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

Table of figures

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          <p>
            <s xml:id="echoid-s12266" xml:space="preserve">
              <pb o="367" file="379" n="379" rhead=""/>
            tur, quàm BC. </s>
            <s xml:id="echoid-s12267" xml:space="preserve">Cum ergo angulus D, neque æqualis ſit angulo A, neque mi-
              <lb/>
            nor, erit vtique maior. </s>
            <s xml:id="echoid-s12268" xml:space="preserve">Quod eſt propoſitum. </s>
            <s xml:id="echoid-s12269" xml:space="preserve">Itaque ſi duo triangula ſphæ-
              <lb/>
            rica, &</s>
            <s xml:id="echoid-s12270" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12271" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s12272" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div964" type="section" level="1" n="500">
          <head xml:id="echoid-head535" xml:space="preserve">THEOR. 11. PROPOS. 13.</head>
          <p>
            <s xml:id="echoid-s12273" xml:space="preserve">DVO ſemicirculi maximorum circulorum
              <lb/>
            ſe mutuo ſecantes continent duos angulos inter
              <lb/>
            ſe æquales.</s>
            <s xml:id="echoid-s12274" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12275" xml:space="preserve">DVO ſemicirculi maximorum circulorum ABC, ADC, ſe mutuo ſe-
              <lb/>
            cent in A, C. </s>
            <s xml:id="echoid-s12276" xml:space="preserve">Dico angulos A, & </s>
            <s xml:id="echoid-s12277" xml:space="preserve">C, æqua-
              <lb/>
              <figure xlink:label="fig-379-01" xlink:href="fig-379-01a" number="212">
                <image file="379-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/379-01"/>
              </figure>
            les eſſe. </s>
            <s xml:id="echoid-s12278" xml:space="preserve">Diuiſo enim ſemicirculo ABC, in
              <lb/>
            B, bifariam, vt AB, BC, quadrantes ſint,
              <lb/>
            ducatur per B, & </s>
            <s xml:id="echoid-s12279" xml:space="preserve">polum circuli ABC, ar-
              <lb/>
              <note position="right" xlink:label="note-379-01" xlink:href="note-379-01a" xml:space="preserve">20. 1. Theo.</note>
            cus circuli maximi BD, ſecans arcũ ADC,
              <lb/>
            in D; </s>
            <s xml:id="echoid-s12280" xml:space="preserve">eritq̀ angulus B, ex vtraque parte
              <lb/>
              <note position="right" xlink:label="note-379-02" xlink:href="note-379-02a" xml:space="preserve">15. 1. Theo.</note>
            rectus. </s>
            <s xml:id="echoid-s12281" xml:space="preserve">Quia igitur duo latera AB, BD,
              <lb/>
            duobus lateribus CB, BD, æqualia, ſunt,
              <lb/>
            cõtinentq̀ angulos æquales, vtpote rectos;
              <lb/>
            </s>
            <s xml:id="echoid-s12282" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s12283" xml:space="preserve">anguli A, & </s>
            <s xml:id="echoid-s12284" xml:space="preserve">C, æquales. </s>
            <s xml:id="echoid-s12285" xml:space="preserve">Quare duo
              <lb/>
              <note position="right" xlink:label="note-379-03" xlink:href="note-379-03a" xml:space="preserve">7. huius.</note>
            ſemicirculi maximorum circulorum, &</s>
            <s xml:id="echoid-s12286" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12287" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s12288" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div966" type="section" level="1" n="501">
          <head xml:id="echoid-head536" xml:space="preserve">THEOR 12. PROPOS. 14.</head>
          <p>
            <s xml:id="echoid-s12289" xml:space="preserve">CVIVSCVNQVE trianguli ſphærici vno
              <lb/>
            latere producto, ſi reliqua latera ſimul ęqualia ſint
              <lb/>
            ſemicirculo, erit angulus externus æqualis angu-
              <lb/>
            lo interno oppoſito ſupra arcum productum: </s>
            <s xml:id="echoid-s12290" xml:space="preserve">Si
              <lb/>
            verò minora ſint ſemicirculo, erit angulus exter-
              <lb/>
            nus eodem interno oppoſito maior: </s>
            <s xml:id="echoid-s12291" xml:space="preserve">ſi denique
              <lb/>
            maiora ſint ſemicirculo, idem angulus externus
              <lb/>
            dicto angulo interno oppoſito minor erit.</s>
            <s xml:id="echoid-s12292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12293" xml:space="preserve">IN triangulo ſphærico ABC, produca-
              <lb/>
              <figure xlink:label="fig-379-02" xlink:href="fig-379-02a" number="213">
                <image file="379-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/379-02"/>
              </figure>
            tur latus BC, ad D, & </s>
            <s xml:id="echoid-s12294" xml:space="preserve">ſint primum reliqua
              <lb/>
            duo latera AB, AC, ſimul ſemicirculo æqua-
              <lb/>
            lia. </s>
            <s xml:id="echoid-s12295" xml:space="preserve">Dico angulum externum ACD, æqualem
              <lb/>
            eſſe interno oppoſito B, ſupra arcum produ-
              <lb/>
            ctum BC, &</s>
            <s xml:id="echoid-s12296" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12297" xml:space="preserve">Coeat enim arcus BA, produ-
              <lb/>
            ctus cum arcu BC, producto in D; </s>
            <s xml:id="echoid-s12298" xml:space="preserve">eritq̀ue
              <lb/>
            BAD, ſemicirculus. </s>
            <s xml:id="echoid-s12299" xml:space="preserve">Quia vero arcus BA,
              <lb/>
              <note position="right" xlink:label="note-379-04" xlink:href="note-379-04a" xml:space="preserve">11. 1. Theo.</note>
            </s>
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