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

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            <s xml:id="echoid-s12010" xml:space="preserve">
              <pb o="361" file="373" n="373" rhead=""/>
            gulus ABC, duobus angulis ABE, EBC, æqualis eſt, appoſito communi an-
              <lb/>
            gulo ABD, erunt duo anguli ABC, ABD, tribus angulis DBA, ABE,
              <lb/>
            EBC, æquales. </s>
            <s xml:id="echoid-s12011" xml:space="preserve">Sed eiſdem his tribus oſtenſum fuit eſſe etiam æquales duos
              <lb/>
            rectos EBD, EBC; </s>
            <s xml:id="echoid-s12012" xml:space="preserve">quæ autem eidem æqualia, inter ſe ſunt æqualia. </s>
            <s xml:id="echoid-s12013" xml:space="preserve">Duo
              <lb/>
            igitur anguli ABC, ABD, æquales ſunt duobus rectis EBD, EBC. </s>
            <s xml:id="echoid-s12014" xml:space="preserve">Cum
              <lb/>
            ergo arcus circuli maximi in ſphæra, &</s>
            <s xml:id="echoid-s12015" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12016" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s12017" xml:space="preserve"/>
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        <div xml:id="echoid-div942" type="section" level="1" n="490">
          <head xml:id="echoid-head525" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s12018" xml:space="preserve">SEQVITVR ex his, duos arcus duorum angulorum, qui
              <lb/>
              <figure xlink:label="fig-373-01" xlink:href="fig-373-01a" number="201">
                <image file="373-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/373-01"/>
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            duobus rectis angulis ſunt æquales, hoc eſt, qui ab ateu circuli
              <lb/>
            maximi arcui alterius cireuli maximi inſiſtente efficiuntur, qua
              <lb/>
            les ſunt duo anguli ABC, ABD, ſemicireulum conſtituere. </s>
            <s xml:id="echoid-s12019" xml:space="preserve">Nam
              <lb/>
            ſi ex polo B, circulus maximus deſeribatur CAD, erunt, ex
              <lb/>
            defin. </s>
            <s xml:id="echoid-s12020" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12021" xml:space="preserve">CA, AD, arcus angulorum ABC, ABD, Perſpicuum
              <lb/>
            autem eſt, arcus CA, AD, ſemicirculum conſicere; </s>
            <s xml:id="echoid-s12022" xml:space="preserve">cum circuli
              <lb/>
            maximi CBD, CAD, ſe mutuo ſecent bifariam in C, D.</s>
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          <note position="right" xml:space="preserve">11. 1. Theod.</note>
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        <div xml:id="echoid-div944" type="section" level="1" n="491">
          <head xml:id="echoid-head526" xml:space="preserve">THEOR. 5. PROPOS. 6.</head>
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            <s xml:id="echoid-s12024" xml:space="preserve">SI duo arcus circulorum maximorũ in ſphæ-
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            ra ſe mutuo ſecuerint, angulos ad verticem æqua-
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            les inter ſe efficient.</s>
            <s xml:id="echoid-s12025" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12026" xml:space="preserve">SECENT ſe duo arcus AB, CD, circulorum maximorum in ſphæra
              <lb/>
            in E, vtcunque. </s>
            <s xml:id="echoid-s12027" xml:space="preserve">Dico angulos, quos faciunt ad verticem E, inter ſe eſſe æqua-
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            les; </s>
            <s xml:id="echoid-s12028" xml:space="preserve">angulum videlicet AED, angulo BEC,
              <lb/>
              <figure xlink:label="fig-373-02" xlink:href="fig-373-02a" number="202">
                <image file="373-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/373-02"/>
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            & </s>
            <s xml:id="echoid-s12029" xml:space="preserve">angulum AEC, angulo BED. </s>
            <s xml:id="echoid-s12030" xml:space="preserve">Quoniam
              <lb/>
            enim tam anguli AED, DEB, quàm angu-
              <lb/>
              <note position="right" xlink:label="note-373-02" xlink:href="note-373-02a" xml:space="preserve">5. huius.</note>
            li DEB, BEC, duobus ſunt rectis æquales,
              <lb/>
            erunt illi duo his duobus æquales: </s>
            <s xml:id="echoid-s12031" xml:space="preserve">ablato
              <lb/>
            ergo communi angulo DEB, remanebit
              <lb/>
            angulus AED, angulo BEC, æqualis. </s>
            <s xml:id="echoid-s12032" xml:space="preserve">Ea-
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            demque ratione conſirmabimus, angulum
              <lb/>
            AEC, angulo BED, æqualem eſſe. </s>
            <s xml:id="echoid-s12033" xml:space="preserve">Si duo
              <lb/>
            ergo arcus circulorum maximorum, &</s>
            <s xml:id="echoid-s12034" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12035" xml:space="preserve">Quod oſtendendum erat.</s>
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        <div xml:id="echoid-div946" type="section" level="1" n="492">
          <head xml:id="echoid-head527" xml:space="preserve">THEOR. 6. PROPOS. 7.</head>
          <p>
            <s xml:id="echoid-s12037" xml:space="preserve">SI duo triangula ſphærica duo latera duobus
              <lb/>
            lateribus æqualia habeant, vtrumque vtrique; </s>
            <s xml:id="echoid-s12038" xml:space="preserve">ha-
              <lb/>
            beant verò & </s>
            <s xml:id="echoid-s12039" xml:space="preserve">angulum angulo æqualẽ ſub æqua-
              <lb/>
            libus arcubus contentũ: </s>
            <s xml:id="echoid-s12040" xml:space="preserve">Et baſim baſi æqualem ha
              <lb/>
            bebunt; </s>
            <s xml:id="echoid-s12041" xml:space="preserve">eritque triangulũ triangulo æquale, ac re-
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            liqui anguli reliquis angulis æquales erunt, vterq;
              <lb/>
            </s>
            <s xml:id="echoid-s12042" xml:space="preserve">vtrique, ſub quibus æqualia latera ſubtenduntur.</s>
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