Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ctum, ita ſecans arcus angulo recto oppoſiti ad aliud, produceturq́; </
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<
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tij arcus, qui quæritur, &</
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<
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<
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arcus eirca
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angulũ re-
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ctum. Dein
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de alter an
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gulus non
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rectus, & at
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cus recto
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angulo op-
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poſitus.</
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<
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">9. DATO alterutro arcuum in triangulo re-
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ctangulo circa angulum rectum, cum angu-
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lo non recto ei adiacente, ſcrutari alterum
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arcum circa angulum rectum, & alium angu
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lum non rectum, cum arcu rectum angulum
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ſubtendente.</
head
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<
s
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">FIAT, vt ſinus totus ad ſinum dati arcus, ita tangẽs dati anguli ad aliud,
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xml:space
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">Probl. 1. pro
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poſ. 44. tri-
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ang. ſphær.</
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produceturq́; </
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<
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">tangens arcus quæſiti. </
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">Qui arcus min or quadrante erit, ſi datus
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angulus ei oppoſitus fuerit acutus; </
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<
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">maior autem, ſi obtuſus.</
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<
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<
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">EX eodem porrò arcu circa angulum rectum dato, & </
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<
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">angulo adiacente,
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reperietur & </
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<
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">alter angulus non rectus, & </
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<
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">arcus recto angulo oppoſitus, vt ſu-
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pra in 5. </
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<
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arcus circa
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angulũ re-
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ctum. Dein
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de alter an
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gulus non
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rectus, & ar
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cus recto
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angulo op-
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poſitus.</
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<
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">10. DATO alterutro arcuum in triangulo re-
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ctangulo circa angulum rectum, cum angu-
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lo ei oppoſito, indagare alterum arcum circa
<
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rectum angulum, & alium angulum non re-
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ctum, cum arcu rectum angulum ſubtenden
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te: ſi modo conſtet, an reliquus arcus circa
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angulum rectum quęſitus quadrante minor
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ſit, aut maior; vel an alter angulus non rectus
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ſit acutus, obtuſusve; vel denique num arcus
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angulo recto oppoſitus ſit minor quadran-
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te, aut maior.</
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<
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">FIAT, vt tangens anguli dati ad tangentem dati arcus, ita ſinus totus ad
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<
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xlink:label
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="
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xml:space
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">Probl. 1. pro
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poſ. 44. tri-
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ang. ſphær.</
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aliud, reperieturq́; </
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<
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">ſinus arcus quæſiti: </
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">qui ex inuento ſinu non cognoſcetur,
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niſi cõſtet, num quadrante minor ſit, aut maior; </
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<
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">vel an alter angulus non re-
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ctus ſit acutus, obtuſusve; </
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<
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">vel denique, an arcus recto angulo oppoſitus ſit
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minor quadrante, aut maior. </
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<
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">Nam ſi alter angulus fuerit acutus, erit quæſi-
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tus arcus ei oppoſitus, quadrante minor; </
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arcus recto angulo oppoſitus fuerit minor quadrante, ſi quidem & </
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<
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cus ſit quadrante minor, erit quæſitus arcus minor quoque quadrante; </
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quadrãte maior, maior quoque: </
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