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

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        <div xml:id="echoid-div1479" type="section" level="1" n="660">
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            <s xml:id="echoid-s17979" xml:space="preserve">
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            ſi datus angulus ſuerit acutus, & </s>
            <s xml:id="echoid-s17980" xml:space="preserve">arcus datus quadrante maior; </s>
            <s xml:id="echoid-s17981" xml:space="preserve">aut ſi datus
              <lb/>
            angulus fuerit obtuſus, & </s>
            <s xml:id="echoid-s17982" xml:space="preserve">arcus datus minor quadrante.</s>
            <s xml:id="echoid-s17983" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17984" xml:space="preserve">IAM vero, per 2. </s>
            <s xml:id="echoid-s17985" xml:space="preserve">problema, ex arcu rectum angulum ſubtendente inuen
              <lb/>
            to, & </s>
            <s xml:id="echoid-s17986" xml:space="preserve">angulo dato, reperietur alter arcus circa angulum rectum dato angulo
              <lb/>
            oppoſitus. </s>
            <s xml:id="echoid-s17987" xml:space="preserve">Ex eodem vero arcu rectum angulum ſubtendente, & </s>
            <s xml:id="echoid-s17988" xml:space="preserve">arcu in prin
              <lb/>
            cipio dato, inuenietur, per 1. </s>
            <s xml:id="echoid-s17989" xml:space="preserve">problema, alter angulus non rectus dato ar-
              <lb/>
            cui oppoſitus.</s>
            <s xml:id="echoid-s17990" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1481" type="section" level="1" n="661">
          <head xml:id="echoid-head696" xml:space="preserve">Aliter.</head>
          <p>
            <s xml:id="echoid-s17991" xml:space="preserve">FIAT, vt ſinus totus ad ſinum complementi anguli dati, ita tangens com
              <lb/>
              <note position="left" xlink:label="note-510-01" xlink:href="note-510-01a" xml:space="preserve">Probl. pro-
                <lb/>
              poſ. 46. tri-
                <lb/>
              ang. ſphær.</note>
            plementi arcus dati ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s17992" xml:space="preserve">tangens complementi arcus recto
              <lb/>
            angulo oppoſiti. </s>
            <s xml:id="echoid-s17993" xml:space="preserve">Reliqua reperientur, vt prius.</s>
            <s xml:id="echoid-s17994" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quæritur
            <lb/>
          angulius nõ
            <lb/>
          rectus. De-
            <lb/>
          inde alter
            <lb/>
          arcus circa
            <lb/>
          rectum an-
            <lb/>
          gulũ, & al.
            <lb/>
          ter angulus
            <lb/>
          non rectus.</note>
        </div>
        <div xml:id="echoid-div1483" type="section" level="1" n="662">
          <head xml:id="echoid-head697" xml:space="preserve">13. DATO alterutro arcuum in triangulo re-
            <lb/>
          ctangulo circa angulum rectum, cum arcu re
            <lb/>
          ctum angulum ſubtendente, reperire angu-
            <lb/>
          lum à dictis arcubus comprehenſum, ſiue da
            <lb/>
          to arcui circa rectum angulum adiacentem,
            <lb/>
          & inſuper reliquum arcum, & angulum.</head>
          <p>
            <s xml:id="echoid-s17995" xml:space="preserve">FIAT, vt tangens arcus recto angulo oppoſiti ad tangentem dati arcus
              <lb/>
              <note position="left" xlink:label="note-510-03" xlink:href="note-510-03a" xml:space="preserve">Probl. 2. pro
                <lb/>
              poſ. 45. tri-
                <lb/>
              ang. ſphær.</note>
            circa angulum rectum, ita ſinus totus ad aliud, produceturq́; </s>
            <s xml:id="echoid-s17996" xml:space="preserve">ſinus comple-
              <lb/>
            menti anguli à dictis arcubus comprehenſi, qui quæritur. </s>
            <s xml:id="echoid-s17997" xml:space="preserve">Hic autem acutus
              <lb/>
            erit, ſi datus arcus recto angulo oppoſitus fuerit quadrante minor, & </s>
            <s xml:id="echoid-s17998" xml:space="preserve">arcus
              <lb/>
            circa rectum angulum datus minor quoque; </s>
            <s xml:id="echoid-s17999" xml:space="preserve">aut ſi tam ille, quam hic quadran
              <lb/>
            te maior fuerit: </s>
            <s xml:id="echoid-s18000" xml:space="preserve">Idem vero angulus quæſitus erit obtuſus, ſi datus arcus an-
              <lb/>
            gulo recto oppoſitus fuerit minor quadrante, & </s>
            <s xml:id="echoid-s18001" xml:space="preserve">datus arcus circa rectum an-
              <lb/>
            gulum quadrante maior; </s>
            <s xml:id="echoid-s18002" xml:space="preserve">aut ſi ille fuerit quadrante maior, & </s>
            <s xml:id="echoid-s18003" xml:space="preserve">hic minor.</s>
            <s xml:id="echoid-s18004" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18005" xml:space="preserve">RELIQVA inueſtigabũtur, vt in præcedenti problemate traditum eſt.</s>
            <s xml:id="echoid-s18006" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1485" type="section" level="1" n="663">
          <head xml:id="echoid-head698" xml:space="preserve">Aliter.</head>
          <p>
            <s xml:id="echoid-s18007" xml:space="preserve">FIAT, vt ſinus totus ad tangentem complementi arcus angulo recto op
              <lb/>
              <note position="left" xlink:label="note-510-04" xlink:href="note-510-04a" xml:space="preserve">Probl. pro-
                <lb/>
              poſ. 51. tri-
                <lb/>
              ang. ſphær.</note>
            poſiti, ita tangens dati arcus circa rectum angulum ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s18008" xml:space="preserve">ſi-
              <lb/>
            nus complementi anguli adia centis, qui deſideratur.</s>
            <s xml:id="echoid-s18009" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quæritur
            <lb/>
          arcus circa
            <lb/>
          angulũ re-
            <lb/>
          ctum. Dein
            <lb/>
          de alter ar-
            <lb/>
          cus circa an
            <lb/>
          gulum re-
            <lb/>
          ctum, cum
            <lb/>
          reliquo an-
            <lb/>
          gulo non
            <lb/>
          recto.</note>
        </div>
        <div xml:id="echoid-div1487" type="section" level="1" n="664">
          <head xml:id="echoid-head699" xml:space="preserve">14. DATO arcu rectum angulum ſubtenden
            <lb/>
          te in triangulo rectangulo, cum alterutro an-
            <lb/>
          gulorum non rectorum, reperire arcum cir-
            <lb/>
          ca angulum rectum huic angulo adiacẽtem,
            <lb/>
          ac præterea alterum arcum circa angulum re
            <lb/>
          ctum, cum altero angulo non recto.</head>
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