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

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            <s xml:id="echoid-s17883" xml:space="preserve">
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            ſitus, & </s>
            <s xml:id="echoid-s17884" xml:space="preserve">non datus, fuerit quadrante minor; </s>
            <s xml:id="echoid-s17885" xml:space="preserve">ſi quidem angulus datus ſit acu-
              <lb/>
            tus, erit quæſitus quoque angulus acutus; </s>
            <s xml:id="echoid-s17886" xml:space="preserve">ſi vero obtuſus, obtuſus: </s>
            <s xml:id="echoid-s17887" xml:space="preserve">At ſi ar-
              <lb/>
            cus angulo recto oppoſitus fuerit maior quadrante; </s>
            <s xml:id="echoid-s17888" xml:space="preserve">ſi quidem datus angulus
              <lb/>
            ſit acutus, erit quæſitus angulus obtuſus; </s>
            <s xml:id="echoid-s17889" xml:space="preserve">ſi vero obtuſus, acutus.</s>
            <s xml:id="echoid-s17890" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17891" xml:space="preserve">EX vtroque porro angulo non recto, quorum vnus datus eſt, & </s>
            <s xml:id="echoid-s17892" xml:space="preserve">alter in-
              <lb/>
            uentus, inuenientur reliqui duo arcus, vt in problemate 4. </s>
            <s xml:id="echoid-s17893" xml:space="preserve">traditum eſt.</s>
            <s xml:id="echoid-s17894" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1462" type="section" level="1" n="651">
          <head xml:id="echoid-head686" xml:space="preserve">Aliter.</head>
          <p>
            <s xml:id="echoid-s17895" xml:space="preserve">FIAT, vt ſinus totus ad ſinum complementi arcus dati, ita ſecans dati
              <lb/>
              <note position="right" xlink:label="note-507-01" xlink:href="note-507-01a" xml:space="preserve">Probl. pro-
                <lb/>
              poſ. 56. tri-
                <lb/>
              ang. ſphær.</note>
            anguliad aliud, reperieturq́; </s>
            <s xml:id="echoid-s17896" xml:space="preserve">ſecans complementi alterius anguli non recti,
              <lb/>
            qui quæritur. </s>
            <s xml:id="echoid-s17897" xml:space="preserve">Reliqua in uenientur, vt ſupra dictum eſt.</s>
            <s xml:id="echoid-s17898" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quæritur
            <lb/>
          arcus recto
            <lb/>
          angulo op-
            <lb/>
          poſitus. De-
            <lb/>
          inde duo
            <lb/>
          anguli non
            <lb/>
          recti.</note>
        </div>
        <div xml:id="echoid-div1464" type="section" level="1" n="652">
          <head xml:id="echoid-head687" xml:space="preserve">7. DATIS duobus arcubus in triangulo re-
            <lb/>
          ctangulo circa angulum rectum, reperire ter
            <lb/>
          tium arcum angulo recto oppoſitũ, & duos
            <lb/>
          angulos non rectos.</head>
          <p>
            <s xml:id="echoid-s17899" xml:space="preserve">FIAT, vt ſinus totus ad ſinũ complementi vtriuſlibet arcuum datorum,
              <lb/>
              <note position="right" xlink:label="note-507-03" xlink:href="note-507-03a" xml:space="preserve">Probl. pro-
                <lb/>
              poſ. 43. tri-
                <lb/>
              ang. ſphær.</note>
            ita ſinus complementi alterius arcus dati ad aliud, produceturq́; </s>
            <s xml:id="echoid-s17900" xml:space="preserve">ſinus com-
              <lb/>
            plementi arcus recto angulo oppoſiti. </s>
            <s xml:id="echoid-s17901" xml:space="preserve">Hic autem arcus quadrante erit mi-
              <lb/>
            nor, ſi vterque arcus circa rectum angulum datus fuerit minor, aut maior qua
              <lb/>
            drante; </s>
            <s xml:id="echoid-s17902" xml:space="preserve">quadrante vero maior, ſi vnus datorum arcuum fuerit quadrante mi-
              <lb/>
            nor, & </s>
            <s xml:id="echoid-s17903" xml:space="preserve">alter maior.</s>
            <s xml:id="echoid-s17904" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17905" xml:space="preserve">EX arcu autem rectum angulum ſubtẽdente inuento, & </s>
            <s xml:id="echoid-s17906" xml:space="preserve">alterutro arcuum
              <lb/>
            circa angulum rectum datorum, inuenietur angulus ei oppoſitus, vt in pro-
              <lb/>
            blemate 1. </s>
            <s xml:id="echoid-s17907" xml:space="preserve">diximus.</s>
            <s xml:id="echoid-s17908" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quæritur
            <lb/>
          arcus circa
            <lb/>
          angulũ re-
            <lb/>
          ctum. Dein
            <lb/>
          de duo an-
            <lb/>
          guli non re
            <lb/>
          cti.</note>
        </div>
        <div xml:id="echoid-div1466" type="section" level="1" n="653">
          <head xml:id="echoid-head688" xml:space="preserve">8. DATO arcu in triangulo rectangulo, qui
            <lb/>
          recto angulo opponitur, cum alterutro ar
            <lb/>
          cuum circa angulũ rectum, inquirere alium
            <lb/>
          arcum circa rectum angulum, & duos angu-
            <lb/>
          los non rectos.</head>
          <p>
            <s xml:id="echoid-s17909" xml:space="preserve">FIAT, vt ſinus complementi arcus dati circa angulum rectum ad ſinum
              <lb/>
              <note position="right" xlink:label="note-507-05" xlink:href="note-507-05a" xml:space="preserve">Probl. pro-
                <lb/>
              poſ. 43. tri-
                <lb/>
              ang. ſphær.</note>
            complementi arcus recto angulo oppoſiti, ita ſinus totus ad aliud, gigneturq́;
              <lb/>
            </s>
            <s xml:id="echoid-s17910" xml:space="preserve">ſinus complementi alterius arcus circa rectum angulum, qui quæritur. </s>
            <s xml:id="echoid-s17911" xml:space="preserve">Hic au
              <lb/>
            tem arcus erit quadrante minor, ſi vterque arcus datus minor quadrante fue-
              <lb/>
            rit, aut maior; </s>
            <s xml:id="echoid-s17912" xml:space="preserve">maior vero, ſi alter datorum arcuum fuerit quadrante minor,
              <lb/>
            & </s>
            <s xml:id="echoid-s17913" xml:space="preserve">alter maior.</s>
            <s xml:id="echoid-s17914" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17915" xml:space="preserve">INVENTO autem arcu rectum angulum ſubtendente, reperientur an-
              <lb/>
            guli, vt in præcedenti problemate dictum eſt.</s>
            <s xml:id="echoid-s17916" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1468" type="section" level="1" n="654">
          <head xml:id="echoid-head689" xml:space="preserve">Aliter.</head>
          <note position="right" xml:space="preserve">Probl. pro-
            <lb/>
          poſ. 53. tri-
            <lb/>
          ang. ſphær.</note>
          <p>
            <s xml:id="echoid-s17917" xml:space="preserve">FIAT, vt ſinus totus ad ſinum complementi dati arcus circa angulum </s>
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