Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

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          <pb o="117" file="527.01.117" n="117" rhead="*DE* H*YDROSTATICES ELEMENTIS.*"/>
        </div>
        <div xml:id="echoid-div480" type="section" level="1" n="345">
          <head xml:id="echoid-head362" xml:space="preserve">6 THE OREMA. 7 PROPOSITIO.</head>
          <p type="title">
            <s xml:id="echoid-s3376" xml:space="preserve">In aquis ponderitatis heterogeneæ erit ut ponderitas ma-
              <lb/>
            teriæ aquæ ponderoſioris ad ponderitatem materiæ aquæ
              <lb/>
            levioris, ſic pars corporis ſolidi in aquam materiæ levioris
              <lb/>
            immerſa ad partem ſolidi ejuſdem in aqua graviore de-
              <lb/>
            merſam.</s>
            <s xml:id="echoid-s3377" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3378" xml:space="preserve">D*ATVM.</s>
            <s xml:id="echoid-s3379" xml:space="preserve">* Aqua AB materiæ ſit gravioris quam DC, corpus ſolidum EF
              <lb/>
            materiâ utrâlibet ipſarum leviore, quod in aquam AB immiſſum parte GF
              <lb/>
            aquæ inſideat, idemq́ue immiſſum in aquam CD mergatur parte KI.</s>
            <s xml:id="echoid-s3380" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3381" xml:space="preserve">Q*VAESITVM.</s>
            <s xml:id="echoid-s3382" xml:space="preserve">* Demonſtrandum materiæ gravitatem aquæ AB, adgra-
              <lb/>
            vitatem materiæ aquæ CD eſſe, ſicut KI ad GF.</s>
            <s xml:id="echoid-s3383" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div481" type="section" level="1" n="346">
          <head xml:id="echoid-head363" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3384" xml:space="preserve">Moles aquæ ex AB æqualis ipſi GF, ponderitate æquabit corpus EF; </s>
            <s xml:id="echoid-s3385" xml:space="preserve">ſic
              <lb/>
            item moles aquea ex CD æqualis ipſi KI æquiponderat p
              <unsure/>
            ci 5 propoſ. </s>
            <s xml:id="echoid-s3386" xml:space="preserve">corpo-
              <lb/>
            ri HI ſive EF cum ex hypotheſi ſit unum
              <lb/>
            idemq́ue corpus; </s>
            <s xml:id="echoid-s3387" xml:space="preserve">& </s>
            <s xml:id="echoid-s3388" xml:space="preserve">moles igitur aquæ ex AB
              <lb/>
              <figure xlink:label="fig-527.01.117-01" xlink:href="fig-527.01.117-01a" number="160">
                <image file="527.01.117-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.117-01"/>
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            ęqualis ipſi GF ponderitate quoque æquat
              <lb/>
            molem aqueam ex CD ęqualem ipſi KI. </s>
            <s xml:id="echoid-s3389" xml:space="preserve">Sed
              <lb/>
            poſitis duabus aquis gravitatis æqualis erit ma-
              <lb/>
            gnitudinum & </s>
            <s xml:id="echoid-s3390" xml:space="preserve">materię ponderitatum propor-
              <lb/>
            tio reciproca, quod neceſſariò deduciturè de-
              <lb/>
            finitione 5. </s>
            <s xml:id="echoid-s3391" xml:space="preserve">quare ratio ponderoſitatis materiæ
              <lb/>
            aquæ AB ad ponderitatem materię aquæ CD eadem erit, quæ magnitudinis
              <lb/>
            KI ad mag
              <unsure/>
            itudinem GF. </s>
            <s xml:id="echoid-s3392" xml:space="preserve">C*ONCLVSIO.</s>
            <s xml:id="echoid-s3393" xml:space="preserve">* Itaque in aquis ponderitatis
              <lb/>
            heterogeneæ ut ponderitas materiæ, &</s>
            <s xml:id="echoid-s3394" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3395" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div483" type="section" level="1" n="347">
          <head xml:id="echoid-head364" xml:space="preserve">7 THE OREMA. 8 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s3396" xml:space="preserve">Corpus ſolidum in aqua levius eſt quàm in aëre, pon-
              <lb/>
            dere aquæ magnitudine ſibiæqualis.</s>
            <s xml:id="echoid-s3397" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3398" xml:space="preserve">D*ATVM.</s>
            <s xml:id="echoid-s3399" xml:space="preserve">* Eſto A corpus ſolidum, aqua BC.</s>
            <s xml:id="echoid-s3400" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3401" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3402" xml:space="preserve">Demonſtrato corpus A in aquam immiſſum iſticlevius
              <lb/>
            eſſe quam in aëre gravitate aqueę molis magnitudine ſibiæqualis.</s>
            <s xml:id="echoid-s3403" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3404" xml:space="preserve">P*RAEPARATIO.</s>
            <s xml:id="echoid-s3405" xml:space="preserve">* Sit D vas ſuperficiarium aquæ plenum, ſimile & </s>
            <s xml:id="echoid-s3406" xml:space="preserve">æqua-
              <lb/>
            leipſi A.</s>
            <s xml:id="echoid-s3407" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div484" type="section" level="1" n="348">
          <head xml:id="echoid-head365" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3408" xml:space="preserve">Vas ſuperficiarium D aqua repletum per 1 propoſ. </s>
            <s xml:id="echoid-s3409" xml:space="preserve">in ipſa aqua nec gravi-
              <lb/>
            tatis neque levitatis habet momentum, quare eſſusâ aquâ D vastanto aquę
              <lb/>
            pondere erit levius, id eſt, perſectè leve; </s>
            <s xml:id="echoid-s3410" xml:space="preserve">in hocſubſti-
              <lb/>
            tuito corpus A ipſi congruum, jam vas ſuperficia-
              <lb/>
              <figure xlink:label="fig-527.01.117-02" xlink:href="fig-527.01.117-02a" number="161">
                <image file="527.01.117-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.117-02"/>
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            rium cum corpore A ſibi inſerto pendet pódus ipſius
              <lb/>
            A ſimul cum dicta levitate, hoc eſt, pendet pondus
              <lb/>
            A dempto pondere aquæ prius effuſę, ſed aqua iſta
              <lb/>
            mole æquat corpus A. </s>
            <s xml:id="echoid-s3411" xml:space="preserve">Quamobrem A </s>
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