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

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        <div xml:id="echoid-div1213" type="section" level="1" n="575">
          <pb o="431" file="443" n="443" rhead=""/>
        </div>
        <div xml:id="echoid-div1215" type="section" level="1" n="576">
          <head xml:id="echoid-head611" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s15118" xml:space="preserve">INFERTVR ex theoremate hoc ſequens problema: </s>
            <s xml:id="echoid-s15119" xml:space="preserve">quod licet demonſtratum
              <lb/>
            quoque ſit problemate 2. </s>
            <s xml:id="echoid-s15120" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15121" xml:space="preserve">44. </s>
            <s xml:id="echoid-s15122" xml:space="preserve">facilius tamen hic abſoluitur, cumin aurea re-
              <lb/>
            gula ſinus to tus primum obtineat locum.</s>
            <s xml:id="echoid-s15123" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15124" xml:space="preserve">IN triangulo ſphærico rectangulo, datis duobus arcubus circa
              <lb/>
            angulum rectum, vtrumlibet angulorum non rectorum, vnà cum
              <lb/>
            arcu reliquo, qui angulo recto opponitur, indagare.</s>
            <s xml:id="echoid-s15125" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15126" xml:space="preserve">IN triangulo ABC, cuius angulus C, rectus,
              <lb/>
              <figure xlink:label="fig-443-01" xlink:href="fig-443-01a" number="299">
                <image file="443-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/443-01"/>
              </figure>
            ſint dati duo arcus AC, CB. </s>
            <s xml:id="echoid-s15127" xml:space="preserve">Dico vtrumuis angulo-
              <lb/>
            rum A, B, & </s>
            <s xml:id="echoid-s15128" xml:space="preserve">arcum AB, quoque dari. </s>
            <s xml:id="echoid-s15129" xml:space="preserve">Nam cum ſit,
              <lb/>
            vt ſinus totus ad ſinum arcus AC, ita tangens comple-
              <lb/>
              <note position="right" xlink:label="note-443-01" xlink:href="note-443-01a" xml:space="preserve">48. huius.</note>
            menti arcus CB, ad tangentem complementi anguli
              <lb/>
            A. </s>
            <s xml:id="echoid-s15130" xml:space="preserve">Item vt ſinus totus ad ſinum arcus CB, ita tan-
              <lb/>
            gens complementi arcus AC, ad tangentem complemen
              <lb/>
            ti anguli B:</s>
            <s xml:id="echoid-s15131" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15132" xml:space="preserve">SI fiat, vt ſinus totus ad ſinum vtrius vis arcuum circa angulum re-
              <lb/>
              <note position="right" xlink:label="note-443-02" xlink:href="note-443-02a" xml:space="preserve">Praxis.</note>
            ctum, ita tangens complementi alterius arcus circa rectum angulum ad
              <lb/>
            aliud, reperietur tangens complementi anguli huic poſterioriarcui oppo-
              <lb/>
            ſiti. </s>
            <s xml:id="echoid-s15133" xml:space="preserve">Ex datis quoque duobus arcubus circa angulum rectum cognoſcetur
              <lb/>
            & </s>
            <s xml:id="echoid-s15134" xml:space="preserve">tertius arcus angulo recto oppoſitus, vt in problemate propoſ. </s>
            <s xml:id="echoid-s15135" xml:space="preserve">43. </s>
            <s xml:id="echoid-s15136" xml:space="preserve">oſten
              <lb/>
            dimus. </s>
            <s xml:id="echoid-s15137" xml:space="preserve">Vel certe ex dato vtrolibet arcu, & </s>
            <s xml:id="echoid-s15138" xml:space="preserve">angulo, qui ei opponitur, in-
              <lb/>
            uento, vt in problemate 3. </s>
            <s xml:id="echoid-s15139" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15140" xml:space="preserve">41. </s>
            <s xml:id="echoid-s15141" xml:space="preserve">traditum eſt.</s>
            <s xml:id="echoid-s15142" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15143" xml:space="preserve">VTRVM autem angulus quæſitus ſit acutus, obtuſusve, docebit arcus ei oppo-
              <lb/>
            ſitus. </s>
            <s xml:id="echoid-s15144" xml:space="preserve">Hic enim ſi minor fuerit quadrante, erit angulus ei oppoſitus, acutus; </s>
            <s xml:id="echoid-s15145" xml:space="preserve">ſi vero
              <lb/>
              <note position="right" xlink:label="note-443-03" xlink:href="note-443-03a" xml:space="preserve">34. huius.</note>
            maior, obtuſus.</s>
            <s xml:id="echoid-s15146" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1219" type="section" level="1" n="577">
          <head xml:id="echoid-head612" xml:space="preserve">THEOR. 47. PROPOS. 49.</head>
          <p>
            <s xml:id="echoid-s15147" xml:space="preserve">IN omni triangulo ſphærico rectangulo, cu-
              <lb/>
            ius omnes arcus ſint minores quadrante: </s>
            <s xml:id="echoid-s15148" xml:space="preserve">ſinus to-
              <lb/>
            tus ad tangentem vtriusvis arcuum circa angulum
              <lb/>
            rectum eandem proportionem habet, quam tan-
              <lb/>
            gens complementi anguli oppoſiti ad ſinum alte-
              <lb/>
            rius arcus circa rectum angulum.</s>
            <s xml:id="echoid-s15149" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15150" xml:space="preserve">IN ſphærico triangulo ADE, cuius arcus omnes quadrante minores, ſit
              <lb/>
            angulus D, rectus. </s>
            <s xml:id="echoid-s15151" xml:space="preserve">Dico ita eſſe ſinum totum ad tangentem arcus DE, vt </s>
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