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

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            <s xml:id="echoid-s1579" xml:space="preserve">
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            rectæ A I, I G, rectis D K, K H, æquales ſunt; </s>
            <s xml:id="echoid-s1580" xml:space="preserve">& </s>
            <s xml:id="echoid-s1581" xml:space="preserve">reliquæ I L, K M, ex
              <lb/>
            ſemidiametris A L, D M, vt in prima figura, vbi puncta I, K, cadunt in ſe-
              <lb/>
            midiametros A L, D M, vel certe erunt & </s>
            <s xml:id="echoid-s1582" xml:space="preserve">totæ I L, K M, æquales, vt in ſe-
              <lb/>
            cunda figura, vbi puncta I, K, cadunt in ſemidiametros A L, D M, productas
              <lb/>
              <figure xlink:label="fig-054-01" xlink:href="fig-054-01a" number="60">
                <image file="054-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/054-01"/>
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            ad A, & </s>
            <s xml:id="echoid-s1583" xml:space="preserve">D. </s>
            <s xml:id="echoid-s1584" xml:space="preserve">Quia igit̃
              <lb/>
            I L, L B, rectis K M,
              <lb/>
            M E, æquales ſunt; </s>
            <s xml:id="echoid-s1585" xml:space="preserve">cõ
              <lb/>
            tinentq́ue angulos ad
              <lb/>
            L, M, æquales, ob æ-
              <lb/>
              <note position="left" xlink:label="note-054-01" xlink:href="note-054-01a" xml:space="preserve">27. tertij.</note>
            qualitatẽ arcuũ A B,
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            D E; </s>
            <s xml:id="echoid-s1586" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s1587" xml:space="preserve">baſes
              <lb/>
            I B, K E, æquales.
              <lb/>
            </s>
            <s xml:id="echoid-s1588" xml:space="preserve">
              <note position="left" xlink:label="note-054-02" xlink:href="note-054-02a" xml:space="preserve">4. primi.</note>
            Quamobrem cum la-
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            tera G I, I B, lateri-
              <lb/>
            bus H K, K E, æqua-
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            lia ſint, contineantq́;
              <lb/>
            </s>
            <s xml:id="echoid-s1589" xml:space="preserve">angulos G I B, H K E,
              <lb/>
            æquales, nimirum rectos, ex defin. </s>
            <s xml:id="echoid-s1590" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1591" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1592" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1593" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1594" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s1595" xml:space="preserve">baſes G B, H E, æ-
              <lb/>
              <note position="left" xlink:label="note-054-03" xlink:href="note-054-03a" xml:space="preserve">4. primi.</note>
            quales. </s>
            <s xml:id="echoid-s1596" xml:space="preserve">quod eſt propoſitum. </s>
            <s xml:id="echoid-s1597" xml:space="preserve">Facilius idem concludetur, ſi perpendiculares
              <lb/>
            ex G, H, in plana circulorum A B C, D E F, demiſſæ cadant in puncta A, D,
              <lb/>
            vt in tertia figura. </s>
            <s xml:id="echoid-s1598" xml:space="preserve">Nam quia rectæ G A, A B, rectis H D, D E, æquales ſunt,
              <lb/>
              <note position="left" xlink:label="note-054-04" xlink:href="note-054-04a" xml:space="preserve">29. tertij.</note>
            ob æquales arcus A G, D H, & </s>
            <s xml:id="echoid-s1599" xml:space="preserve">A B, D E, continentq́; </s>
            <s xml:id="echoid-s1600" xml:space="preserve">angulos æquales, vt-
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            pote rectos, ex defin. </s>
            <s xml:id="echoid-s1601" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1602" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1603" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1604" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1605" xml:space="preserve">erunt baſes G B, H E, æquales. </s>
            <s xml:id="echoid-s1606" xml:space="preserve">Si igitur
              <lb/>
              <note position="left" xlink:label="note-054-05" xlink:href="note-054-05a" xml:space="preserve">4. primi.</note>
            in diametris circulorum æqualium, æqualia ſegmenta, &</s>
            <s xml:id="echoid-s1607" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1608" xml:space="preserve">Quod erat oſten
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            dendum.</s>
            <s xml:id="echoid-s1609" xml:space="preserve"/>
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        <div xml:id="echoid-div170" type="section" level="1" n="89">
          <head xml:id="echoid-head101" xml:space="preserve">THEOREMA 13. PROPOS. 13.</head>
          <note position="left" xml:space="preserve">18.</note>
          <p>
            <s xml:id="echoid-s1610" xml:space="preserve">SI in ſphæra ſint paralleli circuli, & </s>
            <s xml:id="echoid-s1611" xml:space="preserve">deſcriban
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            tur maximi circuli, qui vnum quidem parallelo-
              <lb/>
            rum tangant, reliquos vero ſecent; </s>
            <s xml:id="echoid-s1612" xml:space="preserve">circunferentię
              <lb/>
            parallelorum interceptæ inter eos maximorum
              <lb/>
            circulorum ſemicirculos, qui non concurrunt,
              <lb/>
            ſimiles erunt; </s>
            <s xml:id="echoid-s1613" xml:space="preserve">maximorum vero circulorum cir-
              <lb/>
            cunferentiæ inter duos quoſcunque parallelos in-
              <lb/>
            terceptæ, erunt æquales.</s>
            <s xml:id="echoid-s1614" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1615" xml:space="preserve">SINT in ſphæra paralleli circuli A B, C D E, F G H, quieundem polũ
              <lb/>
              <note position="left" xlink:label="note-054-07" xlink:href="note-054-07a" xml:space="preserve">1. huius.</note>
            habebunt, nempe I. </s>
            <s xml:id="echoid-s1616" xml:space="preserve">Circuli autem maximi A F K, B H K, tangant parallelũ
              <lb/>
            A B, in punctis A, B, & </s>
            <s xml:id="echoid-s1617" xml:space="preserve">reliquos ſecent in punctis F, C, L, M; </s>
            <s xml:id="echoid-s1618" xml:space="preserve">H, E, D, G:
              <lb/>
            </s>
            <s xml:id="echoid-s1619" xml:space="preserve">ſeipſos aũt mutuo ſecent in K, N, vt ſint ſemicirculi K M N, N F K; </s>
            <s xml:id="echoid-s1620" xml:space="preserve">K G N,
              <lb/>
            N H K. </s>
            <s xml:id="echoid-s1621" xml:space="preserve">Maximi enim circuli ſe ſecant mutuo bifariam. </s>
            <s xml:id="echoid-s1622" xml:space="preserve">Sumatur quoque ar
              <lb/>
              <note position="left" xlink:label="note-054-08" xlink:href="note-054-08a" xml:space="preserve">11. 1. huius.</note>
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