Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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æquales erunt, vt in vltima figura præcedentis propoſ. </
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de vterque angulus ad A, datus erit, cum dimidium ſit an-
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guli BAC, dati. </
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gulum habente rectum D, datus eſt arcus AB, recto angu-
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lo oppoſitus, cum angulo BAD, nimirum cum dimidio
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">Schol. 41.
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huius.</
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datianguli BAC; </
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<
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BAD, oppoſitus: </
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<
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">qui duplicatus totum arcum BC, quæ-
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ſitum reddet notum. </
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<
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xml:space
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">Rurſus quia in eodem triangulo ABD,
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vel 45. huiꝰ.</
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rectum habente angulum D, datus eſt arcus AB, angulo
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recto opppoſitus, cum arcu BD, circa angulum rectum:
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<
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huius.</
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poſitus, & </
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</
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">VEL denique, quia datus eſt arcus BD, circa re-
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vel 42. huiꝰ.</
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ctum angulum, vnà cum angulo non recto BAD, qui
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dato arcui BD, opponitur, conſtatq́; </
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<
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reliqui anguli non recti B. </
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te minor, erit angulus B, acutus, ſicut & </
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eſt: </
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lus B, obtuſus, quandoquidem BAD, acutus eſt;
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<
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gulus C, illi æqualis.</
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<
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ſolos ſinus,
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quádo dati
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duo arcus
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ſunt æqua-
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les.</
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poſ. </
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dabit. </
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gulum B; </
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<
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angulo ab ipſis comprehenſo; </
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mus. </
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tione ſecunda huius problemat is, quam theoremate eiuſdem propoſ. </
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nus fieret laborioſa. </
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<
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">Nam cum ſit, vt quadratum ſinus totius ad rectangulum ſub ſi-
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nubus datorum arcuum inæqualium contentum, ita ſinus verſus anguli dati à dictis
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arcubus comprehenſi ad differentiam inter ſinum verſum arcus dato angulo oppoſiti,
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& </
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hoc theoremate propoſ. </
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ſinus verſus dati anguli multiplicandus eſſet per dictum rectangulum. </
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praxi multo breuior fit muliiplicatio, vt patet, quamuis bis regulam auream adhi-
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beamus.</
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