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

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        <div xml:id="echoid-div237" type="section" level="1" n="112">
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            <s xml:id="echoid-s2645" xml:space="preserve">
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            cunferentia A F B, in F, in partes inæquales, & </s>
            <s xml:id="echoid-s2646" xml:space="preserve">ſit F B, minor. </s>
            <s xml:id="echoid-s2647" xml:space="preserve">Ex F, demitta-
              <lb/>
            tur in planum circuli A C B D, perpendicularis F L, quæ ad partes ſegmenti
              <lb/>
            A D B, cadet, propterea quod ſegmentum A F B, ad ſegmentum A D C, eſt
              <lb/>
            inclinatum, ita vt punctum L, ſit vel intra ſegmentum A D B, vel extra, vel
              <lb/>
            certe in ipſa circunferentia A D B. </s>
            <s xml:id="echoid-s2648" xml:space="preserve">Per centrum autem E, & </s>
            <s xml:id="echoid-s2649" xml:space="preserve">punctum L, dia-
              <lb/>
            meter agatur C D, & </s>
            <s xml:id="echoid-s2650" xml:space="preserve">ex F, in circunferentiam A C B, plurimæ rectæ cadant
              <lb/>
            F B, F G, &</s>
            <s xml:id="echoid-s2651" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2652" xml:space="preserve">Dico omnium minimam eſſe F B; </s>
            <s xml:id="echoid-s2653" xml:space="preserve">& </s>
            <s xml:id="echoid-s2654" xml:space="preserve">F G, minorem quàm F H:
              <lb/>
            </s>
            <s xml:id="echoid-s2655" xml:space="preserve">omnium autem maximam eſſe F C: </s>
            <s xml:id="echoid-s2656" xml:space="preserve">Item F A, eſſe omnium minimam, quæ ex
              <lb/>
            F, in circunferentiam A C, cadunt; </s>
            <s xml:id="echoid-s2657" xml:space="preserve">& </s>
            <s xml:id="echoid-s2658" xml:space="preserve">F I, minorem quàm F K. </s>
            <s xml:id="echoid-s2659" xml:space="preserve">Ducantur ex
              <lb/>
            L, rectæ lineæ L B, L G, L H, L A, L I, L K, eruntque omnes anguli ad L,
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            quos facit perpendicularis F L, recti, ex defin. </s>
            <s xml:id="echoid-s2660" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2661" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2662" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2663" xml:space="preserve">Eucl.</s>
            <s xml:id="echoid-s2664" xml:space="preserve"/>
          </p>
          <figure number="88">
            <image file="080-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/080-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s2665" xml:space="preserve">Quoniam igitur recta L D, eſt omnium minima, (hæc autem linea nihil eſt om
              <lb/>
              <note position="left" xlink:label="note-080-01" xlink:href="note-080-01a" xml:space="preserve">7. vel 8. vel
                <lb/>
              15. tertil.</note>
            nino in ea figura, vbi punctum L, cadit in D.) </s>
            <s xml:id="echoid-s2666" xml:space="preserve">& </s>
            <s xml:id="echoid-s2667" xml:space="preserve">L B, minor, quàm L G, L H,
              <lb/>
            L C, L K, L I, L A, & </s>
            <s xml:id="echoid-s2668" xml:space="preserve">omnium maxima L C, &</s>
            <s xml:id="echoid-s2669" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2670" xml:space="preserve">demonſtrabimus, vt in præ-
              <lb/>
              <note position="left" xlink:label="note-080-02" xlink:href="note-080-02a" xml:space="preserve">7. vel 8. vel
                <lb/>
              15. tertij. &
                <lb/>
              47. primi.</note>
            cedenti, rectam F B, eſſe omnium minimam, & </s>
            <s xml:id="echoid-s2671" xml:space="preserve">F G, minorem quàm F H: </s>
            <s xml:id="echoid-s2672" xml:space="preserve">Item
              <lb/>
            F C, omnium maximam, & </s>
            <s xml:id="echoid-s2673" xml:space="preserve">F A, minimam omnium ex F, in circunferentiam
              <lb/>
            A C, cadentium; </s>
            <s xml:id="echoid-s2674" xml:space="preserve">& </s>
            <s xml:id="echoid-s2675" xml:space="preserve">F I, minorem quàm F K. </s>
            <s xml:id="echoid-s2676" xml:space="preserve">Si igitur recta linea ſecans circu-
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            lum, &</s>
            <s xml:id="echoid-s2677" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2678" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s2679" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div239" type="section" level="1" n="113">
          <head xml:id="echoid-head127" xml:space="preserve">THEOREMA 3. PROPOS. 3.</head>
          <p>
            <s xml:id="echoid-s2680" xml:space="preserve">SI in ſphæra duo circuli maximi ſe mutuo ſe-
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            cent, ab eorum verò vtroque æquales circunfe-
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            rentiæ ſumantur vtrinque à puncto, in quo ſe ſe-
              <lb/>
            cant: </s>
            <s xml:id="echoid-s2681" xml:space="preserve">Rectæ lineæ, quæ extrema puncta circunfe-
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            rentiarum connectunt ad eaſdem partes, æquales
              <lb/>
            inter ſe ſunt.</s>
            <s xml:id="echoid-s2682" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2683" xml:space="preserve">IN ſphæra duo circuli maximi A B C, D B E, ſe mutuo ſecent in B, & </s>
            <s xml:id="echoid-s2684" xml:space="preserve">in
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            vno quoque vtrinque à B, ſumantur duo arcus æquales B A, B C, & </s>
            <s xml:id="echoid-s2685" xml:space="preserve">B D, B </s>
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