Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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        <div xml:id="echoid-div146" type="section" level="1" n="47">
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            <s xml:id="echoid-s2135" xml:space="preserve">
              <pb o="36" file="0083" n="83" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ad unum.</s>
            <s xml:id="echoid-s2136" xml:space="preserve">] _Hoc nos proxime demonſtrauimus._</s>
            <s xml:id="echoid-s2137" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2138" xml:space="preserve">Demonſtratum eſt enim ſuperius portionem cuius axis
              <lb/>
              <note position="right" xlink:label="note-0083-01" xlink:href="note-0083-01a" xml:space="preserve">R</note>
            eſt maior, quàm ſeſquialter eius, quæ uſque ad axem, ſiad
              <lb/>
            humidum in grauitate non minorem proportionem ha-
              <lb/>
            beat &</s>
            <s xml:id="echoid-s2139" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2140" xml:space="preserve">] _Illud uero demonſtrauit in quarta propoſitione buius_
              <lb/>
            _libri_.</s>
            <s xml:id="echoid-s2141" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div152" type="section" level="1" n="48">
          <head xml:id="echoid-head53" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s2142" xml:space="preserve">Si portio ad humidum in grauitate minorem
              <lb/>
              <note position="right" xlink:label="note-0083-02" xlink:href="note-0083-02a" xml:space="preserve">A</note>
            quidem proportionem habeat, quàm quadra-
              <lb/>
            tum ſ b ad quadratum b d; </s>
            <s xml:id="echoid-s2143" xml:space="preserve">maiorem uero,
              <lb/>
            quàm quadratum x o ad quadratum b d; </s>
            <s xml:id="echoid-s2144" xml:space="preserve">de-
              <lb/>
            miſſa in humidum, adeo inclinata, ut baſis ip-
              <lb/>
            ſius non contingat humidum, inclinata conſi-
              <lb/>
            ſtet; </s>
            <s xml:id="echoid-s2145" xml:space="preserve">ita ut baſis ſuperficiem humidi nullo modo
              <lb/>
            contingat; </s>
            <s xml:id="echoid-s2146" xml:space="preserve">& </s>
            <s xml:id="echoid-s2147" xml:space="preserve">axis cum humidi ſuperficie angu-
              <lb/>
            lum faciat maiorem angulo χ.</s>
            <s xml:id="echoid-s2148" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div154" type="section" level="1" n="49">
          <head xml:id="echoid-head54" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s2149" xml:space="preserve">Si portio ad humidum in grauitate, eam ha-
              <lb/>
            beat proportionem, quam quadratum x o ad
              <lb/>
            quadratum b d; </s>
            <s xml:id="echoid-s2150" xml:space="preserve">demiſſa in humidum inclinata
              <lb/>
            adeo, ut baſis ipſius non contingat humidum;
              <lb/>
            </s>
            <s xml:id="echoid-s2151" xml:space="preserve">conſiſtet, & </s>
            <s xml:id="echoid-s2152" xml:space="preserve">manebit ita, ut baſis in uno pun-
              <lb/>
            cto humidi ſuperficiem contingat: </s>
            <s xml:id="echoid-s2153" xml:space="preserve">& </s>
            <s xml:id="echoid-s2154" xml:space="preserve">axis cum
              <lb/>
            ſuperficie humidi angulũ faciat angulo χ æqualẽ. </s>
            <s xml:id="echoid-s2155" xml:space="preserve">
              <lb/>
            Quòd ſi portio ad humidum in grauitate cam
              <lb/>
            proportionem habeat, quam quadratum p f </s>
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