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

Page concordance

< >
Scan Original
41 29
42
43 31
44 32
45 33
46 34
47 35
48 36
49 37
50 38
51 39
52 40
53 41
54 42
55 43
56 44
57 45
58 46
59 47
60 48
61 49
62 50
63 51
64 52
65 53
66 54
67 55
68 56
69 57
70 58
< >
page |< < (39) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <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-
              <lb/>
            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-
              <lb/>
            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>
        </div>
        <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-
              <lb/>
            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"/>
          </p>
        </div>
      </text>
    </echo>
Impressum