacente, inuenire ar-
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cum recto angulo oppoſitum, vnà cum reliquo arcu circa angulum
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rectum, & </
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BC, cuius angulus C, rectus, datus
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ſit arcus AC, cum angulo A, ſibi adiacente. </
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quoque arcum
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, vnà cum arcu
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, & </
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Nam cum ſit, vt ſinus totus ad ſinum complementi angu-
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li A, ita tangens complementi arcus
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, ad tangentem
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complementi arcus
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:</
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ti anguli dati, ita tangens complementi arcus da-
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ti ad aliud, producetur tangens complementi ar-
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cus recto angulo oppoſiti, qui quæritur. </
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blemate 1. </
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RCVM autem
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, quæſitum eße quadrante minorem, maioremve, cognoſce-
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mus, vt in dicto problemate 1. </
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omnes arcus quadrante ſint minores: </
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