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

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          <pb o="115" file="527.01.115" n="115" rhead="*DE* H*YDROSTATICES ELEMENTIS*."/>
        </div>
        <div xml:id="echoid-div468" type="section" level="1" n="336">
          <head xml:id="echoid-head353" xml:space="preserve">3 THEOREMA. 3 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s3295" xml:space="preserve">Corpus ſolidum materiæ ponderoſioris quàm aqua ad
              <lb/>
            fundum uſque demergitur.</s>
            <s xml:id="echoid-s3296" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3297" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s3298" xml:space="preserve">Efto corpus ſolidum A materiâ ponderoſiore quàm aqua B C,
              <lb/>
            cujus ſuperſicies ſumma B D, ima E C. </s>
            <s xml:id="echoid-s3299" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3300" xml:space="preserve">A aquæ B C im-
              <lb/>
            poſitum ad fundum E C uſque deſcendere demonſtrator.</s>
            <s xml:id="echoid-s3301" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3302" xml:space="preserve">P*RÆPARATIO*. </s>
            <s xml:id="echoid-s3303" xml:space="preserve">Vas ſuperſiciatium F G aqua plenum ipſi A ſimile & </s>
            <s xml:id="echoid-s3304" xml:space="preserve">
              <lb/>
            æquale deſormato, cujus ſuperſicies ſumma F H in plano B D collocetur.</s>
            <s xml:id="echoid-s3305" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div469" type="section" level="1" n="337">
          <head xml:id="echoid-head354" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3306" xml:space="preserve">Cum A materiæ quidem ponderoſioris ſit ex hy potheſi quam aqua F G,
              <lb/>
            magnitudinis verò æ qualis; </s>
            <s xml:id="echoid-s3307" xml:space="preserve">A quoque gravius erit quam F G. </s>
            <s xml:id="echoid-s3308" xml:space="preserve">Iam ſi in locum
              <lb/>
            aquæ F G ſubſtituatur ipſi pro pter fab team congruum corpu; </s>
            <s xml:id="echoid-s3309" xml:space="preserve">A attamen, ut
              <lb/>
            patet, illo ponderoſius, vas ſuperſiciarium F G per 3 poſtul. </s>
            <s xml:id="echoid-s3310" xml:space="preserve">ab A corpore al-
              <lb/>
            tius demergetur quam ab aqua F G. </s>
            <s xml:id="echoid-s3311" xml:space="preserve">demonſiravimus igitur corpus A mergi;
              <lb/>
            </s>
            <s xml:id="echoid-s3312" xml:space="preserve">fed ad fundum E C uſque demergi ita evincam. </s>
            <s xml:id="echoid-s3313" xml:space="preserve">Si enim fiem poſſit ne deſcen-
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            dat ad E C, ſed interinedio loco hæreat ut in I. </s>
            <s xml:id="echoid-s3314" xml:space="preserve">Iam ſi vice ſolidi corporis I
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            vas ejus ſuperſiciarium aquâ compleatur, eodem loco per I propoſ. </s>
            <s xml:id="echoid-s3315" xml:space="preserve">ſubſiſtet: </s>
            <s xml:id="echoid-s3316" xml:space="preserve">
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            fed æ qua hæc levior eſt iſto ſolido; </s>
            <s xml:id="echoid-s3317" xml:space="preserve">quamobrem gravius
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                <image file="527.01.115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.115-01"/>
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            leviusq́ue in humido eodem hærebuntloco, quod abſur
              <lb/>
            dum 3 poſtulato repugnat. </s>
            <s xml:id="echoid-s3318" xml:space="preserve">Itaque eorpus A inter B D,
              <lb/>
            E C, ſummam imamq́ue ſuperſiciem conſiſtere nequit,
              <lb/>
            ac neceſſariò deſcendet donec ſundo ſubjecto E C im-
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            pactum quieſcat. </s>
            <s xml:id="echoid-s3319" xml:space="preserve">C*ONCLVSIO.</s>
            <s xml:id="echoid-s3320" xml:space="preserve">* Solidum corpus igi-
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            tur materiæ ponderoſioris quam aqua ad fundum uſque demergitur. </s>
            <s xml:id="echoid-s3321" xml:space="preserve">Quod
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            demonſtraſſe oportuit.</s>
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        <div xml:id="echoid-div471" type="section" level="1" n="338">
          <head xml:id="echoid-head355" xml:space="preserve">4 THEOREMA. 4 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s3323" xml:space="preserve">Corpus ſolidum materiâ aquæ æquiponderante, datum
              <lb/>
            inaqua locum ſervat.</s>
            <s xml:id="echoid-s3324" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3325" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s3326" xml:space="preserve">Corpus ſolidum A materiam habeat gravitate æqualem aquæ
              <lb/>
            BC. </s>
            <s xml:id="echoid-s3327" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3328" xml:space="preserve">Corpus A ubicunque in aqua ſtatuetur ſubſiſtere de-
              <lb/>
            monſtrato. </s>
            <s xml:id="echoid-s3329" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s3330" xml:space="preserve">Eſto vas ſuperſiciarium D, ipſi A æquale & </s>
            <s xml:id="echoid-s3331" xml:space="preserve">
              <lb/>
            ſimile.</s>
            <s xml:id="echoid-s3332" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div472" type="section" level="1" n="339">
          <head xml:id="echoid-head356" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3333" xml:space="preserve">Cum A materię ponderitate & </s>
            <s xml:id="echoid-s3334" xml:space="preserve">corporis mole æquale ſit aquæ D, ideo
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            D ipſi A pondere quoque æquatur. </s>
            <s xml:id="echoid-s3335" xml:space="preserve">Iam in vaſe ſuperſiciario D loco aquæ
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            ſubſtituitor corpus A ipſi propter fabricam per omnia congruum, quare per
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            3 poſſul. </s>
            <s xml:id="echoid-s3336" xml:space="preserve">vas ſuperficiarium D ab corpore A nec ma-
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                <image file="527.01.115-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.115-02"/>
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            gis nec minus demergetur quam ab aqua D; </s>
            <s xml:id="echoid-s3337" xml:space="preserve">ſed aqua
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            D per 1 propoſ datum ſibi locum ſervat. </s>
            <s xml:id="echoid-s3338" xml:space="preserve">Itaque etiam
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            ſolidum corpus A in aqua B C tributum ſibi locum
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            retinebit, neque aliò delabetur.</s>
            <s xml:id="echoid-s3339" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3340" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s3341" xml:space="preserve">Quamobrem corpus ſolidum, cujus
              <lb/>
            materies ponderitate aquæ eſt æqualis, datum ſervat locum. </s>
            <s xml:id="echoid-s3342" xml:space="preserve">Quod erat de-
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            monſtrandum.</s>
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