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

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        <div xml:id="echoid-div138" type="section" level="1" n="76">
          <p>
            <s xml:id="echoid-s1215" xml:space="preserve">
              <pb o="33" file="045" n="45" rhead=""/>
            ximus circulus deſcriptus per vnius polos, & </s>
            <s xml:id="echoid-s1216" xml:space="preserve">per
              <lb/>
            contactum amborum circulorũ, per reliqui quo-
              <lb/>
            que circuli polos tranſibit.</s>
            <s xml:id="echoid-s1217" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1218" xml:space="preserve">IN ſphæra duo circuli A B, C B, tangãt ſe mutuo in B, ſintq́ D, E, poli
              <lb/>
            ipſorum. </s>
            <s xml:id="echoid-s1219" xml:space="preserve">Dico maximum circulum per D, polum circuli A B, & </s>
            <s xml:id="echoid-s1220" xml:space="preserve">per conta-
              <lb/>
            ctum B, deſcriptum tranſire quoque per E, polum circuli C B. </s>
            <s xml:id="echoid-s1221" xml:space="preserve">Si enim fieri
              <lb/>
            poteſt, non tranſeat per E, ſed per aliud quoduis punctum F, cuiuſmodi eſt
              <lb/>
            circulus maximus D B F: </s>
            <s xml:id="echoid-s1222" xml:space="preserve">Et per polos D, E, maximus circulus deſcribatur
              <lb/>
              <figure xlink:label="fig-045-01" xlink:href="fig-045-01a" number="50">
                <image file="045-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/045-01"/>
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              <note position="right" xlink:label="note-045-01" xlink:href="note-045-01a" xml:space="preserve">20. 1. huius.</note>
            D E, qui omnino per conta-
              <lb/>
              <note position="right" xlink:label="note-045-02" xlink:href="note-045-02a" xml:space="preserve">4. huius.</note>
            ctum B, tranſibit; </s>
            <s xml:id="echoid-s1223" xml:space="preserve">atque adeo
              <lb/>
            duo circuli maximi D B F,
              <lb/>
            D B E, ſe mutuo ſecabuntin
              <lb/>
            D, & </s>
            <s xml:id="echoid-s1224" xml:space="preserve">B, ac proinde bifariam.
              <lb/>
            </s>
            <s xml:id="echoid-s1225" xml:space="preserve">
              <note position="right" xlink:label="note-045-03" xlink:href="note-045-03a" xml:space="preserve">11. 1. huius.</note>
            Semicirculus ergo erit vterq;
              <lb/>
            </s>
            <s xml:id="echoid-s1226" xml:space="preserve">arcus D B. </s>
            <s xml:id="echoid-s1227" xml:space="preserve">Quoniam vero cir
              <lb/>
            culus maximus per alterũ po-
              <lb/>
            lorũ cuiuſlibet circuli in ſphæ
              <lb/>
            ra tranſiens, tranſit quoque
              <lb/>
              <note position="right" xlink:label="note-045-04" xlink:href="note-045-04a" xml:space="preserve">Coroll. 10.
                <lb/>
              1. huius.</note>
            per reliquum polum, eſtq́; </s>
            <s xml:id="echoid-s1228" xml:space="preserve">in-
              <lb/>
            ter duos polos eiuſdem circu-
              <lb/>
            li ſemicirculus circuli maximi
              <lb/>
            interpoſitus; </s>
            <s xml:id="echoid-s1229" xml:space="preserve">fit, vt exiſtente D, vno polorum circuli A B, punctum B, ſit al
              <lb/>
            ter polus. </s>
            <s xml:id="echoid-s1230" xml:space="preserve">Quod eſt abſurdũ. </s>
            <s xml:id="echoid-s1231" xml:space="preserve">Eſt enim B, in circunferentia circuli. </s>
            <s xml:id="echoid-s1232" xml:space="preserve">Tranſit
              <lb/>
            igitur circulus maximus D B, per E. </s>
            <s xml:id="echoid-s1233" xml:space="preserve">Quocirca, ſi in ſphæra duo circuliſe
              <lb/>
            mutuo tangant, &</s>
            <s xml:id="echoid-s1234" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1235" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s1236" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div140" type="section" level="1" n="77">
          <head xml:id="echoid-head89" xml:space="preserve">THEOREMA 6. PROPOS. 6.</head>
          <note position="right" xml:space="preserve">7.</note>
          <p>
            <s xml:id="echoid-s1237" xml:space="preserve">SI in ſphæra maximus circulus aliquem circu
              <lb/>
            lorum in ſphęrica ſuperficie deſc@iptorum tangat,
              <lb/>
            tanget & </s>
            <s xml:id="echoid-s1238" xml:space="preserve">alterum ei æqualem, & </s>
            <s xml:id="echoid-s1239" xml:space="preserve">parallelum.</s>
            <s xml:id="echoid-s1240" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1241" xml:space="preserve">IN ſphæra maximus circulus A B, tan-
              <lb/>
              <figure xlink:label="fig-045-02" xlink:href="fig-045-02a" number="51">
                <image file="045-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/045-02"/>
              </figure>
            gat circulum A C, in A. </s>
            <s xml:id="echoid-s1242" xml:space="preserve">Dico circulũ A B,
              <lb/>
            tangere quoque alterum circulum ipſi A C,
              <lb/>
            æqualem, & </s>
            <s xml:id="echoid-s1243" xml:space="preserve">parallelum. </s>
            <s xml:id="echoid-s1244" xml:space="preserve">Sit enim D, polus
              <lb/>
              <note position="right" xlink:label="note-045-06" xlink:href="note-045-06a" xml:space="preserve">20. 1. huius.</note>
            circuli A C: </s>
            <s xml:id="echoid-s1245" xml:space="preserve">ac per D, A, circulus maximus
              <lb/>
            deſcribatur D A: </s>
            <s xml:id="echoid-s1246" xml:space="preserve">qui, cum per D, polũ cir-
              <lb/>
            culi A C, & </s>
            <s xml:id="echoid-s1247" xml:space="preserve">per contactum A, tranſeat, tran
              <lb/>
            ſibit per polos quoque circuli A B. </s>
            <s xml:id="echoid-s1248" xml:space="preserve">Aſſum-
              <lb/>
              <note position="right" xlink:label="note-045-07" xlink:href="note-045-07a" xml:space="preserve">5. huius.</note>
            pto autem E, reliquo polo circuli A C, du-
              <lb/>
            catur recta D E, quæ per centrum ſphæræ
              <lb/>
              <note position="right" xlink:label="note-045-08" xlink:href="note-045-08a" xml:space="preserve">10. 1. huius.</note>
            tranſibit, atque adeo ſphæræ diameter erit.</s>
            <s xml:id="echoid-s1249" xml:space="preserve"/>
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