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

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            <s xml:id="echoid-s1484" xml:space="preserve">IN diametris A C, D F, circulorum æqualium A B C, D E F, inſiſtant
              <lb/>
            ipſis circulis ad angulos rectos ſegmenta circulorũ æqualia A G C, D H F:
              <lb/>
            </s>
            <s xml:id="echoid-s1485" xml:space="preserve">ſumanturq́ æquales arcus A G, D H, ita vt puncta G, H, ſecent ſegmenta
              <lb/>
            A G C, D H F, non bifariam. </s>
            <s xml:id="echoid-s1486" xml:space="preserve">Ex G, H, denique in circunferentias circulo-
              <lb/>
            rum A B C, D E F, cadant rectæ æquales G B, H E. </s>
            <s xml:id="echoid-s1487" xml:space="preserve">Dico circunferentias
              <lb/>
            A B, D E, eſſe æquales. </s>
            <s xml:id="echoid-s1488" xml:space="preserve">Demittantur ex G, H, rectæ G I, H K, ad plana cir-
              <lb/>
            culorum A B C, D E F, perpendiculares, quæ in communes ſectiones A C,
              <lb/>
              <note position="left" xlink:label="note-052-01" xlink:href="note-052-01a" xml:space="preserve">11. vndec.</note>
            D F, cadent in puncta I, K. </s>
            <s xml:id="echoid-s1489" xml:space="preserve">Sumptis quoque L, M, centris circulorũ A B C,
              <lb/>
              <note position="left" xlink:label="note-052-02" xlink:href="note-052-02a" xml:space="preserve">33. vndec.</note>
            D E F, ducantur rectæ L B, B I, A G; </s>
            <s xml:id="echoid-s1490" xml:space="preserve">M E, E K, D H: </s>
            <s xml:id="echoid-s1491" xml:space="preserve">cadantq́; </s>
            <s xml:id="echoid-s1492" xml:space="preserve">primum pun
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            cta I, K, in ſemidiametros A L, D M. </s>
            <s xml:id="echoid-s1493" xml:space="preserve">Quoniam igitur arcus A G C, D H F,
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            æquales ſunt, nec non & </s>
            <s xml:id="echoid-s1494" xml:space="preserve">arcus A G, D H; </s>
            <s xml:id="echoid-s1495" xml:space="preserve">æquales quoque erunt arcus, C G,
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            F H; </s>
            <s xml:id="echoid-s1496" xml:space="preserve">ac propterea anguli G A C, H D F, illis inſiſtentes æquales. </s>
            <s xml:id="echoid-s1497" xml:space="preserve">Sunt autem
              <lb/>
              <note position="left" xlink:label="note-052-03" xlink:href="note-052-03a" xml:space="preserve">27. tertij.</note>
            & </s>
            <s xml:id="echoid-s1498" xml:space="preserve">anguli A I G, D K H, æquales, quòd recti ſint ex defin. </s>
            <s xml:id="echoid-s1499" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1500" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1501" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1502" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1503" xml:space="preserve">Ita-
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            que duo triangula A I G, D K H, habent duos angulos G A I, A I G, duo-
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              <figure xlink:label="fig-052-01" xlink:href="fig-052-01a" number="58">
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            bus angulis H D K,
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            D K H, æquales. </s>
            <s xml:id="echoid-s1504" xml:space="preserve">Ha-
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            bent autem & </s>
            <s xml:id="echoid-s1505" xml:space="preserve">latus
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            A G, lateri D H, ęqua
              <lb/>
              <note position="left" xlink:label="note-052-04" xlink:href="note-052-04a" xml:space="preserve">29. tertij.</note>
            le, (ob æqualitatẽ ar
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            cuum A G, D H.)
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            </s>
            <s xml:id="echoid-s1506" xml:space="preserve">quod angulis æquali-
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            bus I, K, ſubtenditur. </s>
            <s xml:id="echoid-s1507" xml:space="preserve">
              <lb/>
            Igitur & </s>
            <s xml:id="echoid-s1508" xml:space="preserve">latus A I, la
              <lb/>
              <note position="left" xlink:label="note-052-05" xlink:href="note-052-05a" xml:space="preserve">26. primi.</note>
            teri D K, & </s>
            <s xml:id="echoid-s1509" xml:space="preserve">latus G I,
              <lb/>
            lateri H K, æquale e-
              <lb/>
            rit. </s>
            <s xml:id="echoid-s1510" xml:space="preserve">Quoniam vero an
              <lb/>
            guli G I B, H K E, re
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            cti ſunt ex defin. </s>
            <s xml:id="echoid-s1511" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1512" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1513" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1514" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1515" xml:space="preserve">erunt quadrata ex G B, H E, quæ inter ſe æ-
              <lb/>
              <note position="left" xlink:label="note-052-06" xlink:href="note-052-06a" xml:space="preserve">47. primi.</note>
            qualia ſunt, ob æqualitatem rectarum G B, H E, quadratis ex G I, I B, & </s>
            <s xml:id="echoid-s1516" xml:space="preserve">ex
              <lb/>
            H K, K E, æqualia, ac {pro}pterea quadrata ex G I, I B, quadratis ex H K, K E,
              <lb/>
            æqualia erunt. </s>
            <s xml:id="echoid-s1517" xml:space="preserve">Ablatis ergo quadratis æqualibus rectarum æqualiũ G I, H K,
              <lb/>
            remanebunt quadrata rectarũ I B, K E, æqualia; </s>
            <s xml:id="echoid-s1518" xml:space="preserve">& </s>
            <s xml:id="echoid-s1519" xml:space="preserve">idcirco & </s>
            <s xml:id="echoid-s1520" xml:space="preserve">rectæ I B, K E,
              <lb/>
            æquales. </s>
            <s xml:id="echoid-s1521" xml:space="preserve">Et quia A L, D M, ſemidiametri circulorum æqualiũ æquales ſunt;
              <lb/>
            </s>
            <s xml:id="echoid-s1522" xml:space="preserve">oſtenſæ autem quoque ſunt æquales A I, D K, erunt & </s>
            <s xml:id="echoid-s1523" xml:space="preserve">reliquæ I L, K M, æ-
              <lb/>
            quales. </s>
            <s xml:id="echoid-s1524" xml:space="preserve">Quare latera I L, L B, lateribus K M, M E, æqualia erunt: </s>
            <s xml:id="echoid-s1525" xml:space="preserve">ſunt au
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            tem & </s>
            <s xml:id="echoid-s1526" xml:space="preserve">baſes I B, K E, oſtenſæ æquales. </s>
            <s xml:id="echoid-s1527" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s1528" xml:space="preserve">anguli L, M, ad centra æqua
              <lb/>
              <note position="left" xlink:label="note-052-07" xlink:href="note-052-07a" xml:space="preserve">8. primi.</note>
            les erunt; </s>
            <s xml:id="echoid-s1529" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s1530" xml:space="preserve">arcus A B, D E, æquales erunt.</s>
            <s xml:id="echoid-s1531" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">26. tertij.</note>
          <p>
            <s xml:id="echoid-s1532" xml:space="preserve">CADANT deinde puncta I, K, in ſemidiametros L A, M D, produ-
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            ctas ad A, & </s>
            <s xml:id="echoid-s1533" xml:space="preserve">D: </s>
            <s xml:id="echoid-s1534" xml:space="preserve">quod quidem contingere poteſt, quando ſegmenta A G C,
              <lb/>
            D H F, ſemicirculo ſunt maiora; </s>
            <s xml:id="echoid-s1535" xml:space="preserve">fiatq́; </s>
            <s xml:id="echoid-s1536" xml:space="preserve">eadem conſtructio, quæ prius. </s>
            <s xml:id="echoid-s1537" xml:space="preserve">Oſten
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            demus, vt prius, angulos G A C, H D F, eſſe æquales; </s>
            <s xml:id="echoid-s1538" xml:space="preserve">ac propterea cum tam
              <lb/>
              <note position="left" xlink:label="note-052-09" xlink:href="note-052-09a" xml:space="preserve">27. tertij.</note>
            G A C, G A I, quàm H D F, H D K, duobus ſint rectis æquales, erũt & </s>
            <s xml:id="echoid-s1539" xml:space="preserve">G A I,
              <lb/>
              <note position="left" xlink:label="note-052-10" xlink:href="note-052-10a" xml:space="preserve">13. primi.</note>
            H D K, æquales. </s>
            <s xml:id="echoid-s1540" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s1541" xml:space="preserve">anguli I, K, æquales ſint, nempe recti, & </s>
            <s xml:id="echoid-s1542" xml:space="preserve">late
              <lb/>
            ra G A, H D, æqualia, ob æquales arcus A G, D H, erunt, vt prius, rectæ
              <lb/>
              <note position="left" xlink:label="note-052-11" xlink:href="note-052-11a" xml:space="preserve">29. tertij.</note>
            G I, I A, rectis H K, K D, æquales; </s>
            <s xml:id="echoid-s1543" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s1544" xml:space="preserve">totæ I L, K M, inter ſe
              <lb/>
              <note position="left" xlink:label="note-052-12" xlink:href="note-052-12a" xml:space="preserve">26. primi.</note>
            æquales erunt. </s>
            <s xml:id="echoid-s1545" xml:space="preserve">Igitur, vt prius, oſtendemus rectam I B, rectæ K E, & </s>
            <s xml:id="echoid-s1546" xml:space="preserve">angu-
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            lum L, angulo M, æqualem eſſe: </s>
            <s xml:id="echoid-s1547" xml:space="preserve">ac denique arcum A B, arcui D E.</s>
            <s xml:id="echoid-s1548" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">47. primi.</note>
          <note position="left" xml:space="preserve">8. primi.</note>
          <p>
            <s xml:id="echoid-s1549" xml:space="preserve">CADANT tertio perpendiculares ex G, H, demiſſæ in plana circulo-
              <lb/>
              <note position="left" xlink:label="note-052-15" xlink:href="note-052-15a" xml:space="preserve">26. tertij.</note>
            </s>
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