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

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          <p>
            <s xml:id="echoid-s317" xml:space="preserve">
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            maximi ſunt, qui per ſphæræ centrũ ducũtur, &</s>
            <s xml:id="echoid-s318" xml:space="preserve">c. </s>
            <s xml:id="echoid-s319" xml:space="preserve">Quod erat demonſtrandũ.</s>
            <s xml:id="echoid-s320" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div41" type="section" level="1" n="29">
          <head xml:id="echoid-head40" xml:space="preserve">THEOREMA 6. PROPOS. 7.</head>
          <note position="right" xml:space="preserve">8.</note>
          <p>
            <s xml:id="echoid-s321" xml:space="preserve">SI in ſphæra ſit circulus, à centro autem ſphæ-
              <lb/>
            ræ ad centrum circuli connectatur recta linea, con
              <lb/>
            nexa linea ad circuli planum recta erit.</s>
            <s xml:id="echoid-s322" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s323" xml:space="preserve">IN ſphæra A B C, cuius centrum D, ſit circulus B F C G, cuius centrũ
              <lb/>
            E: </s>
            <s xml:id="echoid-s324" xml:space="preserve">Et recta D E, connectat duo centra D, E. </s>
            <s xml:id="echoid-s325" xml:space="preserve">Dico D E, rectam eſſe ad planũ
              <lb/>
            circuli B F C G. </s>
            <s xml:id="echoid-s326" xml:space="preserve">Ductis enim duabus diametris vtcunque B C, F G, in circu
              <lb/>
            lo, ducantur ab earum extremis ad D, centrum ſphæræ rectæ lineæ, B D,
              <lb/>
              <figure xlink:label="fig-023-01" xlink:href="fig-023-01a" number="15">
                <image file="023-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/023-01"/>
              </figure>
            C D, F D, G D, quæ omnes inter ſe æqua-
              <lb/>
            les erunt, cum à centro ſphæræ ad eius ſuper
              <lb/>
            ficiem cadant: </s>
            <s xml:id="echoid-s327" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s328" xml:space="preserve">B E, C E, F E,
              <lb/>
            G E, ſemidiametri circuli B F C G, æquales.
              <lb/>
            </s>
            <s xml:id="echoid-s329" xml:space="preserve">Igitur duo triangula D E B, D E C, duo la-
              <lb/>
            tera D E, E B, duobus lateribus D E, E C,
              <lb/>
            & </s>
            <s xml:id="echoid-s330" xml:space="preserve">baſim D B, baſi D C, æqualem habent; </s>
            <s xml:id="echoid-s331" xml:space="preserve">ex
              <lb/>
            quo fit, angulos D E B, D E C, æquales, at-
              <lb/>
              <note position="right" xlink:label="note-023-02" xlink:href="note-023-02a" xml:space="preserve">8. primi.</note>
            que adeò rectos eſſe. </s>
            <s xml:id="echoid-s332" xml:space="preserve">Recta igitur D E, rectę
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            B C, ad rectos inſiſtet angulos. </s>
            <s xml:id="echoid-s333" xml:space="preserve">Non aliter
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            oſtendemus, rectam D E, rectæ F G, ad re-
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            ctos angulos inſiſtere. </s>
            <s xml:id="echoid-s334" xml:space="preserve">Quamobrem & </s>
            <s xml:id="echoid-s335" xml:space="preserve">pla-
              <lb/>
            no circuli B F C G, per rectas B C, F G, du-
              <lb/>
              <note position="right" xlink:label="note-023-03" xlink:href="note-023-03a" xml:space="preserve">4. vndec.</note>
            cto ad rectos angulos inſiſtet. </s>
            <s xml:id="echoid-s336" xml:space="preserve">Si igitur in ſphæra ſit circulus, &</s>
            <s xml:id="echoid-s337" xml:space="preserve">c. </s>
            <s xml:id="echoid-s338" xml:space="preserve">Quod oſten
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            dendum erat.</s>
            <s xml:id="echoid-s339" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div43" type="section" level="1" n="30">
          <head xml:id="echoid-head41" xml:space="preserve">THEOREMA 7. PROPOS. 8.</head>
          <note position="right" xml:space="preserve">9.</note>
          <p>
            <s xml:id="echoid-s340" xml:space="preserve">SI ſit in ſphæra circulus, & </s>
            <s xml:id="echoid-s341" xml:space="preserve">à centro ſphæræ ad
              <lb/>
            circulũ ducatur perpendicularis, quæ ad vtramq;
              <lb/>
            </s>
            <s xml:id="echoid-s342" xml:space="preserve">partẽ producatur, cadet ea in polos ipſius circuli.</s>
            <s xml:id="echoid-s343" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s344" xml:space="preserve">IN ſphæra A B C D,
              <lb/>
              <figure xlink:label="fig-023-02" xlink:href="fig-023-02a" number="16">
                <image file="023-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/023-02"/>
              </figure>
            cuius centrum E, ſit cir-
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            culus B G D H, in cuius
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            planum à centro ſphæræ
              <lb/>
              <note position="right" xlink:label="note-023-05" xlink:href="note-023-05a" xml:space="preserve">11. vndec.</note>
            E, per pendicularis dedu
              <lb/>
            cta ſit E F, quæ in vtram-
              <lb/>
            que partem protracta ca
              <lb/>
            dat in ſuperficiem ſphæ-
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            ræ ad puncta A, C. </s>
            <s xml:id="echoid-s345" xml:space="preserve">Dico
              <lb/>
            A, C, polos eſſe circuli
              <lb/>
            BGDH. </s>
            <s xml:id="echoid-s346" xml:space="preserve">Cadet em̃ per-
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            pendicularis E F, in </s>
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