Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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duo circuli maximi EH, GH, ſe mutuo ſecant in H, & </
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<
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xml:space
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">ex punctis E, F, arcus
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EH, ad arcum GH, ducti ſunt arcus perpendiculares EG, FI; </
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<
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">erit, vt ſinus
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totus quadrantis EH, ad ſecantẽ complementi
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ſcholij 40.
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huius.</
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arcus FI, hoc eſt, ad ſecãtem arcus CF, qui com
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plementum etiam eſt arcus BC, ita ſinus arcus
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FH, hoc eſt, arcus DE, (eſt enim arcus FH, ar-
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cui DE, æqualis, ob quadrantes EH, DF, æqua
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les) qui arcus eſt anguli A, ad ſecantem comple-
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menti arcus EG, id eſt, ad ſecantem arcus EC,
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qui complementum quoque eſt arcus AC: </
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<
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xml:space
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">Et
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permutãdo, vt ſinus totus ad ſinum arcus DE,
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hoc eſt, anguli A, ita ſecans complementi arcus BC, ad ſecantem comple-
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menti arcus AC. </
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<
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">Non ſecus oſtendemus, ſi aliter figura conſtruatur, ita
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eſſe ſinum totum ad ſinum anguli C, vt eſt ſecans complementi arcus AB, ad
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ſecantem complementi arcus AC. </
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<
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xml:space
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">In omni igitur triangulo ſphærico rectan-
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gulo, &</
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<
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nimus in problemate. </
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<
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<
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xml:space
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">IN triangulo ſphęrico rectangulo, dato vtrolibet angulorum non
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rectorum, cum arcu oppoſito, inueſtigare arcum recto angulo op-
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poſitum, vnà cum tertio arcu, & </
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do conſtet, num arcus angulo recto oppoſitus ſit maior quadrante,
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minorve: </
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<
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">aut an alter angulus non rectus ſit acutus, obtuſusve.</
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<
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xml:space
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">IN triangulo ABC, rectum habente angulum C, datus ſit angulus
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, cum ar-
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cu
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. </
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<
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BC, & </
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<
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ſinum anguli B, dati, ita ſecans complementi arcus da-
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ti
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, ad ſecantem complementiarcus
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:</
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<
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ita ſecans complementi dati arcus ad aliud, pro-
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ducetur ſecans complementi arcus recto angulo
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oppoſiti, qui inquiritur. </
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AC, cognitis notus fiet tertius arcus BC, ex problemate propoſ. </
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te 1. </
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<
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, ſit quadrante ma-
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ior, an minor: </
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, ſit acutus, obtuſus ve, alioquin
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neſciremus, qualis arcus pro
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, aſſumendus ſit, cum poßit eße maior quadrante, vel
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minor, vt perſpicuum eſt. </
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copernici, atque Ioan Regiom. </
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