Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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        <div type="section" level="1" n="13">
          <head xml:space="preserve">PROPOSITIO VI.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Solidae</emph>
            magnitudines humido leuiores, in
              <lb/>
            humidum impulſæ ſurſum feruntur tanta ui, quã
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            to humidum molem habens magnitudini æqua-
              <lb/>
            lem, grauius eſt ipſa magnitudine.</s>
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          <p>
            <s xml:space="preserve">SIT enim magnitudo aleuior humido: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit magnitu
              <lb/>
            dinis quidem a grauitas b: </s>
            <s xml:space="preserve">humidi uero molem habentis
              <lb/>
            æqualem ipſi a, grauitas ſit b c. </s>
            <s xml:space="preserve">demonſtrandum eſt magni
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            tudinem a in humidum impulſam tanta ui ſurſum ferri,
              <lb/>
            quanta eſt grauitas c. </s>
            <s xml:space="preserve">accipiatur enim quædam magnitu-
              <lb/>
            do, in qua d habens grauitatem ipſi c æqualem. </s>
            <s xml:space="preserve">Itaque
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            magnitudo ex utriſque magnitudinibus conſtans, in qui-
              <lb/>
            bus a d, leuior eſt humido: </s>
            <s xml:space="preserve">nam magnitudinis quidem quæ
              <lb/>
            ex utriſque conſtat grauitas eſt b c; </s>
            <s xml:space="preserve">humidi uero habentis
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            molem ipſis æ qualem grauitas maior eſt, quàm b c: </s>
            <s xml:space="preserve">quo-
              <lb/>
            niam b c grauitas eſt humidi
              <lb/>
              <anchor type="figure" xlink:label="fig-0020-01a" xlink:href="fig-0020-01"/>
            molẽ habentis æqualem ipſia.
              <lb/>
            </s>
            <s xml:space="preserve">Si ergo demittatur in humidũ
              <lb/>
            magnitudo ex utriſque a d con
              <lb/>
            ſtans; </s>
            <s xml:space="preserve">uſque eò demergetur, ut
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            tanta moles humidi, quanta eſt
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            pars magnitudinis demerſa eã
              <lb/>
            dem, quam tota magnitudo
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            grauitatem habeat. </s>
            <s xml:space="preserve">hoc enim
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            iam demonſtratum eſt. </s>
            <s xml:space="preserve">ſit autẽ
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            ſuperſicies humidi alicuius a b
              <lb/>
            c d circunferentia. </s>
            <s xml:space="preserve">Quoniam igitur tanta moles humidi,
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            quanta eſt magnitudo a grauitatem habet eandem, quam
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            magnitudines a d: </s>
            <s xml:space="preserve">perſpicuum eſt partem ipſius demer-
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            ſam eſſe magnitudinem a; </s>
            <s xml:space="preserve">reliquam uero d totam ex hu-</s>
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