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

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        <div xml:id="echoid-div184" type="section" level="1" n="95">
          <head xml:id="echoid-head107" xml:space="preserve">THEOREMA 15. PROPOS. 17.</head>
          <note position="right" xml:space="preserve">21.</note>
          <p>
            <s xml:id="echoid-s1847" xml:space="preserve">IN ſphæra paralleli circuli, inter quos & </s>
            <s xml:id="echoid-s1848" xml:space="preserve">ma-
              <lb/>
            ximum parallelorum æquales circunferentiæ ma-
              <lb/>
            ximorum circulorum intercipiuntur, ſuntinter ſe
              <lb/>
            æquales: </s>
            <s xml:id="echoid-s1849" xml:space="preserve">Illi vero, inter quos, & </s>
            <s xml:id="echoid-s1850" xml:space="preserve">maximum paralle-
              <lb/>
            lorum maiores maximorum circulorum circun-
              <lb/>
            ferentiæ intercipiuntur, ſunt minores.</s>
            <s xml:id="echoid-s1851" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1852" xml:space="preserve">SINT in ſphæra paralleli circuli A B, C D, E F; </s>
            <s xml:id="echoid-s1853" xml:space="preserve">ſitque C D, maximus
              <lb/>
            parallelorum. </s>
            <s xml:id="echoid-s1854" xml:space="preserve">Inter circulum vero C D, & </s>
            <s xml:id="echoid-s1855" xml:space="preserve">vtrumq; </s>
            <s xml:id="echoid-s1856" xml:space="preserve">parallelorum A B, E F,
              <lb/>
            intercipiantur æquales circunferentiæ A C, C E, maximi alicuius circuli
              <lb/>
              <figure xlink:label="fig-061-01" xlink:href="fig-061-01a" number="70">
                <image file="061-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/061-01"/>
              </figure>
            ACEFDB. </s>
            <s xml:id="echoid-s1857" xml:space="preserve">Dico parallelos A B, E F, ęqua
              <lb/>
            lès eſſe. </s>
            <s xml:id="echoid-s1858" xml:space="preserve">Sint enim communes ſectiones paral-
              <lb/>
            lelorum, & </s>
            <s xml:id="echoid-s1859" xml:space="preserve">circuli A C E F D B, rectæ A B,
              <lb/>
            C D, E F, quæ parallelæ inter ſe erunt. </s>
            <s xml:id="echoid-s1860" xml:space="preserve">Tran
              <lb/>
              <note position="right" xlink:label="note-061-02" xlink:href="note-061-02a" xml:space="preserve">16. vndes.</note>
            ſeat autem primum circulus maximus ACE-
              <lb/>
            F D B, per polos parallelorum. </s>
            <s xml:id="echoid-s1861" xml:space="preserve">Quo poſito,
              <lb/>
            fecabit circulus A C E F D B, parallelos A B,
              <lb/>
            C D, E F, bifariam, & </s>
            <s xml:id="echoid-s1862" xml:space="preserve">ad angulos rectos;
              <lb/>
            </s>
            <s xml:id="echoid-s1863" xml:space="preserve">
              <note position="right" xlink:label="note-061-03" xlink:href="note-061-03a" xml:space="preserve">15. 1. huius.</note>
            atq; </s>
            <s xml:id="echoid-s1864" xml:space="preserve">adeo diametri erunt A B, C D, E F, pa-
              <lb/>
            rallelorum. </s>
            <s xml:id="echoid-s1865" xml:space="preserve">Quoniam vero arcus A C, B D,
              <lb/>
            æquales ſunt, nec non & </s>
            <s xml:id="echoid-s1866" xml:space="preserve">arcus C E, D F; </s>
            <s xml:id="echoid-s1867" xml:space="preserve">po-
              <lb/>
              <note position="right" xlink:label="note-061-04" xlink:href="note-061-04a" xml:space="preserve">10. 1. huius.</note>
            niturque A C, æqualis ipſi C E; </s>
            <s xml:id="echoid-s1868" xml:space="preserve">erunt A C,
              <lb/>
            B D, ſimul ipſis C E, D F, ſimul æquales:
              <lb/>
            </s>
            <s xml:id="echoid-s1869" xml:space="preserve">Sunt autcm ſemicirculi æquales C A B D,
              <lb/>
            C E F D: </s>
            <s xml:id="echoid-s1870" xml:space="preserve">quia circuli maximi C D, A C E F D B, ſe mutuo bifariam diuidunt. </s>
            <s xml:id="echoid-s1871" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-061-05" xlink:href="note-061-05a" xml:space="preserve">11. 1. huius.</note>
            Igitur reliqui arcus A B, E F, æquales erunt; </s>
            <s xml:id="echoid-s1872" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s1873" xml:space="preserve">rectæ A B, E F,
              <lb/>
            hoc eſt, diametri circulorum A B, E F, æquales. </s>
            <s xml:id="echoid-s1874" xml:space="preserve">Circuli ergo A B, E F,
              <lb/>
              <note position="right" xlink:label="note-061-06" xlink:href="note-061-06a" xml:space="preserve">29. tertij.</note>
            æquales ſunt.</s>
            <s xml:id="echoid-s1875" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1876" xml:space="preserve">QVOD ſi arcus A C, maior ponatur arcu C E. </s>
            <s xml:id="echoid-s1877" xml:space="preserve">Dico circulum A B, mi-
              <lb/>
            norem eſſe circulo E F. </s>
            <s xml:id="echoid-s1878" xml:space="preserve">Poſita enim eadem conſtructione, & </s>
            <s xml:id="echoid-s1879" xml:space="preserve">demonſtratione,
              <lb/>
            erunt vt prius, arcus A C, B D, æquales, nec non C E, D F, cum ergo A C, ma
              <lb/>
              <note position="right" xlink:label="note-061-07" xlink:href="note-061-07a" xml:space="preserve">1@. huius.</note>
            ior ponatur quam C E, erunt duo arcus A C, B D, ſimul, maiores duobus ar-
              <lb/>
            cubus C E, D F, ſimul. </s>
            <s xml:id="echoid-s1880" xml:space="preserve">Reliquus igitur A B, ex ſemicirculo C A B D, minor
              <lb/>
            erit reliquo E F, ex ſemicirculo CEFD; </s>
            <s xml:id="echoid-s1881" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s1882" xml:space="preserve">recta A B, hoc eſt,
              <lb/>
            diameter circuli A B, minor erit, quàm recta E F, hoc eſt, quàm diameter cir-
              <lb/>
            culi E F, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s1883" xml:space="preserve">29. </s>
            <s xml:id="echoid-s1884" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1885" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1886" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1887" xml:space="preserve">à nobis eſt demonſtratum, cum
              <lb/>
            arcus A B, E F, ſemicirculo ſint minores. </s>
            <s xml:id="echoid-s1888" xml:space="preserve">Quare minor erit circulus A B, cir-
              <lb/>
            culo E F. </s>
            <s xml:id="echoid-s1889" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s1890" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1891" xml:space="preserve">SED iam circulus maximus A C E F D B, non tranſeat per polos paral-
              <lb/>
            lelorum A B, C D, E F; </s>
            <s xml:id="echoid-s1892" xml:space="preserve">ſintque rurſus arcus A C, C E, æquales. </s>
            <s xml:id="echoid-s1893" xml:space="preserve">Dico adhuc
              <lb/>
            circulos A B, E F, eſſe æquales. </s>
            <s xml:id="echoid-s1894" xml:space="preserve">Sint enim G, H, poli parallelorum A B, C D,
              <lb/>
            E F, & </s>
            <s xml:id="echoid-s1895" xml:space="preserve">per G, H, ac polos circuli maximi A C E F D B, crrculus maximus </s>
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