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

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        <div xml:id="echoid-div946" type="section" level="1" n="492">
          <pb o="362" file="374" n="374" rhead=""/>
          <p>
            <s xml:id="echoid-s12044" xml:space="preserve">SINT duo triangula ſphærica ABC, DEF, habentia duo latera AB,
              <lb/>
            AC, duobus lateribus DE, DF, æqualia, vtrumq; </s>
            <s xml:id="echoid-s12045" xml:space="preserve">vtriq;</s>
            <s xml:id="echoid-s12046" xml:space="preserve">, & </s>
            <s xml:id="echoid-s12047" xml:space="preserve">angulum A, an-
              <lb/>
              <figure xlink:label="fig-374-01" xlink:href="fig-374-01a" number="203">
                <image file="374-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/374-01"/>
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            gulo D, æqualem. </s>
            <s xml:id="echoid-s12048" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s12049" xml:space="preserve">baſem BC, ba-
              <lb/>
            ſi EF, æqualem eſſe, & </s>
            <s xml:id="echoid-s12050" xml:space="preserve">triangulum ABC,
              <lb/>
            triangulo DEF, & </s>
            <s xml:id="echoid-s12051" xml:space="preserve">reliquos angulos B,
              <lb/>
            C, reliquis angulis E, F, vtrumq; </s>
            <s xml:id="echoid-s12052" xml:space="preserve">vtriq;</s>
            <s xml:id="echoid-s12053" xml:space="preserve">.
              <lb/>
            Quoniam enim arcus AB, arcui DE, æ-
              <lb/>
            qualis ponitur, fit, vt ſi alter alteri intel-
              <lb/>
            ligatur ſuperponi in ſuperficie ſphæræ,
              <lb/>
            collocato puncto A, in puncto D, & </s>
            <s xml:id="echoid-s12054" xml:space="preserve">pun
              <lb/>
            cto B, in puncto E, plana circulorum AB,
              <lb/>
            DE, ſibi mutuo congruant, & </s>
            <s xml:id="echoid-s12055" xml:space="preserve">proinde ar
              <lb/>
            cus AB, arcui DE, congruat. </s>
            <s xml:id="echoid-s12056" xml:space="preserve">Alias ſe
              <lb/>
            mutuo ſecarent bifariam circuli illorum arcuum in A, & </s>
            <s xml:id="echoid-s12057" xml:space="preserve">B, atq; </s>
            <s xml:id="echoid-s12058" xml:space="preserve">adeo ſemicir
              <lb/>
              <note position="left" xlink:label="note-374-01" xlink:href="note-374-01a" xml:space="preserve">11. 1. Theod.</note>
            culi eſſent AB, DE. </s>
            <s xml:id="echoid-s12059" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s12060" xml:space="preserve">Eſt enim ſemicirculo vterq; </s>
            <s xml:id="echoid-s12061" xml:space="preserve">mi-
              <lb/>
              <note position="left" xlink:label="note-374-02" xlink:href="note-374-02a" xml:space="preserve">2. huius.</note>
            nor. </s>
            <s xml:id="echoid-s12062" xml:space="preserve">Cum ergo angulus A, angulo D, ponatur æqualis, congruet quoq; </s>
            <s xml:id="echoid-s12063" xml:space="preserve">ar-
              <lb/>
            cus AC, arcui DF, punctumq; </s>
            <s xml:id="echoid-s12064" xml:space="preserve">C, in punctum F, cadet, ob æqualitatem ar-
              <lb/>
            cuum AC, DF. </s>
            <s xml:id="echoid-s12065" xml:space="preserve">Baſis igitur BC, baſi EF, congruet quoq;</s>
            <s xml:id="echoid-s12066" xml:space="preserve">: alias, ſi ſupra ca
              <lb/>
            deret, aut infra, cuiuſmodi eſt arcus EGF, eſſent arcus EF, EGF, vel BC,
              <lb/>
            ſe mutuo ſecantes in E, F, ſemicitculi; </s>
            <s xml:id="echoid-s12067" xml:space="preserve">cum circuli maximi ſe mutuo ſecent
              <lb/>
              <note position="left" xlink:label="note-374-03" xlink:href="note-374-03a" xml:space="preserve">11. 1. Theod.</note>
            bifariam. </s>
            <s xml:id="echoid-s12068" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s12069" xml:space="preserve">Singuli enim ſemicirculo minores ſunt. </s>
            <s xml:id="echoid-s12070" xml:space="preserve">Quo-
              <lb/>
              <note position="left" xlink:label="note-374-04" xlink:href="note-374-04a" xml:space="preserve">a. huius.</note>
            circa baſis BC, baſi EF, æqualis erit, cum neutra alteram excedat; </s>
            <s xml:id="echoid-s12071" xml:space="preserve">& </s>
            <s xml:id="echoid-s12072" xml:space="preserve">trian
              <lb/>
            gulum ABC, triangulo DEF; </s>
            <s xml:id="echoid-s12073" xml:space="preserve">& </s>
            <s xml:id="echoid-s12074" xml:space="preserve">anguli B, C, angulis E, F, vterq; </s>
            <s xml:id="echoid-s12075" xml:space="preserve">vtrique,
              <lb/>
            æquales erunt, ob eandem cauſam. </s>
            <s xml:id="echoid-s12076" xml:space="preserve">Quare ſi duo trangula ſphærica, &</s>
            <s xml:id="echoid-s12077" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s12078" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s12079" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div948" type="section" level="1" n="493">
          <head xml:id="echoid-head528" xml:space="preserve">THEOR. 7. PROPOS. 8.</head>
          <p>
            <s xml:id="echoid-s12080" xml:space="preserve">ISOSCELIVM triangulorum ſphærico-
              <lb/>
            rum, qui ad baſim ſunt, anguli inter ſe ſunt æqua-
              <lb/>
            les: </s>
            <s xml:id="echoid-s12081" xml:space="preserve">Et productis æqualibus arcubus, qui ſub baſi
              <lb/>
            ſunt, anguli inter ſe æquales erunt.</s>
            <s xml:id="echoid-s12082" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12083" xml:space="preserve">SIT triangulum ſphæricum Iſoſceles ABC, cuius duo latera AB, AC,
              <lb/>
            æqualia ſint. </s>
            <s xml:id="echoid-s12084" xml:space="preserve">Dico angulos B, C, ſupra baſim BC, æquales eſſe: </s>
            <s xml:id="echoid-s12085" xml:space="preserve">Item ſi pro-
              <lb/>
            ducantur arcus æquales AB, AC, infra baſim BC, quantumlibet, angulos
              <lb/>
            quoque B, C, ſub baſi BC, æquales eſſe. </s>
            <s xml:id="echoid-s12086" xml:space="preserve">Quoniam enim arcus AB, ſemicir-
              <lb/>
              <note position="left" xlink:label="note-374-05" xlink:href="note-374-05a" xml:space="preserve">2. huius.</note>
            culo minor eſt, poterit in eo producto accipi adhuc arcus minor ſemicircu-
              <lb/>
            lo. </s>
            <s xml:id="echoid-s12087" xml:space="preserve">Sit igitur arcus AD, ſemicirculo minor; </s>
            <s xml:id="echoid-s12088" xml:space="preserve">& </s>
            <s xml:id="echoid-s12089" xml:space="preserve">ex arcu AE, quantumcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s12090" xml:space="preserve">
              <note position="left" xlink:label="note-374-06" xlink:href="note-374-06a" xml:space="preserve">1. huius.</note>
            producto abſcindatur arcus AF, æqualis arcui AD; </s>
            <s xml:id="echoid-s12091" xml:space="preserve">& </s>
            <s xml:id="echoid-s12092" xml:space="preserve">per duo puncta B, F,
              <lb/>
            nec non per C, D, ducantur duo arcus maximorum circulorum BF, CD.
              <lb/>
            </s>
            <s xml:id="echoid-s12093" xml:space="preserve">
              <note position="left" xlink:label="note-374-07" xlink:href="note-374-07a" xml:space="preserve">20. 1. Theo.</note>
            Quia ergo duo latera AB, AF, trianguli ABF, æqualia ſunt duobus late-
              <lb/>
            ribus AC, AD, trianguli ACD, vtrumque vtrique, continentq́; </s>
            <s xml:id="echoid-s12094" xml:space="preserve">angulum
              <lb/>
            communem A; </s>
            <s xml:id="echoid-s12095" xml:space="preserve">erit baſis BF, baſi CD, æqualis, & </s>
            <s xml:id="echoid-s12096" xml:space="preserve">anguli ABF, & </s>
            <s xml:id="echoid-s12097" xml:space="preserve">F, angu-
              <lb/>
              <note position="left" xlink:label="note-374-08" xlink:href="note-374-08a" xml:space="preserve">7. huius.</note>
            lis ACD, & </s>
            <s xml:id="echoid-s12098" xml:space="preserve">D. </s>
            <s xml:id="echoid-s12099" xml:space="preserve">Rurſus, quoniam arcus AD, AF, æquales ſunt; </s>
            <s xml:id="echoid-s12100" xml:space="preserve">ſi </s>
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