Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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361 - 372
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arcuum quadrans. </
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<
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xml:space
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plementi arcus v. </
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<
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">AB, vt eſt, ſinus complementi reliqui arcus BC, ad ſi-
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num totum. </
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<
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ponitur quadrans, nullus reliquorum angu-
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lorum erit rectus. </
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<
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xml:space
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duos angulos habens rectos haberet duos ar-
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huius.</
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cus quadrantes. </
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<
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<
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primum angulus A, acutus, & </
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<
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& </
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<
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</
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<
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xml:space
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adeo omnes arcus trianguli ABC, quadran-
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te minores. </
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<
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xml:space
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fiant quadrantes AD, AE; </
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<
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">ac per puncta D,
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E, arcus DE, circuli maximi ducatur DE,
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conueniens cum arcu BC, producto in F. </
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ergo vterque angulus D, E, rectus, ob quadrantes AD, AE; </
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<
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& </
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<
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">angulus B, ponatur rectus, erit vterq; </
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<
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">arcus BF, DF, quadrans, ob rectos
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angulos B, D. </
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<
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<
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">propterea quòd F, polus eſt
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<
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">26. huius.</
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arcus BD, ob quadrantes BF, DF. </
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<
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</
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">& </
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<
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">BD, CE, complementa arcuum AB, AC, ob quadrantes BF, AD, AE. </
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Manifeſtum autem eſt in triangulo CEF, ita eſſe ſinum arcus CE, hoc eſt, ſi-
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">41. huius.</
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num complementi arcus AC, ad ſinum anguli F, hoc eſt, ad ſinum arcus BD,
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ſeu complementi arcus AB, vt eſt ſinus arcus CF, hoc eſt, ſinus complemen
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ti arcus BC, ad ſinum anguli recti E, id eſt, ad ſinum totum. </
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poſitum.</
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</
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<
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<
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<
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quoque arcu AB, fiat quadrans AE, & </
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<
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">20. 1 Theod.</
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circuli maximi ſecans arcum AC, in F. </
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<
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">Et quia duo anguli DAB, DBA,
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recti ſunt, erunt arcus AD, BD, quadrantes; </
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huius.</
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ſit quadrans, & </
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<
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arcus DE, quadrans; </
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<
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">26. huius.</
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drantes BD, ED, erit arcus anguli BDE,
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hoc eſt, anguli CDF, qui illi ad verticem eſt
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<
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æqualis. </
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<
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<
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ED, erit & </
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<
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">arcus AF, quadrans, cum arcus
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<
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">Coroll. 16.</
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EF, quadrante ſemper abſit à ſuo polo; </
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non & </
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<
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<
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<
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ctus. </
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<
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tum arcus AC; </
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<
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">& </
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<
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">arcus BE, complementum
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arcus AB; </
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<
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<
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">arcus CD, complementum ar-
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cus BC, ob quadrantes AF, AE, BD. </
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<
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ſpicuum autem eſt in triãgulo CDF, ita eſſe
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ſinum arcus CF, hoc eſt, ſinum complementi
<
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<
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xlink:label
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">41. huius.</
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arcus AC, ad ſinum anguli CDF, hoc eſt, ad ſinum arcus BE, ſiue comple-
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menti arcus AB, vt eſt ſinus arcus CD, nempe ſinus complementi arcus BC,
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ad ſinum anguli recti F, hoc eſt, ad ſinum totum. </
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<
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<
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