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

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          <pb o="441" file="453" n="453" rhead=""/>
          <p>
            <s xml:id="echoid-s15503" xml:space="preserve">IN triangulo ſphærico rectangulo, dato vtrouis arcuum circa an-
              <lb/>
            gulum rectum, cum angulo non recto oppoſito, inquirere teliquum
              <lb/>
            angulum non rectum, & </s>
            <s xml:id="echoid-s15504" xml:space="preserve">iuſuper reliquos duos arcus: </s>
            <s xml:id="echoid-s15505" xml:space="preserve">modo conſter,
              <lb/>
            an quæſitus angulus ſit acutus, obtuſusve: </s>
            <s xml:id="echoid-s15506" xml:space="preserve">Vel certe, an alter arcus
              <lb/>
            circa angulum rectum ſit minor quadrante, an maior.</s>
            <s xml:id="echoid-s15507" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15508" xml:space="preserve">IN triangulo ABC, angulum C, rectum habente, datus ſit arcus
              <emph style="sc">AC</emph>
            , cum an-
              <lb/>
            gulo
              <emph style="sc">B</emph>
            . </s>
            <s xml:id="echoid-s15509" xml:space="preserve">Dico dari quoque engulum
              <emph style="sc">A</emph>
            , cum arcubus
              <emph style="sc">BC</emph>
            ,
              <lb/>
              <figure xlink:label="fig-453-01" xlink:href="fig-453-01a" number="314">
                <image file="453-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/453-01"/>
              </figure>
              <emph style="sc">AB</emph>
            . </s>
            <s xml:id="echoid-s15510" xml:space="preserve">Cum enim ſit, vt ſinus totus ad ſinum complementi
              <lb/>
            arcus
              <emph style="sc">AC</emph>
            , dati, ita ſecans anguli dati
              <emph style="sc">B</emph>
            , ad ſecantem
              <lb/>
              <note position="right" xlink:label="note-453-01" xlink:href="note-453-01a" xml:space="preserve">56. huius.</note>
            complementi anguli
              <emph style="sc">A</emph>
            :</s>
            <s xml:id="echoid-s15511" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15512" xml:space="preserve">SI fiat, vt ſinus totus ad ſinum complementi
              <lb/>
              <note position="right" xlink:label="note-453-02" xlink:href="note-453-02a" xml:space="preserve">Praxis.</note>
            arcus dati, ita ſecans dati anguli ad aliud, repe-
              <lb/>
            rietur ſecans complementi anguli alterius non re-
              <lb/>
            cti. </s>
            <s xml:id="echoid-s15513" xml:space="preserve">Hinc ex duobus angulis non rectis notis inue-
              <lb/>
            ſtigabitur arcus recto oppoſitus angulo, vt in problemate propoſ. </s>
            <s xml:id="echoid-s15514" xml:space="preserve">50. </s>
            <s xml:id="echoid-s15515" xml:space="preserve">mon
              <lb/>
            ſtrauimus, ac proinde & </s>
            <s xml:id="echoid-s15516" xml:space="preserve">reliquus arcus, ex arcu, qui recto angulo oppo-
              <lb/>
            nitur, & </s>
            <s xml:id="echoid-s15517" xml:space="preserve">ex noto angulo, qui reliquo arcui opponitur, vt in problemate 2.
              <lb/>
            </s>
            <s xml:id="echoid-s15518" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15519" xml:space="preserve">41. </s>
            <s xml:id="echoid-s15520" xml:space="preserve">diximus.</s>
            <s xml:id="echoid-s15521" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15522" xml:space="preserve">OTORTET autem conſtare, an reliquus angulus non rectus, qui quæritur ſit
              <lb/>
            acutus, obtuſusve; </s>
            <s xml:id="echoid-s15523" xml:space="preserve">vel, an reliquus arcus circa angulum rectum ſit minor, aut maior
              <lb/>
            quadrante, vt ad calcem problematis 2. </s>
            <s xml:id="echoid-s15524" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15525" xml:space="preserve">42. </s>
            <s xml:id="echoid-s15526" xml:space="preserve">monuimus, vbi errorem etiam
              <lb/>
            Nicolai Copernici deteximus.</s>
            <s xml:id="echoid-s15527" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15528" xml:space="preserve">QVONIAM vero abſolutus iam eſt triangulorum ſphæricorum rectangulorum
              <lb/>
            calculus, libet hoc loco omnia problemata hactenus explicata in tabulam quandam
              <lb/>
            referre, vt facilius quilibet id, quod maxime ſcire deſiderat, poſsit inuenire. </s>
            <s xml:id="echoid-s15529" xml:space="preserve">Itaque
              <lb/>
            cum in omni triangulo ſphærico rectangulo id, quod primo loco quæritur, ſit vel ar-
              <lb/>
            cus recto angulo oppoſitus, vel vterlibet arcuum circa rectum angulum, vel denique
              <lb/>
            alteruter angulorum non rectorum, (quamuis eo, quod potiſsimum quæritur, inuen-
              <lb/>
            to, cætera quoque reperiantur, vt ad praxes ſingulorum problematum monuimus)
              <lb/>
            trimembrem tabulam, pro numero quæſitorum, conſecimus, appoſuimuſque problema-
              <lb/>
            ta propoſitionum, in quibus inuentiones quæſitorum demonſtratæ ſunt.</s>
            <s xml:id="echoid-s15530" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1259" type="section" level="1" n="593">
          <head xml:id="echoid-head628" xml:space="preserve">Sequuntur problemata ſuperiorum propoſi-
            <lb/>
          tionum in trimembrem tabel-
            <lb/>
          lam digeſta.</head>
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