Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
101 43
102
103
104
105
106
107
108
109
110
111
112
113 1
114
115 2
116
117 3
118
119 4
120
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div146" type="section" level="1" n="47">
          <pb file="0082" n="82" rhead="ARCHIMEDIS"/>
          <p style="it">
            <s xml:id="echoid-s2098" xml:space="preserve">_Etenim c b ad b d eſt ut ſex ad quindecim.</s>
            <s xml:id="echoid-s2099" xml:space="preserve">]_ Poſuimus
              <lb/>
              <note position="left" xlink:label="note-0082-01" xlink:href="note-0082-01a" xml:space="preserve">N</note>
            enim b K duplam eſſe ipſius K d. </s>
            <s xml:id="echoid-s2100" xml:space="preserve">quare componendo b d ad k d erit,
              <lb/>
            ut tria ad unum; </s>
            <s xml:id="echoid-s2101" xml:space="preserve">hoc eſt ut quindecim ad quinque. </s>
            <s xml:id="echoid-s2102" xml:space="preserve">ſed b d ad K c
              <lb/>
            erat ut quídecim
              <lb/>
              <figure xlink:label="fig-0082-01" xlink:href="fig-0082-01a" number="51">
                <image file="0082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0082-01"/>
              </figure>
            ad quatuor. </s>
            <s xml:id="echoid-s2103" xml:space="preserve">ergo
              <lb/>
            b d ad d c, ut quin
              <lb/>
            decim ad nouem:
              <lb/>
            </s>
            <s xml:id="echoid-s2104" xml:space="preserve">& </s>
            <s xml:id="echoid-s2105" xml:space="preserve">per conuerſio
              <lb/>
            nem rationis, con
              <lb/>
            uertendôq; </s>
            <s xml:id="echoid-s2106" xml:space="preserve">c b ad
              <lb/>
            b d, ut ſex ad quí
              <lb/>
            decim.</s>
            <s xml:id="echoid-s2107" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2108" xml:space="preserve">Etut c b ad
              <lb/>
              <note position="left" xlink:label="note-0082-02" xlink:href="note-0082-02a" xml:space="preserve">O</note>
            b d, ita e b ad
              <lb/>
            b a, & </s>
            <s xml:id="echoid-s2109" xml:space="preserve">d z ad
              <lb/>
            d a.</s>
            <s xml:id="echoid-s2110" xml:space="preserve">] _Nam cum_
              <lb/>
            _triangula c b e,_
              <lb/>
            _d b a ſint ſimilia,_
              <lb/>
            _erit ut c b ad b e,_
              <lb/>
            _ita d b, ad b a & </s>
            <s xml:id="echoid-s2111" xml:space="preserve">permutando, ut c b ad b d; </s>
            <s xml:id="echoid-s2112" xml:space="preserve">ita e b ad b a. </s>
            <s xml:id="echoid-s2113" xml:space="preserve">Rurſus_
              <lb/>
            _ut b c ad c e, ita b d ad d a: </s>
            <s xml:id="echoid-s2114" xml:space="preserve">permutandôq; </s>
            <s xml:id="echoid-s2115" xml:space="preserve">ut c b ad b d, ita c e, hoc_
              <lb/>
            _eſt d z ei æqualis ad d a._</s>
            <s xml:id="echoid-s2116" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2117" xml:space="preserve">Harum autem d z d a duplæ ſuntipſæ l i, la.</s>
            <s xml:id="echoid-s2118" xml:space="preserve">] _Lineam_
              <lb/>
              <note position="left" xlink:label="note-0082-03" xlink:href="note-0082-03a" xml:space="preserve">P</note>
            _quidem l a duplam eſſe ipſius d a, cum b d ſit portionis diameter,_
              <lb/>
            _manifeſte conſtat. </s>
            <s xml:id="echoid-s2119" xml:space="preserve">At uero l i ipſius d z dupla hoc pacto demon-_
              <lb/>
            _ſtrabitur. </s>
            <s xml:id="echoid-s2120" xml:space="preserve">Quoniam enim z d ad d a eſt, ut duo ad quinque; </s>
            <s xml:id="echoid-s2121" xml:space="preserve">erit có_
              <lb/>
            _uertendo, diuidendôq; </s>
            <s xml:id="echoid-s2122" xml:space="preserve">a z, hoc eſt i z ad z d, ut tria ad duo: </s>
            <s xml:id="echoid-s2123" xml:space="preserve">&_</s>
            <s xml:id="echoid-s2124" xml:space="preserve">
              <lb/>
            _rurſus diuidendo i d ad d z, ut
              <gap/>
            m ad duo. </s>
            <s xml:id="echoid-s2125" xml:space="preserve">erat autem z d ad_
              <lb/>
            _d a, hoc eſt ad d l, ut duo ad quinque. </s>
            <s xml:id="echoid-s2126" xml:space="preserve">ergo ex æquali, conuertendóq;_
              <lb/>
            </s>
            <s xml:id="echoid-s2127" xml:space="preserve">_l d ad d i, ut quinque ad unum: </s>
            <s xml:id="echoid-s2128" xml:space="preserve">& </s>
            <s xml:id="echoid-s2129" xml:space="preserve">per conuerſionem rationis d l ad_
              <lb/>
            _li, ut quinque ad quatuor. </s>
            <s xml:id="echoid-s2130" xml:space="preserve">ſed d z ad d l erat, ut duo ad quinque._ </s>
            <s xml:id="echoid-s2131" xml:space="preserve">
              <lb/>
            _ergo rurſus ex æquali d z ad l i, ut duo ad quatuor. </s>
            <s xml:id="echoid-s2132" xml:space="preserve">dupla eſt igitur_
              <lb/>
            _l i ipſius d z. </s>
            <s xml:id="echoid-s2133" xml:space="preserve">quod demonſtrandum fuerat._</s>
            <s xml:id="echoid-s2134" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2135" xml:space="preserve">Et a d ad d i eam proportionem habet, quã quinque
              <lb/>
              <note position="left" xlink:label="note-0082-04" xlink:href="note-0082-04a" xml:space="preserve">Q</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum