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

Page concordance

< >
Scan Original
61 49
62 50
63 51
64 52
65 53
66 54
67 55
68 56
69 57
70 58
71 59
72 60
73 61
74 62
75 63
76 64
77 65
78 66
79 67
80 68
81 69
82 70
83 71
84 72
85 73
86 74
87 75
88 76
89 77
90 78
< >
page |< < (49) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div183" type="section" level="1" n="94">
          <pb o="49" file="061" n="61" rhead=""/>
        </div>
        <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>
          </p>
        </div>
      </text>
    </echo>
Impressum