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

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            <s xml:id="echoid-s631" xml:space="preserve">
              <pb o="18" file="030" n="30" rhead=""/>
            B D, communem ſectionem cadet. </s>
            <s xml:id="echoid-s632" xml:space="preserve">Cadat autem in punctum G. </s>
            <s xml:id="echoid-s633" xml:space="preserve">Et quoniam
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              <note position="left" xlink:label="note-030-01" xlink:href="note-030-01a" xml:space="preserve">38. vndec.
                <lb/>
              Coroll. 1.
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              huius.</note>
            eadem cadit quoq; </s>
            <s xml:id="echoid-s634" xml:space="preserve">in centrum circuli B E D, erit G, centrum circuli B E D;
              <lb/>
            </s>
            <s xml:id="echoid-s635" xml:space="preserve">
              <figure xlink:label="fig-030-01" xlink:href="fig-030-01a" number="24">
                <image file="030-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/030-01"/>
              </figure>
            atq; </s>
            <s xml:id="echoid-s636" xml:space="preserve">adeo B D, per G, ducta, diameter eiuſ-
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            dem: </s>
            <s xml:id="echoid-s637" xml:space="preserve">quæ cum diuidat eirculum B E D, bi-
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            fariam, diuidet quoq; </s>
            <s xml:id="echoid-s638" xml:space="preserve">eundem bifariam cir-
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            culus maximus A B C D, per rectam B D,
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            ductus. </s>
            <s xml:id="echoid-s639" xml:space="preserve">Quod eſt primo loco propoſitum.
              <lb/>
            </s>
            <s xml:id="echoid-s640" xml:space="preserve">Quoniam verò recta F G, in plano eſt circu
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            li A B C D, cadet ea producta in circum-
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            ferentiam ad A, C, puncta, quæ in ſuperfi-
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            cie ſphæræ ſunt: </s>
            <s xml:id="echoid-s641" xml:space="preserve">cadit autem & </s>
            <s xml:id="echoid-s642" xml:space="preserve">in vtrumq; </s>
            <s xml:id="echoid-s643" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-030-02" xlink:href="note-030-02a" xml:space="preserve">8. huius.</note>
            polum circuli B E D, quòd ex F, centro
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            ſphæræ ad circuli planum perpendicularis
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            ſit ducta. </s>
            <s xml:id="echoid-s644" xml:space="preserve">Igitur A, C, poli ſunt circuli B E D,
              <lb/>
            ac proinde circulus maximus A B C D, per
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            polos circuli B E D, tranſit. </s>
            <s xml:id="echoid-s645" xml:space="preserve">quod ſecundo loco proponebatur demonſtrã-
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            dum. </s>
            <s xml:id="echoid-s646" xml:space="preserve">Si igitur in ſphæra ma ximus circulus circulum quempiam, &</s>
            <s xml:id="echoid-s647" xml:space="preserve">c. </s>
            <s xml:id="echoid-s648" xml:space="preserve">Quod
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            oſtendendum erat.</s>
            <s xml:id="echoid-s649" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div73" type="section" level="1" n="45">
          <head xml:id="echoid-head56" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s650" xml:space="preserve">_CAETERVM_ hæc propoſ. </s>
            <s xml:id="echoid-s651" xml:space="preserve">vnà cum 8. </s>
            <s xml:id="echoid-s652" xml:space="preserve">9. </s>
            <s xml:id="echoid-s653" xml:space="preserve">10. </s>
            <s xml:id="echoid-s654" xml:space="preserve">& </s>
            <s xml:id="echoid-s655" xml:space="preserve">earum ſcholijs intelligenda
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            etiam eſt, quando circulus _B D,_ maximus eſt, & </s>
            <s xml:id="echoid-s656" xml:space="preserve">per ſphæræ centrum tranſit. </s>
            <s xml:id="echoid-s657" xml:space="preserve">_E_adem
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            enim eſt ferè ſemper demonſtratio, vtperſpicuum eſt.</s>
            <s xml:id="echoid-s658" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div74" type="section" level="1" n="46">
          <head xml:id="echoid-head57" xml:space="preserve">THEOR. 13. PROPOS. 14.</head>
          <note position="left" xml:space="preserve">19.</note>
          <p>
            <s xml:id="echoid-s659" xml:space="preserve">SI in ſphæra maximus circulus circulum non
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            maximum bifariam ſecet; </s>
            <s xml:id="echoid-s660" xml:space="preserve">ad angulos rectos eum
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            ſecat, & </s>
            <s xml:id="echoid-s661" xml:space="preserve">per polos.</s>
            <s xml:id="echoid-s662" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s663" xml:space="preserve">IN ſphęra maximus circulus A B C D, non maximum B E D, ſecet bifa-
              <lb/>
              <figure xlink:label="fig-030-02" xlink:href="fig-030-02a" number="25">
                <image file="030-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/030-02"/>
              </figure>
            riam in punctis B, D, ſitq́; </s>
            <s xml:id="echoid-s664" xml:space="preserve">communis eorum
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            ſectio recta B D. </s>
            <s xml:id="echoid-s665" xml:space="preserve">Dico circulum A B C D,
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            ſecare circulum B E D, ad angulos rectos,
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            & </s>
            <s xml:id="echoid-s666" xml:space="preserve">per polos. </s>
            <s xml:id="echoid-s667" xml:space="preserve">Quia enim circulus B E D, bi
              <lb/>
            fariam ſecatur in B, D, hoc eſt, in ſemicircu
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            los, erit B D, communis ſectio diameter eius.
              <lb/>
            </s>
            <s xml:id="echoid-s668" xml:space="preserve">Diuiſa ergo B D, bifariam in F, erit F, cen-
              <lb/>
              <note position="left" xlink:label="note-030-04" xlink:href="note-030-04a" xml:space="preserve">2. huius.</note>
            trum circuli B E D. </s>
            <s xml:id="echoid-s669" xml:space="preserve">Sumpto autem G, cen
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            tro ſphæræ, quod & </s>
            <s xml:id="echoid-s670" xml:space="preserve">centrũ erit maximi cir-
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            culi A B C D, ducatur ex G, ad F, recta F G,
              <lb/>
              <note position="left" xlink:label="note-030-05" xlink:href="note-030-05a" xml:space="preserve">7. huius.</note>
            quæ perpendicularis erit ad planum circuli
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            B E D. </s>
            <s xml:id="echoid-s671" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s672" xml:space="preserve">planum circuli maximi
              <lb/>
              <note position="left" xlink:label="note-030-06" xlink:href="note-030-06a" xml:space="preserve">18. vndec.</note>
            A B C D, per rectã F G, ductum ad idẽ planũ circuli B E D, rectũ erit. </s>
            <s xml:id="echoid-s673" xml:space="preserve">Secat </s>
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