Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <pb o="37" file="0073" n="73" rhead="DE IIS QVAE VEH. IN AQVA."/>
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            <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"/>
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        <div xml:id="echoid-div135" type="section" level="1" n="42">
          <head xml:id="echoid-head47" xml:space="preserve">LEMMA I.</head>
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            <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-
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              <note position="right" xlink:label="note-0073-03" xlink:href="note-0073-03a" xml:space="preserve">9. quinti.</note>
            ti, quod eſt
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            cbſurdum.
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            <s xml:id="echoid-s1830" xml:space="preserve">Idem ab-
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            ſurdum ſe
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            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"/>
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