Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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          <p>
            <s xml:id="echoid-s17917" xml:space="preserve">
              <pb o="496" file="508" n="508" rhead=""/>
            ctum, ita ſecans arcus angulo recto oppoſiti ad aliud, produceturq́; </s>
            <s xml:id="echoid-s17918" xml:space="preserve">ſecans ter
              <lb/>
            tij arcus, qui quæritur, &</s>
            <s xml:id="echoid-s17919" xml:space="preserve">c.</s>
            <s xml:id="echoid-s17920" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quæritur
            <lb/>
          arcus eirca
            <lb/>
          angulũ re-
            <lb/>
          ctum. Dein
            <lb/>
          de alter an
            <lb/>
          gulus non
            <lb/>
          rectus, & at
            <lb/>
          cus recto
            <lb/>
          angulo op-
            <lb/>
          poſitus.</note>
        </div>
        <div xml:id="echoid-div1469" type="section" level="1" n="655">
          <head xml:id="echoid-head690" xml:space="preserve">9. DATO alterutro arcuum in triangulo re-
            <lb/>
          ctangulo circa angulum rectum, cum angu-
            <lb/>
          lo non recto ei adiacente, ſcrutari alterum
            <lb/>
          arcum circa angulum rectum, & alium angu
            <lb/>
          lum non rectum, cum arcu rectum angulum
            <lb/>
          ſubtendente.</head>
          <p>
            <s xml:id="echoid-s17921" xml:space="preserve">FIAT, vt ſinus totus ad ſinum dati arcus, ita tangẽs dati anguli ad aliud,
              <lb/>
              <note position="left" xlink:label="note-508-02" xlink:href="note-508-02a" xml:space="preserve">Probl. 1. pro
                <lb/>
              poſ. 44. tri-
                <lb/>
              ang. ſphær.</note>
            produceturq́; </s>
            <s xml:id="echoid-s17922" xml:space="preserve">tangens arcus quæſiti. </s>
            <s xml:id="echoid-s17923" xml:space="preserve">Qui arcus min or quadrante erit, ſi datus
              <lb/>
            angulus ei oppoſitus fuerit acutus; </s>
            <s xml:id="echoid-s17924" xml:space="preserve">maior autem, ſi obtuſus.</s>
            <s xml:id="echoid-s17925" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17926" xml:space="preserve">EX eodem porrò arcu circa angulum rectum dato, & </s>
            <s xml:id="echoid-s17927" xml:space="preserve">angulo adiacente,
              <lb/>
            reperietur & </s>
            <s xml:id="echoid-s17928" xml:space="preserve">alter angulus non rectus, & </s>
            <s xml:id="echoid-s17929" xml:space="preserve">arcus recto angulo oppoſitus, vt ſu-
              <lb/>
            pra in 5. </s>
            <s xml:id="echoid-s17930" xml:space="preserve">problemate docuimus.</s>
            <s xml:id="echoid-s17931" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quæritur
            <lb/>
          arcus circa
            <lb/>
          angulũ re-
            <lb/>
          ctum. Dein
            <lb/>
          de alter an
            <lb/>
          gulus non
            <lb/>
          rectus, & ar
            <lb/>
          cus recto
            <lb/>
          angulo op-
            <lb/>
          poſitus.</note>
        </div>
        <div xml:id="echoid-div1471" type="section" level="1" n="656">
          <head xml:id="echoid-head691" xml:space="preserve">10. DATO alterutro arcuum in triangulo re-
            <lb/>
          ctangulo circa angulum rectum, cum angu-
            <lb/>
          lo ei oppoſito, indagare alterum arcum circa
            <lb/>
          rectum angulum, & alium angulum non re-
            <lb/>
          ctum, cum arcu rectum angulum ſubtenden
            <lb/>
          te: ſi modo conſtet, an reliquus arcus circa
            <lb/>
          angulum rectum quęſitus quadrante minor
            <lb/>
          ſit, aut maior; vel an alter angulus non rectus
            <lb/>
          ſit acutus, obtuſusve; vel denique num arcus
            <lb/>
          angulo recto oppoſitus ſit minor quadran-
            <lb/>
          te, aut maior.</head>
          <p>
            <s xml:id="echoid-s17932" xml:space="preserve">FIAT, vt tangens anguli dati ad tangentem dati arcus, ita ſinus totus ad
              <lb/>
              <note position="left" xlink:label="note-508-04" xlink:href="note-508-04a" xml:space="preserve">Probl. 1. pro
                <lb/>
              poſ. 44. tri-
                <lb/>
              ang. ſphær.</note>
            aliud, reperieturq́; </s>
            <s xml:id="echoid-s17933" xml:space="preserve">ſinus arcus quæſiti: </s>
            <s xml:id="echoid-s17934" xml:space="preserve">qui ex inuento ſinu non cognoſcetur,
              <lb/>
            niſi cõſtet, num quadrante minor ſit, aut maior; </s>
            <s xml:id="echoid-s17935" xml:space="preserve">vel an alter angulus non re-
              <lb/>
            ctus ſit acutus, obtuſusve; </s>
            <s xml:id="echoid-s17936" xml:space="preserve">vel denique, an arcus recto angulo oppoſitus ſit
              <lb/>
            minor quadrante, aut maior. </s>
            <s xml:id="echoid-s17937" xml:space="preserve">Nam ſi alter angulus fuerit acutus, erit quæſi-
              <lb/>
            tus arcus ei oppoſitus, quadrante minor; </s>
            <s xml:id="echoid-s17938" xml:space="preserve">ſi vero obtuſus, maior. </s>
            <s xml:id="echoid-s17939" xml:space="preserve">Sic etiam, ſi
              <lb/>
            arcus recto angulo oppoſitus fuerit minor quadrante, ſi quidem & </s>
            <s xml:id="echoid-s17940" xml:space="preserve">datus ar-
              <lb/>
            cus ſit quadrante minor, erit quæſitus arcus minor quoque quadrante; </s>
            <s xml:id="echoid-s17941" xml:space="preserve">ſi vero
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            quadrãte maior, maior quoque: </s>
            <s xml:id="echoid-s17942" xml:space="preserve">At ſi arcus recto angulo oppoſitus fuerit </s>
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