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

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        <div xml:id="echoid-div161" type="section" level="1" n="86">
          <p>
            <s xml:id="echoid-s1451" xml:space="preserve">
              <pb o="39" file="051" n="51" rhead=""/>
            circunferentias vero maximorum circulorum inter parallelos, nempe A E,
              <lb/>
            B F, C G, D H, æquales eſſe. </s>
            <s xml:id="echoid-s1452" xml:space="preserve">Sintenim communes ſectiones circuli A I C, & </s>
            <s xml:id="echoid-s1453" xml:space="preserve">
              <lb/>
            parallelorum rectæ A C, E G, quæ parallelæ erunt: </s>
            <s xml:id="echoid-s1454" xml:space="preserve">communes vero ſectiones
              <lb/>
              <note position="right" xlink:label="note-051-01" xlink:href="note-051-01a" xml:space="preserve">16. vndec.</note>
            circuli B I D, & </s>
            <s xml:id="echoid-s1455" xml:space="preserve">parallelorum eorundem, rectæ B D, F H, quæ ſimiliter pa-
              <lb/>
              <figure xlink:label="fig-051-01" xlink:href="fig-051-01a" number="57">
                <image file="051-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/051-01"/>
              </figure>
            rallelæ erũt. </s>
            <s xml:id="echoid-s1456" xml:space="preserve">Et quia circuli maximi A I C,
              <lb/>
            B I D, per polos parallelorum deſcripti ſe-
              <lb/>
            cant parallelos bifariam; </s>
            <s xml:id="echoid-s1457" xml:space="preserve">erunt A C, B D,
              <lb/>
              <note position="right" xlink:label="note-051-02" xlink:href="note-051-02a" xml:space="preserve">15. 1. huius.</note>
            diametri circuli A B C D, & </s>
            <s xml:id="echoid-s1458" xml:space="preserve">punctum L, vbi
              <lb/>
            ſe interſecant, centrũ eiuſdem: </s>
            <s xml:id="echoid-s1459" xml:space="preserve">Item E G,
              <lb/>
            F H, diametri circuli E F G H, & </s>
            <s xml:id="echoid-s1460" xml:space="preserve">punctum
              <lb/>
            K, vbi ſe interſecant, centrum eiuſdẽ. </s>
            <s xml:id="echoid-s1461" xml:space="preserve">Quo
              <lb/>
            niam igitur rectæ E K, K F, rectis A L, L B,
              <lb/>
            parallelæ ſunt, ſuntq́; </s>
            <s xml:id="echoid-s1462" xml:space="preserve">in diuerſis planis, e-
              <lb/>
            runt anguli E K F, A L B, ad centra K, L,
              <lb/>
              <note position="right" xlink:label="note-051-03" xlink:href="note-051-03a" xml:space="preserve">10. vndeo.</note>
            æquales. </s>
            <s xml:id="echoid-s1463" xml:space="preserve">Quare circunſerentiæ A B, E F,
              <lb/>
            per ea, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s1464" xml:space="preserve">33. </s>
            <s xml:id="echoid-s1465" xml:space="preserve">lib 6. </s>
            <s xml:id="echoid-s1466" xml:space="preserve">Eu-
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            clid. </s>
            <s xml:id="echoid-s1467" xml:space="preserve">oſtendimus, ſimiles erunt. </s>
            <s xml:id="echoid-s1468" xml:space="preserve">Eodemq́;
              <lb/>
            </s>
            <s xml:id="echoid-s1469" xml:space="preserve">modo ſimiles erunt B C, F G, & </s>
            <s xml:id="echoid-s1470" xml:space="preserve">C D, G H, nec non D A, H E.</s>
            <s xml:id="echoid-s1471" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1472" xml:space="preserve">RVRSVS, quia rectæ ex polo I, ad puncta A, B, C, D, demiſſæ æquales
              <lb/>
            ſunt, ex defin. </s>
            <s xml:id="echoid-s1473" xml:space="preserve">poli, erunt quoque arcus I A, I B, I C, I D, æquales: </s>
            <s xml:id="echoid-s1474" xml:space="preserve">Et eo-
              <lb/>
              <note position="right" xlink:label="note-051-04" xlink:href="note-051-04a" xml:space="preserve">28. tertij.</note>
            dem modo æquales erunt arcus I E, I F, I G, I H. </s>
            <s xml:id="echoid-s1475" xml:space="preserve">Reliquæ igitur circunfe-
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            rentiæ A E, B F, C G, D H, æquales inter ſe erunt. </s>
            <s xml:id="echoid-s1476" xml:space="preserve">Quapropter, ſi ſint in
              <lb/>
            ſphæra paralleli circuli, &</s>
            <s xml:id="echoid-s1477" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1478" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1479" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div164" type="section" level="1" n="87">
          <head xml:id="echoid-head99" xml:space="preserve">THEOR. 11. PROP. 11</head>
          <note position="right" xml:space="preserve">16.</note>
          <p>
            <s xml:id="echoid-s1480" xml:space="preserve">SI in diametris circulorum æqualium æqua-
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            lia circulorum ſegmenta ad angulos rectos inſi-
              <lb/>
            ſtant, à quibus ſumantur æquales circunferentiæ,
              <lb/>
            quarum quælibet inchoata ab extremitate ſui ſe-
              <lb/>
            gmenti, ſit minor ſemiſſe circunferentiæ integri
              <lb/>
            ſegmenti, à punctis autem æquales circunferen-
              <lb/>
            tias terminantibus ducátur æquales rectæ lineę ad
              <lb/>
            circunferentias circulorum primo poſitorum; </s>
            <s xml:id="echoid-s1481" xml:space="preserve">ip-
              <lb/>
            ſæ circulorum primo poſitorum circunferentiæ
              <lb/>
            interceptæ inter illas rectas lineas, & </s>
            <s xml:id="echoid-s1482" xml:space="preserve">extremitates
              <lb/>
            diametrorum, erunt æquales.</s>
            <s xml:id="echoid-s1483" xml:space="preserve"/>
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