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

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        <div xml:id="echoid-div1187" type="section" level="1" n="566">
          <pb o="426" file="438" n="438" rhead=""/>
        </div>
        <div xml:id="echoid-div1189" type="section" level="1" n="567">
          <head xml:id="echoid-head602" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s14915" xml:space="preserve">EX hoc theoremate abſoluemus ſequentia tria problemata.</s>
            <s xml:id="echoid-s14916" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1190" type="section" level="1" n="568">
          <head xml:id="echoid-head603" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s14917" xml:space="preserve">IN triangulo ſphærico rectangulo, dato alterutro arcuum circa
              <lb/>
            angulum rectum, cum angulo non recto adiacente, inuenire arcum
              <lb/>
            recto angulo oppoſitum, & </s>
            <s xml:id="echoid-s14918" xml:space="preserve">reliquum arcum circa angulum rectum,
              <lb/>
            cum reliquo angulo non recto.</s>
            <s xml:id="echoid-s14919" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14920" xml:space="preserve">IN triangulo
              <emph style="sc">ABc</emph>
            , cuius angulus C, rectus, datus ſit arcus AC, & </s>
            <s xml:id="echoid-s14921" xml:space="preserve">angulus
              <lb/>
            A. </s>
            <s xml:id="echoid-s14922" xml:space="preserve">Dico dari quoq; </s>
            <s xml:id="echoid-s14923" xml:space="preserve">arcum AB, cum arcu
              <emph style="sc">BC</emph>
            , & </s>
            <s xml:id="echoid-s14924" xml:space="preserve">angulo B. </s>
            <s xml:id="echoid-s14925" xml:space="preserve">Cum enim ſit, vt ſinus
              <lb/>
            totus ad ſinũ complementi anguli A, ita tangens arcus
              <emph style="sc">Ab</emph>
            , ad tangentem arcus AC;
              <lb/>
            </s>
            <s xml:id="echoid-s14926" xml:space="preserve">
              <note position="left" xlink:label="note-438-01" xlink:href="note-438-01a" xml:space="preserve">45. huius.</note>
            Et conuertendo, vt ſinus complementi anguli
              <emph style="sc">A</emph>
            , ad ſinum totum, ita tangens arcus
              <lb/>
            AC, ad tangentem arcus AB:</s>
            <s xml:id="echoid-s14927" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14928" xml:space="preserve">SI fiat, vt ſinus complementi anguli dati
              <lb/>
              <note position="left" xlink:label="note-438-02" xlink:href="note-438-02a" xml:space="preserve">Praxis.</note>
            ad ſinum totum, ita tangens arcus dati ad aliud,
              <lb/>
              <figure xlink:label="fig-438-01" xlink:href="fig-438-01a" number="292">
                <image file="438-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/438-01"/>
              </figure>
            reperietur tangens arcus recto angulo oppoſiti,
              <lb/>
            qui quæritur. </s>
            <s xml:id="echoid-s14929" xml:space="preserve">Ex arcu vero AB, & </s>
            <s xml:id="echoid-s14930" xml:space="preserve">angulo A,
              <lb/>
            inuenietur arcus BC, per problema 2. </s>
            <s xml:id="echoid-s14931" xml:space="preserve">propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s14932" xml:space="preserve">41. </s>
            <s xml:id="echoid-s14933" xml:space="preserve">Et ex arcubus AB, AC, angulus B, arcui
              <lb/>
            AC, oppoſitus, per problema 1. </s>
            <s xml:id="echoid-s14934" xml:space="preserve">eiuſdem pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s14935" xml:space="preserve">41.</s>
            <s xml:id="echoid-s14936" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14937" xml:space="preserve">ITA autem ſciemus, an arcus quæſitus AB, ſit quadrante maior, an minor. </s>
            <s xml:id="echoid-s14938" xml:space="preserve">Si datus
              <lb/>
            angulus A, fuerit acutus, erit arcus BC, quadrante minor. </s>
            <s xml:id="echoid-s14939" xml:space="preserve">Si ergo datus arcus
              <emph style="sc">Ac</emph>
            ,
              <lb/>
              <note position="left" xlink:label="note-438-03" xlink:href="note-438-03a" xml:space="preserve">34. huius.</note>
            ſit quoq; </s>
            <s xml:id="echoid-s14940" xml:space="preserve">minor, erit & </s>
            <s xml:id="echoid-s14941" xml:space="preserve">arcus AB, minor quadrante, Si vero
              <emph style="sc">A</emph>
            C, ſit quadrante ma-
              <lb/>
              <note position="left" xlink:label="note-438-04" xlink:href="note-438-04a" xml:space="preserve">35. huius.</note>
            ior, erit & </s>
            <s xml:id="echoid-s14942" xml:space="preserve">
              <emph style="sc">Ab</emph>
            , maior. </s>
            <s xml:id="echoid-s14943" xml:space="preserve">At ſi datus angulus
              <emph style="sc">A</emph>
            , ſuerit, obtuſus, erit arcus BC, qua-
              <lb/>
              <note position="left" xlink:label="note-438-05" xlink:href="note-438-05a" xml:space="preserve">34. huius.</note>
            drante maior: </s>
            <s xml:id="echoid-s14944" xml:space="preserve">Si ergo datus arcus
              <emph style="sc">Ac</emph>
            , ſit quoque maior, erit arcus AB, minor qua-
              <lb/>
              <note position="left" xlink:label="note-438-06" xlink:href="note-438-06a" xml:space="preserve">35. huius.</note>
            drante; </s>
            <s xml:id="echoid-s14945" xml:space="preserve">Si vero AC, ſit minor quadrante, erit AB, maior.</s>
            <s xml:id="echoid-s14946" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1194" type="section" level="1" n="569">
          <head xml:id="echoid-head604" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s14947" xml:space="preserve">IN triangulo ſphęrico rectangulo, dato alterutro arcuum circa
              <lb/>
            angulum rectum, cum arcu, qui recto angulo opponitur, inueſtigare
              <lb/>
            angulum à dictis arcubus comprehenſum, hoc eſt, arcui, qui circa
              <lb/>
            angulum rectum datus eſt, adiacentem, cum reliquo arcu, & </s>
            <s xml:id="echoid-s14948" xml:space="preserve">angulo.</s>
            <s xml:id="echoid-s14949" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14950" xml:space="preserve">IN eodem triangulo dati ſint arcus AC, AB. </s>
            <s xml:id="echoid-s14951" xml:space="preserve">Dico dari etiam angulum A, cum
              <lb/>
              <note position="left" xlink:label="note-438-07" xlink:href="note-438-07a" xml:space="preserve">45. huius.</note>
            arcu BC, & </s>
            <s xml:id="echoid-s14952" xml:space="preserve">angulo B. </s>
            <s xml:id="echoid-s14953" xml:space="preserve">Quoniam enim eſt, vt ſinus totus ad ſinum complementi angu
              <lb/>
            li A, ita tangens arcus AB, ad tangentem arcus AC: </s>
            <s xml:id="echoid-s14954" xml:space="preserve">Hoc eſt, vt tangens arcus AB,
              <lb/>
            ad tangentem arcus AC, ita ſinus totus ad ſinum complementi anguli A:</s>
            <s xml:id="echoid-s14955" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14956" xml:space="preserve">SI fiat, vt tangens arcus recto angulo oppoſiti ad tangentem dati
              <lb/>
              <note position="left" xlink:label="note-438-08" xlink:href="note-438-08a" xml:space="preserve">Praxis.</note>
            arcus circa rectum angulum, ita ſinus totus ad aliud, procreabitur ſinus
              <lb/>
            complementi anguli quæſiti. </s>
            <s xml:id="echoid-s14957" xml:space="preserve">Hinc reliqua inuenientur, vt in præcedenti
              <lb/>
            problemate.</s>
            <s xml:id="echoid-s14958" xml:space="preserve"/>
          </p>
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