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

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          <p>
            <s xml:id="echoid-s12339" xml:space="preserve">
              <pb o="369" file="381" n="381" rhead=""/>
            miarcu AB, erunt duo arcus AB, AC, minores ſemicirculo BAD. </s>
            <s xml:id="echoid-s12340" xml:space="preserve">Quod
              <lb/>
            eſt propoſitum.</s>
            <s xml:id="echoid-s12341" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12342" xml:space="preserve">SIT poſtremò angulus ACD, minor angulo B, hoc eſt, angulo D, qui
              <lb/>
              <note position="right" xlink:label="note-381-01" xlink:href="note-381-01a" xml:space="preserve">13. huius.</note>
            angulo B, æqualis eſt; </s>
            <s xml:id="echoid-s12343" xml:space="preserve">eritq́ue arcus AC, maior arcu AD. </s>
            <s xml:id="echoid-s12344" xml:space="preserve">Addito ergo com-
              <lb/>
              <note position="right" xlink:label="note-381-02" xlink:href="note-381-02a" xml:space="preserve">11. huius.</note>
            muniarcu AB, erunt duo arcus AB, AC, maiores ſemicirculo BAD. </s>
            <s xml:id="echoid-s12345" xml:space="preserve">Quod
              <lb/>
            eſt propoſitum. </s>
            <s xml:id="echoid-s12346" xml:space="preserve">Si igitur cuiuſcunque trianguli ſphærici, &</s>
            <s xml:id="echoid-s12347" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12348" xml:space="preserve">Quod erat de-
              <lb/>
            monſtrandum.</s>
            <s xml:id="echoid-s12349" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div974" type="section" level="1" n="503">
          <head xml:id="echoid-head538" xml:space="preserve">THEOR. 14. PROP. 16.</head>
          <p>
            <s xml:id="echoid-s12350" xml:space="preserve">SI cuiuſcunque trianguli ſphærici duo latera
              <lb/>
            ſimul æqualia ſint ſemicirculo, erunt duo angu-
              <lb/>
            li ſupra baſim duobus rectis æquales: </s>
            <s xml:id="echoid-s12351" xml:space="preserve">Si verò mi-
              <lb/>
            nora ſint ſemicirculo, erunt duobus rectis mino-
              <lb/>
            res:</s>
            <s xml:id="echoid-s12352" xml:space="preserve">Si denique ſemicirculo ſint maiora, erunt duo-
              <lb/>
            bus rectis maiores.</s>
            <s xml:id="echoid-s12353" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12354" xml:space="preserve">IN triangulo ſphærico ABC, ſint primum duo latera AB, AC, ſemi-
              <lb/>
            circulo æqualia. </s>
            <s xml:id="echoid-s12355" xml:space="preserve">Dico duos angulos B, C, effe æquales duobus rectis, &</s>
            <s xml:id="echoid-s12356" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s12357" xml:space="preserve">Producto enim arcu BC, ad D, erit angulus ACD, angulo B, æqualis. </s>
            <s xml:id="echoid-s12358" xml:space="preserve">Cum
              <lb/>
              <note position="right" xlink:label="note-381-03" xlink:href="note-381-03a" xml:space="preserve">14. huius.</note>
            ergo duo anguli ad C, duobus ſint rectis æquales; </s>
            <s xml:id="echoid-s12359" xml:space="preserve">erũt
              <lb/>
              <note position="right" xlink:label="note-381-04" xlink:href="note-381-04a" xml:space="preserve">5 huius.</note>
              <figure xlink:label="fig-381-01" xlink:href="fig-381-01a" number="216">
                <image file="381-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/381-01"/>
              </figure>
            quoque duo anguli B, & </s>
            <s xml:id="echoid-s12360" xml:space="preserve">ACB, æquales duobus rectis.</s>
            <s xml:id="echoid-s12361" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12362" xml:space="preserve">SINT deinde latera AB, AC, ſemicirculo mi-
              <lb/>
            nora. </s>
            <s xml:id="echoid-s12363" xml:space="preserve">Cum ergo duo anguli ad C, ſint duobus rectis
              <lb/>
              <note position="right" xlink:label="note-381-05" xlink:href="note-381-05a" xml:space="preserve">5. huius.</note>
            æquales; </s>
            <s xml:id="echoid-s12364" xml:space="preserve">& </s>
            <s xml:id="echoid-s12365" xml:space="preserve">angulus B, minor ſit angulo ACD; </s>
            <s xml:id="echoid-s12366" xml:space="preserve">erunt
              <lb/>
              <note position="right" xlink:label="note-381-06" xlink:href="note-381-06a" xml:space="preserve">14. huius.</note>
            anguli B, & </s>
            <s xml:id="echoid-s12367" xml:space="preserve">ACB, duobus rectis minores.</s>
            <s xml:id="echoid-s12368" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12369" xml:space="preserve">SINT tandem latera AB, AC, ſemicirculo ma-
              <lb/>
            iora. </s>
            <s xml:id="echoid-s12370" xml:space="preserve">Quoniam igitur duo anguli C, ſunt duobus re-
              <lb/>
              <note position="right" xlink:label="note-381-07" xlink:href="note-381-07a" xml:space="preserve">5. huius.</note>
            ctis æquales, eſtq́ue angulus B, maior angulo ACB;
              <lb/>
            </s>
            <s xml:id="echoid-s12371" xml:space="preserve">
              <note position="right" xlink:label="note-381-08" xlink:href="note-381-08a" xml:space="preserve">14. huius.</note>
            erunt anguli B, & </s>
            <s xml:id="echoid-s12372" xml:space="preserve">ACB, maiores duobus rectis. </s>
            <s xml:id="echoid-s12373" xml:space="preserve">Si igitur cuiuſcun que trian
              <lb/>
            guli ſphærici, &</s>
            <s xml:id="echoid-s12374" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12375" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s12376" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div978" type="section" level="1" n="504">
          <head xml:id="echoid-head539" xml:space="preserve">THEOR. 15. PROP. 17.</head>
          <p>
            <s xml:id="echoid-s12377" xml:space="preserve">SI cuiuſcunque trianguli ſphærici duo anguli
              <lb/>
            ſupra vnum latus duobus rectis æquales fuerint,
              <lb/>
            erunt reliqua duo latera ſemicirculo æqualia: </s>
            <s xml:id="echoid-s12378" xml:space="preserve">Si
              <lb/>
            vero duobus rectis fuerint minores, erunt minora
              <lb/>
            ſemicirculo: </s>
            <s xml:id="echoid-s12379" xml:space="preserve">Si denique maiores extiterint duo-
              <lb/>
            bus rectis, erunt ſemicirculo maiora.</s>
            <s xml:id="echoid-s12380" xml:space="preserve"/>
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