Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div141" type="section" level="1" n="45">
          <p style="it">
            <s xml:id="echoid-s1978" xml:space="preserve">
              <pb file="0078" n="78" rhead="ARCHIMEDIS"/>
            & </s>
            <s xml:id="echoid-s1979" xml:space="preserve">per conuer-
              <lb/>
              <figure xlink:label="fig-0078-01" xlink:href="fig-0078-01a" number="48">
                <image file="0078-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0078-01"/>
              </figure>
            ſionem rationis
              <lb/>
            ut e b ad e g,
              <lb/>
            ita f d ad f h.
              <lb/>
            </s>
            <s xml:id="echoid-s1980" xml:space="preserve">eſt autem ut a e
              <lb/>
            ad e b, ita c f
              <lb/>
            ad f d. </s>
            <s xml:id="echoid-s1981" xml:space="preserve">ex æqua
              <lb/>
            li igitur ut a e
              <lb/>
            ad e g, ita c f
              <lb/>
            ad f h.</s>
            <s xml:id="echoid-s1982" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1983" xml:space="preserve">
              <emph style="sc">A_liter_</emph>
            . </s>
            <s xml:id="echoid-s1984" xml:space="preserve">Aptentur lineæ a b, c d inter ſe ſe, ita ut ad partes
              <lb/>
            a c angulum faciant; </s>
            <s xml:id="echoid-s1985" xml:space="preserve">& </s>
            <s xml:id="echoid-s1986" xml:space="preserve">ſint a c in uno atque eodem puncto: </s>
            <s xml:id="echoid-s1987" xml:space="preserve">deinde
              <lb/>
            iungantur d b, h g, fe. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">cum igitur ſit ut a e ad e b, ita c f, hoc eſt
              <lb/>
            a f ad f d; </s>
            <s xml:id="echoid-s1989" xml:space="preserve">æquidiſtabit fe ipſi d b: </s>
            <s xml:id="echoid-s1990" xml:space="preserve">& </s>
            <s xml:id="echoid-s1991" xml:space="preserve">ſimiliter h g eidem d b
              <lb/>
              <note position="left" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve">2. ſexti:</note>
            æquidiſtabit: </s>
            <s xml:id="echoid-s1992" xml:space="preserve">quoniam a h ad h d eſt, ut a g ad g b. </s>
            <s xml:id="echoid-s1993" xml:space="preserve">ergo f c, h g
              <lb/>
              <note position="left" xlink:label="note-0078-02" xlink:href="note-0078-02a" xml:space="preserve">30. primi</note>
            inter ſe ſe æquidiſtant: </s>
            <s xml:id="echoid-s1994" xml:space="preserve">& </s>
            <s xml:id="echoid-s1995" xml:space="preserve">idcirco ut a e ad e g, ita a f; </s>
            <s xml:id="echoid-s1996" xml:space="preserve">hoc eſt c f ad
              <lb/>
            fh. </s>
            <s xml:id="echoid-s1997" xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s1998" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div144" type="section" level="1" n="46">
          <head xml:id="echoid-head51" xml:space="preserve">LEMMA V.</head>
          <p style="it">
            <s xml:id="echoid-s1999" xml:space="preserve">Sint rurſus duæ portiones ſimiles, contentæ rectis li-
              <lb/>
            neis, & </s>
            <s xml:id="echoid-s2000" xml:space="preserve">rectangulorum conorum ſectionibus, ut in ſupe-
              <lb/>
            riori figura a b c, cuius diameter b d: </s>
            <s xml:id="echoid-s2001" xml:space="preserve">& </s>
            <s xml:id="echoid-s2002" xml:space="preserve">e f c, cuius
              <lb/>
            diameter f g: </s>
            <s xml:id="echoid-s2003" xml:space="preserve">ducaturque à puncto e linea e h, diame-
              <lb/>
            tris b d, f g æquidiſtans, quæ ſectionem a b c in _k_ ſe-
              <lb/>
            cet: </s>
            <s xml:id="echoid-s2004" xml:space="preserve">& </s>
            <s xml:id="echoid-s2005" xml:space="preserve">à puncto c ducatur c h contingens ſectionem
              <lb/>
            a b c in c conueniensque cumlinea e h in h, quæ ſectio
              <lb/>
            nem quoque e f c in eodem c puncto continget, ut demon
              <lb/>
            strabitur. </s>
            <s xml:id="echoid-s2006" xml:space="preserve">Dico lineam ductam ab ipſa c h uſque ad ſe-
              <lb/>
            ctionem e f c, ita ut lineæ e h æquidistet, in eandem pro
              <lb/>
            portionem diuidi à ſectione a b c; </s>
            <s xml:id="echoid-s2007" xml:space="preserve">in quam linea c a </s>
          </p>
        </div>
      </text>
    </echo>
Impressum