Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
121 5
122
123 6
124
125 7
126
127 8
128
129 9
130
131 10
132
133 11
134
135 12
136
137 13
138
139 14
140
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
< >
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>
Impressum