Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
< >
page |< < of 213 > >|
ARCHIMEDIS
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="47">
          <pb file="0082" n="82" rhead="ARCHIMEDIS"/>
          <p style="it">
            <s xml:space="preserve">_Etenim c b ad b d eſt ut ſex ad quindecim.</s>
            <s xml:space="preserve">]_ Poſuimus
              <lb/>
              <anchor type="note" xlink:label="note-0082-01a" xlink:href="note-0082-01"/>
            enim b K duplam eſſe ipſius K d. </s>
            <s xml:space="preserve">quare componendo b d ad k d erit,
              <lb/>
            ut tria ad unum; </s>
            <s xml:space="preserve">hoc eſt ut quindecim ad quinque. </s>
            <s xml:space="preserve">ſed b d ad K c
              <lb/>
            erat ut quídecim
              <lb/>
              <anchor type="figure" xlink:label="fig-0082-01a" xlink:href="fig-0082-01"/>
            ad quatuor. </s>
            <s xml:space="preserve">ergo
              <lb/>
            b d ad d c, ut quin
              <lb/>
            decim ad nouem:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per conuerſio
              <lb/>
            nem rationis, con
              <lb/>
            uertendôq; </s>
            <s xml:space="preserve">c b ad
              <lb/>
            b d, ut ſex ad quí
              <lb/>
            decim.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="left" xlink:label="note-0082-01" xlink:href="note-0082-01a" xml:space="preserve">N</note>
            <figure xlink:label="fig-0082-01" xlink:href="fig-0082-01a">
              <image file="0082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0082-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Etut c b ad
              <lb/>
              <anchor type="note" xlink:label="note-0082-02a" xlink:href="note-0082-02"/>
            b d, ita e b ad
              <lb/>
            b a, & </s>
            <s xml:space="preserve">d z ad
              <lb/>
            d a.</s>
            <s 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:space="preserve">permutando, ut c b ad b d; </s>
            <s xml:space="preserve">ita e b ad b a. </s>
            <s xml:space="preserve">Rurſus_
              <lb/>
            _ut b c ad c e, ita b d ad d a: </s>
            <s xml:space="preserve">permutandôq; </s>
            <s 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:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="left" xlink:label="note-0082-02" xlink:href="note-0082-02a" xml:space="preserve">O</note>
          </div>
          <p>
            <s xml:space="preserve">Harum autem d z d a duplæ ſuntipſæ l i, la.</s>
            <s xml:space="preserve">] _Lineam_
              <lb/>
              <anchor type="note" xlink:label="note-0082-03a" xlink:href="note-0082-03"/>
            _quidem l a duplam eſſe ipſius d a, cum b d ſit portionis diameter,_
              <lb/>
            _manifeſte conſtat. </s>
            <s xml:space="preserve">At uero l i ipſius d z dupla hoc pacto demon-_
              <lb/>
            _ſtrabitur. </s>
            <s xml:space="preserve">Quoniam enim z d ad d a eſt, ut duo ad quinque; </s>
            <s xml:space="preserve">erit có_
              <lb/>
            _uertendo, diuidendôq; </s>
            <s xml:space="preserve">a z, hoc eſt i z ad z d, ut tria ad duo: </s>
            <s xml:space="preserve">&_</s>
            <s xml:space="preserve">
              <lb/>
            _rurſus diuidendo i d ad d z, ut
              <gap/>
            m ad duo. </s>
            <s xml:space="preserve">erat autem z d ad_
              <lb/>
            _d a, hoc eſt ad d l, ut duo ad quinque. </s>
            <s xml:space="preserve">ergo ex æquali, conuertendóq;_
              <lb/>
            </s>
            <s xml:space="preserve">_l d ad d i, ut quinque ad unum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per conuerſionem rationis d l ad_
              <lb/>
            _li, ut quinque ad quatuor. </s>
            <s xml:space="preserve">ſed d z ad d l erat, ut duo ad quinque._ </s>
            <s xml:space="preserve">
              <lb/>
            _ergo rurſus ex æquali d z ad l i, ut duo ad quatuor. </s>
            <s xml:space="preserve">dupla eſt igitur_
              <lb/>
            _l i ipſius d z. </s>
            <s xml:space="preserve">quod demonſtrandum fuerat._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <note position="left" xlink:label="note-0082-03" xlink:href="note-0082-03a" xml:space="preserve">P</note>
          </div>
          <p>
            <s xml:space="preserve">Et a d ad d i eam proportionem habet, quã quinque
              <lb/>
              <anchor type="note" xlink:label="note-0082-04a" xlink:href="note-0082-04"/>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum