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

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        <div xml:id="echoid-div1058" type="section" level="1" n="529">
          <p>
            <s xml:id="echoid-s13426" xml:space="preserve">
              <pb o="391" file="403" n="403" rhead=""/>
            quadrante eſſe. </s>
            <s xml:id="echoid-s13427" xml:space="preserve">Fiat enim rurſus angulus CBD, rectus, conuenlatq́ue arcus
              <lb/>
            BD, cum CA, protracto in D; </s>
            <s xml:id="echoid-s13428" xml:space="preserve">eritq́ue, vt prius, vterque arcus BD, CD,
              <lb/>
              <note position="right" xlink:label="note-403-01" xlink:href="note-403-01a" xml:space="preserve">25. huius.</note>
            quadrans. </s>
            <s xml:id="echoid-s13429" xml:space="preserve">Abſciſſo autem quadrante BG, ducatur per puncta D, G, arcus cir
              <lb/>
              <note position="right" xlink:label="note-403-02" xlink:href="note-403-02a" xml:space="preserve">20.1 Theod.</note>
            culi maximi DG, ſecans arcum AB, in H. </s>
            <s xml:id="echoid-s13430" xml:space="preserve">Quoniam igitur arcus BD, BG,
              <lb/>
              <note position="right" xlink:label="note-403-03" xlink:href="note-403-03a" xml:space="preserve">25. & 26.
                <lb/>
              huius.</note>
            quadrantes ſunt, erit vterque angulus BDG, BGD, rectus, & </s>
            <s xml:id="echoid-s13431" xml:space="preserve">B, polus ar-
              <lb/>
            cus DG. </s>
            <s xml:id="echoid-s13432" xml:space="preserve">Rectus ergo erit angulus ad H; </s>
            <s xml:id="echoid-s13433" xml:space="preserve">ac proinde vterque arcus BG, BH,
              <lb/>
              <note position="right" xlink:label="note-403-04" xlink:href="note-403-04a" xml:space="preserve">25. 1 Theod.</note>
            erit quadrans. </s>
            <s xml:id="echoid-s13434" xml:space="preserve">Quare AB, quadrante maior erit.</s>
            <s xml:id="echoid-s13435" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">25. huius.</note>
          <p>
            <s xml:id="echoid-s13436" xml:space="preserve">ET quoniam arcus CD, ſemper oſtenſus eſt eſſe quadrans, erit arcus AC,
              <lb/>
            quadrante minor. </s>
            <s xml:id="echoid-s13437" xml:space="preserve">Quapropter in omni triangulo ſphærico, &</s>
            <s xml:id="echoid-s13438" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13439" xml:space="preserve">Quod oſten-
              <lb/>
            dendum erat.</s>
            <s xml:id="echoid-s13440" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1062" type="section" level="1" n="530">
          <head xml:id="echoid-head565" xml:space="preserve">THEOR. 31. PROPOS. 33.</head>
          <p>
            <s xml:id="echoid-s13441" xml:space="preserve">IN omni triangulo ſphærico, cuius vnus an-
              <lb/>
            gulus rectus, & </s>
            <s xml:id="echoid-s13442" xml:space="preserve">alter reliquorum acutus, ſi quidem
              <lb/>
            arcus illis angulis adiacens ſuerit quadrans, erit re-
              <lb/>
            liquus angulus rectus: </s>
            <s xml:id="echoid-s13443" xml:space="preserve">ſi verò minor quadrante,
              <lb/>
            acutus: </s>
            <s xml:id="echoid-s13444" xml:space="preserve">ſi denique quadrante maior, obtuſus.</s>
            <s xml:id="echoid-s13445" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13446" xml:space="preserve">SIT in triangulo ABC, ſphærico angulus C, rectus, & </s>
            <s xml:id="echoid-s13447" xml:space="preserve">B, acutus, ſitq́ue
              <lb/>
            primum arcus BC, quadrans. </s>
            <s xml:id="echoid-s13448" xml:space="preserve">Dico reliquum angulum A, rectum eſſe. </s>
            <s xml:id="echoid-s13449" xml:space="preserve">Erit
              <lb/>
              <note position="right" xlink:label="note-403-06" xlink:href="note-403-06a" xml:space="preserve">32. huius.</note>
            enim, & </s>
            <s xml:id="echoid-s13450" xml:space="preserve">AB, quadrans. </s>
            <s xml:id="echoid-s13451" xml:space="preserve">Igitur vterque angulus C,
              <lb/>
              <note position="right" xlink:label="note-403-07" xlink:href="note-403-07a" xml:space="preserve">25. huius.</note>
              <figure xlink:label="fig-403-01" xlink:href="fig-403-01a" number="249">
                <image file="403-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/403-01"/>
              </figure>
            A, rectus.</s>
            <s xml:id="echoid-s13452" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13453" xml:space="preserve">SIT deinde arcus BC, quadrante minor. </s>
            <s xml:id="echoid-s13454" xml:space="preserve">Dico
              <lb/>
            angulum A, eſſe acutum. </s>
            <s xml:id="echoid-s13455" xml:space="preserve">Erit enim & </s>
            <s xml:id="echoid-s13456" xml:space="preserve">arcus AB,
              <lb/>
              <note position="right" xlink:label="note-403-08" xlink:href="note-403-08a" xml:space="preserve">32. huius.</note>
            quadrante minor; </s>
            <s xml:id="echoid-s13457" xml:space="preserve">atque adeo arcus AB, BC, ſimul
              <lb/>
            ſemicirculo erunt minores. </s>
            <s xml:id="echoid-s13458" xml:space="preserve">Quare anguli A, C, duo-
              <lb/>
              <note position="right" xlink:label="note-403-09" xlink:href="note-403-09a" xml:space="preserve">16. huius.</note>
            bus rectis ſunt minores; </s>
            <s xml:id="echoid-s13459" xml:space="preserve">ac proinde, cum C, ſit re-
              <lb/>
            ctus, erit A, acutus.</s>
            <s xml:id="echoid-s13460" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13461" xml:space="preserve">SIT tandem arcus BC, maior quadrante. </s>
            <s xml:id="echoid-s13462" xml:space="preserve">Dico
              <lb/>
            angulum A, obtuſum eſſe. </s>
            <s xml:id="echoid-s13463" xml:space="preserve">Erit enim & </s>
            <s xml:id="echoid-s13464" xml:space="preserve">AB, quadran
              <lb/>
              <note position="right" xlink:label="note-403-10" xlink:href="note-403-10a" xml:space="preserve">32. huius.</note>
            te maior; </s>
            <s xml:id="echoid-s13465" xml:space="preserve">ac proptcrea arcus AB, BC, ſimul ſemi-
              <lb/>
            circulo maiores erunt. </s>
            <s xml:id="echoid-s13466" xml:space="preserve">Igitur anguli A, C, duobus rectis ſunt maiores; </s>
            <s xml:id="echoid-s13467" xml:space="preserve">atque
              <lb/>
              <note position="right" xlink:label="note-403-11" xlink:href="note-403-11a" xml:space="preserve">16. huius.</note>
            adeo, cum C, ſit rectus, erit A, obtuſus. </s>
            <s xml:id="echoid-s13468" xml:space="preserve">Quocirca in omni triangulo ſphæ-
              <lb/>
            rico, cuius vnus angulus, &</s>
            <s xml:id="echoid-s13469" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13470" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s13471" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1066" type="section" level="1" n="531">
          <head xml:id="echoid-head566" xml:space="preserve">THEOR. 32. PROPOS. 34.</head>
          <p>
            <s xml:id="echoid-s13472" xml:space="preserve">IN omni triangulo ſphærico, cuius vnus angu-
              <lb/>
            lus rectus, ſi vteruis reliquorum angulorum ſit re-
              <lb/>
            ctus, erit arcus eum ſubtendens, quadrans: </s>
            <s xml:id="echoid-s13473" xml:space="preserve">ſi </s>
          </p>
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