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 |< < (23) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div94" type="section" level="1" n="55">
          <pb o="23" file="035" n="35" rhead=""/>
        </div>
        <div xml:id="echoid-div97" type="section" level="1" n="56">
          <head xml:id="echoid-head67" xml:space="preserve">LEMMA.</head>
          <p>
            <s xml:id="echoid-s850" xml:space="preserve">IN omni circulo quadratum ſemidiametri dimidium eſt qua-
              <lb/>
            drati in ipſo circulo deſcripti.</s>
            <s xml:id="echoid-s851" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s852" xml:space="preserve">_IN_ circulo, cuius centrum E, ductæ ſint duæ diametri A C, B D,
              <lb/>
              <figure xlink:label="fig-035-01" xlink:href="fig-035-01a" number="32">
                <image file="035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/035-01"/>
              </figure>
            ſeſe ad angulos rectos ſecantes in E, cen-
              <lb/>
            tro. </s>
            <s xml:id="echoid-s853" xml:space="preserve">lunctis igitur rectis A B, B C, C D,
              <lb/>
            _D A,_ quadratum erit A B C D, in circu
              <lb/>
            lo inſcriptum, vt conſtat ex propoſ. </s>
            <s xml:id="echoid-s854" xml:space="preserve">6. </s>
            <s xml:id="echoid-s855" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s856" xml:space="preserve">4. </s>
            <s xml:id="echoid-s857" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s858" xml:space="preserve">Quoniam vero quadrata ex ſemi-
              <lb/>
            diametris æqualibus E A, E B, æqualia
              <lb/>
            inter ſe, æqualia ſimul ſunt quadrato ex
              <lb/>
            A B; </s>
            <s xml:id="echoid-s859" xml:space="preserve">dimidium erit quadratum ſemidia
              <lb/>
              <note position="right" xlink:label="note-035-01" xlink:href="note-035-01a" xml:space="preserve">47. primi.</note>
            metri E A, quadrati ex A B, quod in cir
              <lb/>
            culo deſcribitur. </s>
            <s xml:id="echoid-s860" xml:space="preserve">Quod eſt propoſitum. </s>
            <s xml:id="echoid-s861" xml:space="preserve">Ex
              <lb/>
            quo conſtat, in ſuperiorifigura, quadratum ſemidiametri B E, dimidium
              <lb/>
            eſſe quadrati ex C B, quod æquale ponitur ei, quod in circulo A B, in-
              <lb/>
            ſcribitur.</s>
            <s xml:id="echoid-s862" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div99" type="section" level="1" n="57">
          <head xml:id="echoid-head68" xml:space="preserve">THEOR. 16. PROPOS. 17.</head>
          <note position="right" xml:space="preserve">27.</note>
          <p>
            <s xml:id="echoid-s863" xml:space="preserve">SI in ſphæra ſit circulus, à cuius polo in ipſius
              <lb/>
            circunferentiam ducta recta linea æqualis ſit late-
              <lb/>
            ri quadrati in ſcripti in maximo circulo, ipſe circu
              <lb/>
            lus maximus erit.</s>
            <s xml:id="echoid-s864" xml:space="preserve"/>
          </p>
          <figure number="33">
            <image file="035-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/035-02"/>
          </figure>
          <p>
            <s xml:id="echoid-s865" xml:space="preserve">IN ſphæra ſit circulus A B, à cuius polo
              <lb/>
            C, ad eius circunferentiam recta ducta C A,
              <lb/>
            æqualis ſit lateri quadrati in maximo circulo
              <lb/>
            ſphæræ deſcripti. </s>
            <s xml:id="echoid-s866" xml:space="preserve">Dico A B, circulum eſſe ma
              <lb/>
            ximum. </s>
            <s xml:id="echoid-s867" xml:space="preserve">Per rectam enim A C, & </s>
            <s xml:id="echoid-s868" xml:space="preserve">centrũ ſphæ
              <lb/>
            ræ planum ducatur, faciens in ſphæra circulũ
              <lb/>
              <note position="right" xlink:label="note-035-03" xlink:href="note-035-03a" xml:space="preserve">1. huius.</note>
            A C B, qui maximus erit, cum per ſphæræ cen
              <lb/>
              <note position="right" xlink:label="note-035-04" xlink:href="note-035-04a" xml:space="preserve">6. huius.</note>
            trum ducatur. </s>
            <s xml:id="echoid-s869" xml:space="preserve">Ducatur quoq; </s>
            <s xml:id="echoid-s870" xml:space="preserve">ex C, recta li-
              <lb/>
            nea C B, ad B, punctũ, in quo circulus maxi-
              <lb/>
            mus A C B, circulũ A B, ſecat; </s>
            <s xml:id="echoid-s871" xml:space="preserve">eritq́; </s>
            <s xml:id="echoid-s872" xml:space="preserve">per deſi
              <lb/>
            nit. </s>
            <s xml:id="echoid-s873" xml:space="preserve">poli, recta C B, rectæ C A, æqualis. </s>
            <s xml:id="echoid-s874" xml:space="preserve">Cũ
              <lb/>
            ergo A C, ponatur latus quadrati in maximo circulo A C B, deſcripti, erit
              <lb/>
            quoque C B, latus eiuſdem quadrati; </s>
            <s xml:id="echoid-s875" xml:space="preserve">atque adeò duo arcus A C, C B, qua-
              <lb/>
            drantes erunt conſicientes ſemicirculũ A C B, quòd quatuor latera quadra-
              <lb/>
            ti æqualia ſubtendãt quatuor circuli arcus æquales. </s>
            <s xml:id="echoid-s876" xml:space="preserve">Recta igitur A B, com-
              <lb/>
              <note position="right" xlink:label="note-035-05" xlink:href="note-035-05a" xml:space="preserve">28. tertij.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum