Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <head xml:id="echoid-head16" xml:space="preserve">PROPOSITIO VI.</head>
          <p>
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              <emph style="sc">Solidae</emph>
            magnitudines humido leuiores, in
              <lb/>
            humidum impulſæ ſurſum feruntur tanta ui, quã
              <lb/>
            to humidum molem habens magnitudini æqua-
              <lb/>
            lem, grauius eſt ipſa magnitudine.</s>
            <s xml:id="echoid-s290" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s291" xml:space="preserve">SIT enim magnitudo aleuior humido: </s>
            <s xml:id="echoid-s292" xml:space="preserve">& </s>
            <s xml:id="echoid-s293" xml:space="preserve">ſit magnitu
              <lb/>
            dinis quidem a grauitas b: </s>
            <s xml:id="echoid-s294" xml:space="preserve">humidi uero molem habentis
              <lb/>
            æqualem ipſi a, grauitas ſit b c. </s>
            <s xml:id="echoid-s295" xml:space="preserve">demonſtrandum eſt magni
              <lb/>
            tudinem a in humidum impulſam tanta ui ſurſum ferri,
              <lb/>
            quanta eſt grauitas c. </s>
            <s xml:id="echoid-s296" xml:space="preserve">accipiatur enim quædam magnitu-
              <lb/>
            do, in qua d habens grauitatem ipſi c æqualem. </s>
            <s xml:id="echoid-s297" xml:space="preserve">Itaque
              <lb/>
            magnitudo ex utriſque magnitudinibus conſtans, in qui-
              <lb/>
            bus a d, leuior eſt humido: </s>
            <s xml:id="echoid-s298" xml:space="preserve">nam magnitudinis quidem quæ
              <lb/>
            ex utriſque conſtat grauitas eſt b c; </s>
            <s xml:id="echoid-s299" xml:space="preserve">humidi uero habentis
              <lb/>
            molem ipſis æ qualem grauitas maior eſt, quàm b c: </s>
            <s xml:id="echoid-s300" xml:space="preserve">quo-
              <lb/>
            niam b c grauitas eſt humidi
              <lb/>
              <figure xlink:label="fig-0020-01" xlink:href="fig-0020-01a" number="9">
                <image file="0020-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0020-01"/>
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            molẽ habentis æqualem ipſia.
              <lb/>
            </s>
            <s xml:id="echoid-s301" xml:space="preserve">Si ergo demittatur in humidũ
              <lb/>
            magnitudo ex utriſque a d con
              <lb/>
            ſtans; </s>
            <s xml:id="echoid-s302" xml:space="preserve">uſque eò demergetur, ut
              <lb/>
            tanta moles humidi, quanta eſt
              <lb/>
            pars magnitudinis demerſa eã
              <lb/>
            dem, quam tota magnitudo
              <lb/>
            grauitatem habeat. </s>
            <s xml:id="echoid-s303" xml:space="preserve">hoc enim
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            iam demonſtratum eſt. </s>
            <s xml:id="echoid-s304" xml:space="preserve">ſit autẽ
              <lb/>
            ſuperſicies humidi alicuius a b
              <lb/>
            c d circunferentia. </s>
            <s xml:id="echoid-s305" xml:space="preserve">Quoniam igitur tanta moles humidi,
              <lb/>
            quanta eſt magnitudo a grauitatem habet eandem, quam
              <lb/>
            magnitudines a d: </s>
            <s xml:id="echoid-s306" xml:space="preserve">perſpicuum eſt partem ipſius demer-
              <lb/>
            ſam eſſe magnitudinem a; </s>
            <s xml:id="echoid-s307" xml:space="preserve">reliquam uero d totam ex </s>
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