Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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gulus D, rectus ſit; </
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xml:space
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arcus AC, ad ſinum anguli ADC: </
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<
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xml:space
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">& </
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<
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xml:space
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">permutando, vt ſinus arcus AD, ad ſi-
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num arcus AC, ita ſinus anguli ACD, ad ſinum anguli ADC, hoc eſt, ad
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ſinum anguli ADB, cum anguli ad D, ſint recti. </
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<
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<
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turbata proportione, erit, vt ſinus arcus AB, ad ſinum arcus AC, ita ſinus an-
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guli ACD, ad ſinum anguli B; </
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<
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<
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xml:space
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<
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mutando erit, vt ſinus arcus AB, in triangulo ABC, ad ſinum anguli ACB,
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in eodem triangulo ABC, ita ſinus arcus AC, eiuſdem
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trianguli ABC, ad ſinum anguli B, in eodem triangulo ABC.</
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arcus # anguli
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AB. # ACD.
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AD. # ADB.
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AC. # B.
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<
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<
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ductus in arcum BC, productum ad E, eritq́; </
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<
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note
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ctus. </
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<
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xml:space
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">Quoniam igitur in triangulo ABE, angulus E, rectus
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eſt; </
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<
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">erit, vt demonſtratum eſt, vt ſinus arcus AB, ad ſinum
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anguli E, ita ſinus arcus AE, ad ſinum anguli B: </
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<
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xml:space
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<
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xml:space
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tando, vt ſinus arcus AB, ad ſinum arcus AE, ita ſinus anguli E, ad ſinum
<
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anguli B. </
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<
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xml:space
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">Sed eadem ratione, cum in triangulo ACE, angulus E, rectus ſit,
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eſt, vt ſinus arcus AE, ad ſinum anguli ACE, ita ſinus arcus AC, ad ſi-
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num anguli E: </
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<
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<
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xml:space
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">permutando, vt ſinus arcus AE, ad ſinum arcus AC, ita
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ſinus anguli ACE, ad ſinum anguli E. </
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<
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proportione, erit vt ſinus arcus AB, ad ſinum arcus AC,
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ita ſinus anguli ACE, hoc eſt, anguli ACB, (cum idem ſit
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arcus # anguli
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AB. # ACE.
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AE. # E.
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AC. # B.
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</
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ſinus vtriuſq; </
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">anguli ad C, quòd eorum arcus ſemicirculum
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conſtituant, vt conſtat ex coroll. </
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<
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tus. </
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diximus, duos arcus ſemicirculum conficientes, eundem ha-
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bere ſinum.) </
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<
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paret. </
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<
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">permutando erit, vt ſinus arcus AB, in triangulo ABC,
<
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ad ſinum anguli ACB, eiuſdem trianguli ABC, ita ſinus arcus AC, in
<
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eodem triangulo ABC, ad ſinum anguli B, eiuſdem trianguli ABC. </
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<
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ſi ex B, ad arcum AC, ducatur alius arcus perpendicularis, qui vel intra trian
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gulum cadet, vel in arcum productum, oſtendemus eodem modo, ita eſſe ſinũ
<
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arcus AB, ad ſinum anguli ACB, vt eſt ſinus arcus BC, ad ſinum anguli
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BAC. </
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<
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">Itaque in omni triangulo ſphærico, ſinus cuiuſlibet arcus, &</
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erat oſtendendum.</
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<
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">HINC perſpicuum eſt, in omni triangulo ſphærico rectangulo, vt eſt ſinus arcus rectum
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angulum ſubtendentis ad ſinum totum, nempe ad ſinum anguli recti, quem ſubtendit, ita
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eſſe ſinum cuiuſ@@bet reliquorum arcuum ad ſinum anguli, quem ſubtendit. </
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<
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</
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ftra propoſitione 41. </
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vniuerſalem reddere, prout nimirum complectitur & </
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<
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& </
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<
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<
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corum triangulorum rectangulorum calculus perficitur, quæq́; </
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<
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bus eliciuntur, Quanquam autem nonnunquam in problemate aliquo plura </
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