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

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        <div xml:id="echoid-div110" type="section" level="1" n="62">
          <head xml:id="echoid-head73" xml:space="preserve">PROBL. 5. PROP. 21.</head>
          <note position="right" xml:space="preserve">32.</note>
          <p>
            <s xml:id="echoid-s994" xml:space="preserve">CVIVSLIBET circuli in ſphæra dati po-
              <lb/>
            lum inuenire.</s>
            <s xml:id="echoid-s995" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s996" xml:space="preserve">SIT inueniendus polus circuli A B, in ſphæra dati, ſitq́; </s>
            <s xml:id="echoid-s997" xml:space="preserve">primum circu-
              <lb/>
            lus A B, non maximus. </s>
            <s xml:id="echoid-s998" xml:space="preserve">Sumptis duobus punctis in circunferentia vtcumque
              <lb/>
            C, D, diuidatur vterque arcus C A D, C B D, bifariam in A, & </s>
            <s xml:id="echoid-s999" xml:space="preserve">B, punctis, per
              <lb/>
              <note position="right" xlink:label="note-039-02" xlink:href="note-039-02a" xml:space="preserve">30. tertij.</note>
            quæ deſcribatur maximus circulus A E B; </s>
            <s xml:id="echoid-s1000" xml:space="preserve">ſeceturq́; </s>
            <s xml:id="echoid-s1001" xml:space="preserve">arcus A E B, bifariam
              <lb/>
              <note position="right" xlink:label="note-039-03" xlink:href="note-039-03a" xml:space="preserve">20. huius.</note>
            in E. </s>
            <s xml:id="echoid-s1002" xml:space="preserve">Dico E, polum eſſe circuli A B; </s>
            <s xml:id="echoid-s1003" xml:space="preserve">Quoniam enim arcus A C, A D, æqua-
              <lb/>
            les ſunt, necnon B C, B D, erunt toti arcus A C B, A D B, æquales. </s>
            <s xml:id="echoid-s1004" xml:space="preserve">Qua-
              <lb/>
              <figure xlink:label="fig-039-01" xlink:href="fig-039-01a" number="39">
                <image file="039-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/039-01"/>
              </figure>
            re maximus circulus
              <lb/>
            A E B, cum circulum
              <lb/>
            non maximum A B,
              <lb/>
            bifariam ſecet in A,
              <lb/>
            & </s>
            <s xml:id="echoid-s1005" xml:space="preserve">B, ſecabit eum per
              <lb/>
            polos. </s>
            <s xml:id="echoid-s1006" xml:space="preserve">Punctum ergo
              <lb/>
              <note position="right" xlink:label="note-039-04" xlink:href="note-039-04a" xml:space="preserve">14. huius.</note>
            E, æqualiter diſtans
              <lb/>
            a circunferentia cir-
              <lb/>
            culi A B, polus eſt cir
              <lb/>
            culi A B. </s>
            <s xml:id="echoid-s1007" xml:space="preserve">Eodem mo-
              <lb/>
            do ſi reliquus arcus
              <lb/>
            A F B, ſecetur bifa-
              <lb/>
            riam in F, erit F, al-
              <lb/>
            ter polus circuli A B.</s>
            <s xml:id="echoid-s1008" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1009" xml:space="preserve">SED ſit iam datus circulus A B, maximus. </s>
            <s xml:id="echoid-s1010" xml:space="preserve">Sumptis rurſus punctis C, D,
              <lb/>
            vtcumque, & </s>
            <s xml:id="echoid-s1011" xml:space="preserve">diuiſis arcubus C A D, C B D, bifariam in A, B, oſtendemus,
              <lb/>
              <note position="right" xlink:label="note-039-05" xlink:href="note-039-05a" xml:space="preserve">30. tertij.</note>
            vt prius, totos arcus A C B, A D B, eſſe æquales, ac propterea vtrumque eſ
              <lb/>
            ſe ſemicirculũ circuli maximi. </s>
            <s xml:id="echoid-s1012" xml:space="preserve">Diuiſo ergo altero ſemicirculo, nempe A C B,
              <lb/>
            bifariam in G, erit recta G A, ſubtendens quadrantem circuli, latus quadrati
              <lb/>
            in maximo circulo A B, deſcripti; </s>
            <s xml:id="echoid-s1013" xml:space="preserve">vt ex prop.</s>
            <s xml:id="echoid-s1014" xml:space="preserve">6.</s>
            <s xml:id="echoid-s1015" xml:space="preserve">lib.</s>
            <s xml:id="echoid-s1016" xml:space="preserve">4.</s>
            <s xml:id="echoid-s1017" xml:space="preserve">Eucl.</s>
            <s xml:id="echoid-s1018" xml:space="preserve">cõſtat. </s>
            <s xml:id="echoid-s1019" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s1020" xml:space="preserve">ex po
              <lb/>
            lo G, & </s>
            <s xml:id="echoid-s1021" xml:space="preserve">in teruallo G A, circulus deſcribatur A E B, qui maximus erit, cũ recta
              <lb/>
              <note position="right" xlink:label="note-039-06" xlink:href="note-039-06a" xml:space="preserve">17. huius.</note>
            ex G, polo ad eius circunſerentiã ducta nimirũ ad punctũ A, ſit æqualis lateri
              <lb/>
            quadrati in circulo maximo A B, deſcripti, Diuidatur deniq; </s>
            <s xml:id="echoid-s1022" xml:space="preserve">arcus A E B, biſa
              <lb/>
            riam in E. </s>
            <s xml:id="echoid-s1023" xml:space="preserve">Dico E, polum eſſe circuli A B. </s>
            <s xml:id="echoid-s1024" xml:space="preserve">Cum enim maximus circulus A C B,
              <lb/>
            tranſeat per G, polum maximi circuli A E B, tranſibit viciſsim maximus cir
              <lb/>
              <note position="right" xlink:label="note-039-07" xlink:href="note-039-07a" xml:space="preserve">Schol. 15.
                <lb/>
              huius.</note>
            culus A E B, per polos maximi circuli A C B. </s>
            <s xml:id="echoid-s1025" xml:space="preserve">Quare punctum E, æqualiter
              <lb/>
            remotum à circunferentia circuli A C B, polus eſt circuli A C B. </s>
            <s xml:id="echoid-s1026" xml:space="preserve">Eodem mo
              <lb/>
            do diuiſo arcu A F B, bifariam in F, erit F, alter polus circuli A C B. </s>
            <s xml:id="echoid-s1027" xml:space="preserve">Cuiuſli
              <lb/>
            bet ergo circuli in ſphæra dati polum inuenimus. </s>
            <s xml:id="echoid-s1028" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s1029" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div113" type="section" level="1" n="63">
          <head xml:id="echoid-head74" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1030" xml:space="preserve">_IN_ alia verſione demonſtrantur ſequentia duo theoremata.</s>
            <s xml:id="echoid-s1031" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div114" type="section" level="1" n="64">
          <head xml:id="echoid-head75" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s1032" xml:space="preserve">SI in ſuperſicie ſphæræ acceptum fuerit punctum aliquod, & </s>
            <s xml:id="echoid-s1033" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-039-08" xlink:href="note-039-08a" xml:space="preserve">33.</note>
            </s>
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