Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
161 25
162
163 26
164
165 27
166
167 28
168
169 29
170
171 30
172
173 31
174
175 32
176
177 33
178
179 34
180
< >
page |< < (37) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div123" type="section" level="1" n="41">
          <pb o="37" file="0073" n="73" rhead="DE IIS QVAE VEH. IN AQVA."/>
          <p>
            <s xml:id="echoid-s1813" xml:space="preserve">Cum ergo tres portiones ſint a p o i, a ei, atd, con-
              <lb/>
              <note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">M</note>
            tentæ rectis lineis, & </s>
            <s xml:id="echoid-s1814" xml:space="preserve">rectãgulorum conorum ſectionibus;
              <lb/>
            </s>
            <s xml:id="echoid-s1815" xml:space="preserve">rectæq;</s>
            <s xml:id="echoid-s1816" xml:space="preserve">, ſimiles, & </s>
            <s xml:id="echoid-s1817" xml:space="preserve">inæquales, quæ contingunt ſe ſe ſuper
              <lb/>
            unam quamque baſim.</s>
            <s xml:id="echoid-s1818" xml:space="preserve">] _Poſt ea uerba, ſuper unamquanque_
              <lb/>
            _baſim, in trans latione aliqua deſiderari uidentur. </s>
            <s xml:id="echoid-s1819" xml:space="preserve">Ad borum autem_
              <lb/>
            _demonſtrationem non nulla præmittere oportet, quæ etiam ad alia,_
              <lb/>
            _quæ ſequuntur, neceſſaria erunt._</s>
            <s xml:id="echoid-s1820" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div135" type="section" level="1" n="42">
          <head xml:id="echoid-head47" xml:space="preserve">LEMMA I.</head>
          <p style="it">
            <s xml:id="echoid-s1821" xml:space="preserve">Sit recta linea a b, quam ſecent duæ lineæ inter ſeſe
              <lb/>
            æquidiſtantes a c, d e, ita ut quam proportionem ba-
              <lb/>
            bet a b ad b d, eandern haheat a c ad de. </s>
            <s xml:id="echoid-s1822" xml:space="preserve">Dico li-
              <lb/>
            neam, quæ c b puncta coniungit, etiam per ipſum e
              <lb/>
            tr anſire.</s>
            <s xml:id="echoid-s1823" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1824" xml:space="preserve">SI enim fieri poteſt, non tranſeat pere, ſed nel ſupra, uel infra.
              <lb/>
            </s>
            <s xml:id="echoid-s1825" xml:space="preserve">tranſeat primum infra, ut per f. </s>
            <s xml:id="echoid-s1826" xml:space="preserve">erunt triangula a b c, d b f inter ſe
              <lb/>
            ſimilia. </s>
            <s xml:id="echoid-s1827" xml:space="preserve">quare ut a b ad b d, ita a c ad d f. </s>
            <s xml:id="echoid-s1828" xml:space="preserve">ſed ut a b ad bd, ita
              <lb/>
              <note position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve">4. ſexti.</note>
            erat a c ad d e. </s>
            <s xml:id="echoid-s1829" xml:space="preserve">ergo d f ipſi d e æqualis erit, uidelicet pars to-
              <lb/>
              <note position="right" xlink:label="note-0073-03" xlink:href="note-0073-03a" xml:space="preserve">9. quinti.</note>
            ti, quod eſt
              <lb/>
              <figure xlink:label="fig-0073-01" xlink:href="fig-0073-01a" number="45">
                <image file="0073-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0073-01"/>
              </figure>
            cbſurdum.
              <lb/>
            </s>
            <s xml:id="echoid-s1830" xml:space="preserve">Idem ab-
              <lb/>
            ſurdum ſe
              <lb/>
            quetur, ſi
              <lb/>
            linea c b
              <lb/>
            ſupra e pú
              <lb/>
            ctum tran
              <lb/>
            ſire pona-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s1831" xml:space="preserve">quare
              <lb/>
            c b etiam
              <lb/>
            per e ne-
              <lb/>
            ceſſario tranſibit. </s>
            <s xml:id="echoid-s1832" xml:space="preserve">quod oportebat demonſtrare.</s>
            <s xml:id="echoid-s1833" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum