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

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        <div xml:id="echoid-div156" type="section" level="1" n="85">
          <pb o="38" file="050" n="50" rhead=""/>
          <p>
            <s xml:id="echoid-s1422" xml:space="preserve">SI in ſphæra duo circuli ſe mutuo ſecent, maximus circulus ſe-
              <lb/>
              <note position="left" xlink:label="note-050-01" xlink:href="note-050-01a" xml:space="preserve">14.</note>
            cans bifariam duo illorum ſegmenta quæcumque, habens tamen
              <lb/>
            arcum inter illa ſegmenta poſitum ſemicirculo inæqualem; </s>
            <s xml:id="echoid-s1423" xml:space="preserve">tranfit
              <lb/>
            per polos ipſorum, duoq́; </s>
            <s xml:id="echoid-s1424" xml:space="preserve">reliqua ſegmenta bifariam ſecat.</s>
            <s xml:id="echoid-s1425" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1426" xml:space="preserve">_IN_ ſphæra duo circuli _
              <emph style="sc">Ab</emph>
            CD,
              <emph style="sc">Eb</emph>
            FD,_ ſe mutuo ſecent in punctis _
              <emph style="sc">B</emph>
            , D:_ </s>
            <s xml:id="echoid-s1427" xml:space="preserve">Et
              <lb/>
              <figure xlink:label="fig-050-01" xlink:href="fig-050-01a" number="56">
                <image file="050-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/050-01"/>
              </figure>
            maximus circulus _A F C E,_ ſecet
              <lb/>
            duo quæcumque illorum ſegmẽta,
              <lb/>
            nempe, _
              <emph style="sc">B</emph>
            AD,
              <emph style="sc">B</emph>
            ED,_ bifariam
              <lb/>
            in punctis _A, E,_ & </s>
            <s xml:id="echoid-s1428" xml:space="preserve">arcus _A F C E,_
              <lb/>
            interceptus inter dicta ſegmenta
              <lb/>
            non ſit ſemicirculus. </s>
            <s xml:id="echoid-s1429" xml:space="preserve">Dico circu-
              <lb/>
            lum _A F C E,_ tranſire per polos
              <lb/>
            circulorum _
              <emph style="sc">Ab</emph>
            CD,
              <emph style="sc">Eb</emph>
            FD,_
              <lb/>
            ſecareé; </s>
            <s xml:id="echoid-s1430" xml:space="preserve">reliqua ſegmenta _
              <emph style="sc">B</emph>
            CD,_
              <lb/>
            _
              <emph style="sc">B</emph>
            FD,_ bifariam. </s>
            <s xml:id="echoid-s1431" xml:space="preserve">Si enim circulus
              <lb/>
            _A F C E,_ non tranſeat per ipſorũ
              <lb/>
            polos, deſcribatur, ſi fieri poteſt,
              <lb/>
            alius circulus maximus _A G E,_ per
              <lb/>
            eorum polos, qui ſegmenta ipſo-
              <lb/>
            rum bifariam ſecabit; </s>
            <s xml:id="echoid-s1432" xml:space="preserve">atque adeo per puncta _A, E,_ tranſibit. </s>
            <s xml:id="echoid-s1433" xml:space="preserve">Secabunt ſe igitur cir
              <lb/>
              <note position="left" xlink:label="note-050-02" xlink:href="note-050-02a" xml:space="preserve">9. huius.</note>
              <note position="left" xlink:label="note-050-03" xlink:href="note-050-03a" xml:space="preserve">11. 1. huius.</note>
            culi maximi _A F C E, A G E,_ in _A, E,_ bifariam: </s>
            <s xml:id="echoid-s1434" xml:space="preserve">ac propterea ſemicirculus erit
              <lb/>
            _AFCE._ </s>
            <s xml:id="echoid-s1435" xml:space="preserve">Quod eſt contra hypotheſim. </s>
            <s xml:id="echoid-s1436" xml:space="preserve">Tranſit ergo circulus _A F C E,_ per polos cir-
              <lb/>
              <note position="left" xlink:label="note-050-04" xlink:href="note-050-04a" xml:space="preserve">9. huius.</note>
            culorum _A B C D,
              <emph style="sc">Eb</emph>
            FD._ </s>
            <s xml:id="echoid-s1437" xml:space="preserve">Quare omnia ſegmenta ipſorum ſecabit bifariam. </s>
            <s xml:id="echoid-s1438" xml:space="preserve">Quod
              <lb/>
            eſt propoſitum.</s>
            <s xml:id="echoid-s1439" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div161" type="section" level="1" n="86">
          <head xml:id="echoid-head98" xml:space="preserve">THEOR, 10. PROP. 10.</head>
          <note position="left" xml:space="preserve">15.</note>
          <p>
            <s xml:id="echoid-s1440" xml:space="preserve">SI ſint in ſphæra paralleli circuli, per quo-
              <lb/>
            rum polos deſcribantur maximi circuli; </s>
            <s xml:id="echoid-s1441" xml:space="preserve">paralle-
              <lb/>
            lorum quidem circunferentiæ inter maximos cir-
              <lb/>
            culos interceptæ, ſimiles ſunt; </s>
            <s xml:id="echoid-s1442" xml:space="preserve">maximorum autem
              <lb/>
            circulorum circunferentiæ inter parallelos circu-
              <lb/>
            los interceptæ, ſuntæ quales.</s>
            <s xml:id="echoid-s1443" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1444" xml:space="preserve">SINT in ſphæra circuli paralleli A B C D, E F G H, quorũ polus I:</s>
            <s xml:id="echoid-s1445" xml:space="preserve">(ſunt
              <lb/>
            enim paralleli circuli in ſphæra circa eoſdem polos.) </s>
            <s xml:id="echoid-s1446" xml:space="preserve">Per I, autẽ circuli maxi
              <lb/>
              <note position="left" xlink:label="note-050-06" xlink:href="note-050-06a" xml:space="preserve">1. huius.</note>
            mi deſcribantur vtcumque A E I G C, B F I H D. </s>
            <s xml:id="echoid-s1447" xml:space="preserve">Dico circunferentias paral-
              <lb/>
            lelorum A B, E F, ſimiles, nec non B C, F G; </s>
            <s xml:id="echoid-s1448" xml:space="preserve">Item C D, G H; </s>
            <s xml:id="echoid-s1449" xml:space="preserve">& </s>
            <s xml:id="echoid-s1450" xml:space="preserve">D A, H E:</s>
            <s xml:id="echoid-s1451" xml:space="preserve"/>
          </p>
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