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-div120" type="section" level="1" n="40">
          <p>
            <s xml:id="echoid-s1694" xml:space="preserve">
              <pb file="0070" n="70" rhead="ARCHIMEDIS"/>
            dem circa e z diametrum; </s>
            <s xml:id="echoid-s1695" xml:space="preserve">a t d uero circa diametrum t h;
              <lb/>
            </s>
            <s xml:id="echoid-s1696" xml:space="preserve">
              <note position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve">K</note>
            quæ ſimiles ſint portioni a b l. </s>
            <s xml:id="echoid-s1697" xml:space="preserve">tranſibit igitur a e i coni
              <lb/>
              <note position="left" xlink:label="note-0070-02" xlink:href="note-0070-02a" xml:space="preserve">L</note>
            ſectio per _K_: </s>
            <s xml:id="echoid-s1698" xml:space="preserve">& </s>
            <s xml:id="echoid-s1699" xml:space="preserve">quæ ab r ducta eſt perpendicularis ad b d,
              <lb/>
            ipſam a e i ſecabit. </s>
            <s xml:id="echoid-s1700" xml:space="preserve">ſecet in punctis y g: </s>
            <s xml:id="echoid-s1701" xml:space="preserve">& </s>
            <s xml:id="echoid-s1702" xml:space="preserve">per y g ducan
              <lb/>
            tur ipſi b d æquidiſtantes p y q, o g n, quæ ſecent a t d in
              <lb/>
            f x. </s>
            <s xml:id="echoid-s1703" xml:space="preserve">ducantur poſtremo, & </s>
            <s xml:id="echoid-s1704" xml:space="preserve">p χ, o φ contingentes ſectionẽ
              <lb/>
            a p o l in punctis p o. </s>
            <s xml:id="echoid-s1705" xml:space="preserve">cũ
              <unsure/>
            ergo tres portiones ſint a p o l,
              <lb/>
              <note position="left" xlink:label="note-0070-03" xlink:href="note-0070-03a" xml:space="preserve">M</note>
            a e i, a t d, contentæ rectis lineis, & </s>
            <s xml:id="echoid-s1706" xml:space="preserve">rectangulorum cono-
              <lb/>
            rum ſectionibus; </s>
            <s xml:id="echoid-s1707" xml:space="preserve">rectæq, ſimiles, & </s>
            <s xml:id="echoid-s1708" xml:space="preserve">inæquales, quæ contin
              <lb/>
            gunt ſe ſe ſuper unamquanque baſim: </s>
            <s xml:id="echoid-s1709" xml:space="preserve">à puncto autem n
              <lb/>
            ſurſum ducta ſit n x g o; </s>
            <s xml:id="echoid-s1710" xml:space="preserve">& </s>
            <s xml:id="echoid-s1711" xml:space="preserve">à q ipſa q fy p: </s>
            <s xml:id="echoid-s1712" xml:space="preserve">habebit o g ad
              <lb/>
            g x proportionem compoſitam ex proportione, quam ha
              <lb/>
            bet i l ad l a; </s>
            <s xml:id="echoid-s1713" xml:space="preserve">& </s>
            <s xml:id="echoid-s1714" xml:space="preserve">ex proportione, quam a d habet ad d i.
              <lb/>
            </s>
            <s xml:id="echoid-s1715" xml:space="preserve">Sed i l ad l a
              <lb/>
              <figure xlink:label="fig-0070-01" xlink:href="fig-0070-01a" number="44">
                <image file="0070-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0070-01"/>
              </figure>
            habet eandem,
              <lb/>
            quam duo ad
              <lb/>
            quinque. </s>
            <s xml:id="echoid-s1716" xml:space="preserve">ete-
              <lb/>
            nim c b ad b d
              <lb/>
              <note position="left" xlink:label="note-0070-04" xlink:href="note-0070-04a" xml:space="preserve">N</note>
            eſt, ut ſex ad
              <lb/>
            quĩdecim; </s>
            <s xml:id="echoid-s1717" xml:space="preserve">hoc
              <lb/>
            eſt ut duo ad
              <lb/>
            quinque: </s>
            <s xml:id="echoid-s1718" xml:space="preserve">& </s>
            <s xml:id="echoid-s1719" xml:space="preserve">ut
              <lb/>
              <note position="left" xlink:label="note-0070-05" xlink:href="note-0070-05a" xml:space="preserve">O</note>
            c b ad b d, ita
              <lb/>
            e b ad b a: </s>
            <s xml:id="echoid-s1720" xml:space="preserve">& </s>
            <s xml:id="echoid-s1721" xml:space="preserve">
              <lb/>
            d z ad d a. </s>
            <s xml:id="echoid-s1722" xml:space="preserve">ha-
              <lb/>
            rum autẽ d z,
              <lb/>
              <note position="left" xlink:label="note-0070-06" xlink:href="note-0070-06a" xml:space="preserve">P</note>
            d a duplæ ſunt
              <lb/>
            ipſæ l i, l a: </s>
            <s xml:id="echoid-s1723" xml:space="preserve">& </s>
            <s xml:id="echoid-s1724" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0070-07" xlink:href="note-0070-07a" xml:space="preserve">Q</note>
            a d ad d i eã pro
              <lb/>
            portionem habet, quam quinque ad unum. </s>
            <s xml:id="echoid-s1725" xml:space="preserve">ſed proportio
              <lb/>
            compoſita ex proportione, quam habet duo ad quinque;
              <lb/>
            </s>
            <s xml:id="echoid-s1726" xml:space="preserve">& </s>
            <s xml:id="echoid-s1727" xml:space="preserve">ex proportione, quam quinque ad unum; </s>
            <s xml:id="echoid-s1728" xml:space="preserve">eſt eadem,
              <lb/>
            quam habent duo ad unum: </s>
            <s xml:id="echoid-s1729" xml:space="preserve">duo autem ad unum duplam
              <lb/>
            proportionem habent. </s>
            <s xml:id="echoid-s1730" xml:space="preserve">dupla eſt igitur g b ipſius g x: </s>
            <s xml:id="echoid-s1731" xml:space="preserve">&</s>
            <s xml:id="echoid-s1732" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>