Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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        <div xml:id="echoid-div39" type="section" level="1" n="21">
          <p>
            <s xml:id="echoid-s555" xml:space="preserve">
              <pb o="10" file="0031" n="31" rhead="DE IIS QVAE VEH. IN AQVA."/>
            æqualis magnitudini f a; </s>
            <s xml:id="echoid-s556" xml:space="preserve">ſitq, ipſi f æqualis n: </s>
            <s xml:id="echoid-s557" xml:space="preserve">& </s>
            <s xml:id="echoid-s558" xml:space="preserve">ipſi a æ-
              <lb/>
            qualis i. </s>
            <s xml:id="echoid-s559" xml:space="preserve">magnitudinis autem f a grauitas ſit b: </s>
            <s xml:id="echoid-s560" xml:space="preserve">& </s>
            <s xml:id="echoid-s561" xml:space="preserve">magni-
              <lb/>
            tudinis n i grauitas o r; </s>
            <s xml:id="echoid-s562" xml:space="preserve">& </s>
            <s xml:id="echoid-s563" xml:space="preserve">ipſius i ſit r. </s>
            <s xml:id="echoid-s564" xml:space="preserve">magnitudo igi-
              <lb/>
            tur f a ad n i eam proportionem habet, quam grauitas b
              <lb/>
            ad grauitatem or. </s>
            <s xml:id="echoid-s565" xml:space="preserve">Sed quoniam magnitudo f a in humi-
              <lb/>
            dum demiſſa leuior eſt humido; </s>
            <s xml:id="echoid-s566" xml:space="preserve">patet tantam humidi mo-
              <lb/>
            lem, quanta eſt pars magnitudin_i_s demerſa, eandem quam
              <lb/>
            magnitudo f a habere grauitatem. </s>
            <s xml:id="echoid-s567" xml:space="preserve">hoc enim ſuperius de-
              <lb/>
              <note position="right" xlink:label="note-0031-01" xlink:href="note-0031-01a" xml:space="preserve">5. priml
                <lb/>
              huius.</note>
            monſtratum eſt. </s>
            <s xml:id="echoid-s568" xml:space="preserve">Atipſi a reſpondet humidum i, cuius qui
              <lb/>
            dem grauitas eſt r; </s>
            <s xml:id="echoid-s569" xml:space="preserve">& </s>
            <s xml:id="echoid-s570" xml:space="preserve">ipſius f a grauitas b. </s>
            <s xml:id="echoid-s571" xml:space="preserve">ergo b graui-
              <lb/>
            tas eius, quod habet molem æqualem toti magnitudini
              <lb/>
            f a, æqualis erit grauitati humidi i, uidelicetipſi r. </s>
            <s xml:id="echoid-s572" xml:space="preserve">Et quo
              <lb/>
            niam ut magnitudo f a ad humidum n i ſibi reſpondens,
              <lb/>
            ita eſt b ad o r: </s>
            <s xml:id="echoid-s573" xml:space="preserve">eſt autem b æqualis ipſi r: </s>
            <s xml:id="echoid-s574" xml:space="preserve">& </s>
            <s xml:id="echoid-s575" xml:space="preserve">utr ad o r, ita
              <lb/>
            i ad n i; </s>
            <s xml:id="echoid-s576" xml:space="preserve">& </s>
            <s xml:id="echoid-s577" xml:space="preserve">a ad f a. </s>
            <s xml:id="echoid-s578" xml:space="preserve">Sequitur ut f a ad humidum æqualis
              <lb/>
              <note position="right" xlink:label="note-0031-02" xlink:href="note-0031-02a" xml:space="preserve">11. quinta
                <unsure/>
              </note>
            molis eam in grauitate proportionem habeat, quam ma-
              <lb/>
            gnitudo a habet ad f a. </s>
            <s xml:id="echoid-s579" xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s580" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div41" type="section" level="1" n="22">
          <head xml:id="echoid-head27" xml:space="preserve">PROPOSITIO II.</head>
          <p>
            <s xml:id="echoid-s581" xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
              <note position="right" xlink:label="note-0031-03" xlink:href="note-0031-03a" xml:space="preserve">A</note>
            axem habuerit minorem, quam ſeſquialterum
              <lb/>
            eius, quæ uſque ad axem, quamcunque propor-
              <lb/>
            tionem habens ad humidum in grauitate; </s>
            <s xml:id="echoid-s582" xml:space="preserve">demiſ
              <lb/>
            ſa in humidum, ita ut baſis ipſius humidum non
              <lb/>
            contingat; </s>
            <s xml:id="echoid-s583" xml:space="preserve">& </s>
            <s xml:id="echoid-s584" xml:space="preserve">poſita inelinata, non manebit incli
              <lb/>
            nata; </s>
            <s xml:id="echoid-s585" xml:space="preserve">ſed recta reſtituetur. </s>
            <s xml:id="echoid-s586" xml:space="preserve">Rectam dico conſi-
              <lb/>
            ſtere talem portionem, quando planum quod ip
              <lb/>
            ſam ſecuit, ſuperficiei humidi fuerit æquidiſtans.</s>
            <s xml:id="echoid-s587" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s588" xml:space="preserve">SIT portio rectanguli conoidis, qualis dicta eſt; </s>
            <s xml:id="echoid-s589" xml:space="preserve">& </s>
            <s xml:id="echoid-s590" xml:space="preserve"/>
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