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

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          <p>
            <s xml:id="echoid-s17856" xml:space="preserve">FIAT, vt ſinus anguli dati quæſito arcui adiacentis ad ſinum totum, ita
              <lb/>
              <note position="left" xlink:label="note-506-01" xlink:href="note-506-01a" xml:space="preserve">Probl. 1. pro
                <lb/>
              poſ. 42. tri-
                <lb/>
              ang. ſphær.</note>
            ſinus complementi alterius anguli dati ad aliud, produceturq́; </s>
            <s xml:id="echoid-s17857" xml:space="preserve">ſinus comple-
              <lb/>
            menti arcus huic poſteriori angulo oppoſiti. </s>
            <s xml:id="echoid-s17858" xml:space="preserve">Erit autem vterlibet arcus inuen
              <lb/>
            tus quadrante minor, ſi datus angulus ei oppoſitus fuerit acutus; </s>
            <s xml:id="echoid-s17859" xml:space="preserve">maior vero,
              <lb/>
            ſi obtuſus.</s>
            <s xml:id="echoid-s17860" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17861" xml:space="preserve">IAM inuento vtroque arcu circa angulum rectum, inuenietur, per pro-
              <lb/>
            blema 3. </s>
            <s xml:id="echoid-s17862" xml:space="preserve">ex vtrolibet illorum, & </s>
            <s xml:id="echoid-s17863" xml:space="preserve">angulo ei oppoſito dato, arcus quoque recto
              <lb/>
            angulo oppoſitus.</s>
            <s xml:id="echoid-s17864" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1456" type="section" level="1" n="648">
          <head xml:id="echoid-head683" xml:space="preserve">Aliter.</head>
          <p>
            <s xml:id="echoid-s17865" xml:space="preserve">FIAT, vt ſinus totus ad ſinum anguli non recti quæſito arcui adiacen-
              <lb/>
              <note position="left" xlink:label="note-506-02" xlink:href="note-506-02a" xml:space="preserve">Probl. pro-
                <lb/>
              poſ 52. tri
                <lb/>
              ang. ſphær.</note>
            tis, ita ſecans alterius anguli non recti ad aliud, reperieturq́; </s>
            <s xml:id="echoid-s17866" xml:space="preserve">ſecans arcus huic
              <lb/>
            poſteriori angulo oppoſiti, qui quæritur.</s>
            <s xml:id="echoid-s17867" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quæritur
            <lb/>
          angulus nõ
            <lb/>
          rectus, Dein
            <lb/>
          de alij duo
            <lb/>
          arcus.</note>
        </div>
        <div xml:id="echoid-div1458" type="section" level="1" n="649">
          <head xml:id="echoid-head684" xml:space="preserve">5. DATO alterutro arcuum in triangulo re-
            <lb/>
          ctangulo circa angulum rectum, cum angu-
            <lb/>
          lo ei adiacente, inueſtigare alium angulum
            <lb/>
          eidẽ arcui oppoſitũ, & reliquos duos arcus.</head>
          <p>
            <s xml:id="echoid-s17868" xml:space="preserve">FIAT, vt ſinus totus ad ſinum anguli dati, ita ſinus complementi arcus
              <lb/>
              <note position="left" xlink:label="note-506-04" xlink:href="note-506-04a" xml:space="preserve">Probl 2 pro
                <lb/>
              poſ. 42. tri-
                <lb/>
              ang ſphær.</note>
            dati ad aliud, procreabiturq́; </s>
            <s xml:id="echoid-s17869" xml:space="preserve">ſinus complementi alterius anguli, quem quæri-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s17870" xml:space="preserve">Hic autem angulus erit acutus, ſi datus arcus ſuerit quadrante minor;
              <lb/>
            </s>
            <s xml:id="echoid-s17871" xml:space="preserve">obtuſus vero, ſi maior.</s>
            <s xml:id="echoid-s17872" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17873" xml:space="preserve">EX vtroque autem angulo non recto, quorum vnus datus eſt, & </s>
            <s xml:id="echoid-s17874" xml:space="preserve">alter in-
              <lb/>
            uentus, reperientur reliqui duo arcus, vt in præcedenti problemate dictũ eſt.</s>
            <s xml:id="echoid-s17875" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quæritur
            <lb/>
          angulus nõ
            <lb/>
          rectus. Dein
            <lb/>
          de alij duo
            <lb/>
          arcus.</note>
        </div>
        <div xml:id="echoid-div1460" type="section" level="1" n="650">
          <head xml:id="echoid-head685" xml:space="preserve">6. DATO alterutro arcuum in triangulo re-
            <lb/>
          ctangulo circa angulum rectum, cum angu-
            <lb/>
          lo ei oppoſito, in ueſtigare alium angulum
            <lb/>
          non rectum eidem arcui adiacentem, & reli-
            <lb/>
          quos duos arcus: ſi modo conſtet, num alius
            <lb/>
          ille angulus non rectus quæſitus ſit acutus,
            <lb/>
          obtuſusve; vel an alteruter arcuum quæſito-
            <lb/>
          rum quadrante minor ſit, vel maior.</head>
          <p>
            <s xml:id="echoid-s17876" xml:space="preserve">FIAT, vt ſinus complementi arcus dati ad ſinum complementi anguli da
              <lb/>
              <note position="left" xlink:label="note-506-06" xlink:href="note-506-06a" xml:space="preserve">Probl 2. pro
                <lb/>
              poſ. 42. tri-
                <lb/>
              ang. ſphær.</note>
            ti, ita ſinus totus ad aliud, reperieturq́; </s>
            <s xml:id="echoid-s17877" xml:space="preserve">ſinus alterius anguli non recti quæſi-
              <lb/>
            ti: </s>
            <s xml:id="echoid-s17878" xml:space="preserve">qui ex inuento ſinu non elicietur, niſi prius conſtet, an acutus ſit, an ob-
              <lb/>
            tuſus: </s>
            <s xml:id="echoid-s17879" xml:space="preserve">Aut, an alteruter reliquorum duorum arcuum non datorum ſit qua-
              <lb/>
            drante minor, aut maior. </s>
            <s xml:id="echoid-s17880" xml:space="preserve">Nam ſi alter arcus circa angulum rectum non da-
              <lb/>
            tus, & </s>
            <s xml:id="echoid-s17881" xml:space="preserve">quæſito angulo oppoſitus, fuerit minor quadrante, erit quæſitus angu
              <lb/>
            lus acutus; </s>
            <s xml:id="echoid-s17882" xml:space="preserve">ſi vero maior, obtuſus. </s>
            <s xml:id="echoid-s17883" xml:space="preserve">Pari ratione, ſi arcus recto angulo </s>
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