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

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        <div xml:id="echoid-div490" type="section" level="1" n="353">
          <pb o="119" file="527.01.119" n="119" rhead="*DE* H*YDROSTATICES ELEMENTIS.*"/>
          <p>
            <s xml:id="echoid-s3440" xml:space="preserve">Tertium quoddam exemplum excogitari potuit, cum ratio ponderitatum
              <lb/>
            utriuſque materiæ aqueæ ſcilicet & </s>
            <s xml:id="echoid-s3441" xml:space="preserve">ſolidę ęqualis erit: </s>
            <s xml:id="echoid-s3442" xml:space="preserve">ſed eo caſu, normam for-
              <lb/>
            mamq́ue antecedentis pragmatiæ ſecutus, deprehendes ſolidum corpus in tali
              <lb/>
            aqua nec grave eſſe neque leve. </s>
            <s xml:id="echoid-s3443" xml:space="preserve">demonſtratio autem omniũ horum per 8 prop.
              <lb/>
            </s>
            <s xml:id="echoid-s3444" xml:space="preserve">manifeſta eſt. </s>
            <s xml:id="echoid-s3445" xml:space="preserve">C*ONCLVSIO.</s>
            <s xml:id="echoid-s3446" xml:space="preserve">* Itaq; </s>
            <s xml:id="echoid-s3447" xml:space="preserve">corporis ſolidi gravitate, ejuſdemq́; </s>
            <s xml:id="echoid-s3448" xml:space="preserve">ma-
              <lb/>
            teriæ ponderitatis ad ponderitatem aqueam ratione data; </s>
            <s xml:id="echoid-s3449" xml:space="preserve">ejus ſitus gravitatem
              <lb/>
            in aqua invenimus. </s>
            <s xml:id="echoid-s3450" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s3451" xml:space="preserve"/>
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        <div xml:id="echoid-div491" type="section" level="1" n="354">
          <head xml:id="echoid-head371" xml:space="preserve">8 THE OREMA. 10 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s3452" xml:space="preserve">Aquæ fundo horizonti parallelo tantum inſidet pon-
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            dus, quantum eſt aqueæ columnæ cujus baſis fundo, alti-
              <lb/>
            tudo perpendiculari ab aquæ ſuperſicie ſumma ad imam
              <lb/>
            demiſſæ æqualis ſit.</s>
            <s xml:id="echoid-s3453" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3454" xml:space="preserve">D*ATVM.</s>
            <s xml:id="echoid-s3455" xml:space="preserve">* ABCD aquæ figura ſolida rectangula, AB ſuperficies ſumma,
              <lb/>
            EF pars fundi horizonti paralleli, GE perpendicularis à ſumma ad imam aquæ
              <lb/>
            ſuperficiem, columna GHFE comprehenſa ſub baſi EF & </s>
            <s xml:id="echoid-s3456" xml:space="preserve">altitudine EG.</s>
            <s xml:id="echoid-s3457" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3458" xml:space="preserve">Q*VAESITVM.</s>
            <s xml:id="echoid-s3459" xml:space="preserve">* Demonſtrato baſe ſeu fundo EF ſuſtineri pondus æqua-
              <lb/>
            le columnæ aqueæ GHFE.</s>
            <s xml:id="echoid-s3460" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div492" type="section" level="1" n="355">
          <head xml:id="echoid-head372" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3461" xml:space="preserve">Sifundo EF plus ponderis inſideat quàm aquæ GHFE, id erit ab aqua
              <lb/>
            finitima, atque ideò ſi ſieri poſſit eſto ab AGED & </s>
            <s xml:id="echoid-s3462" xml:space="preserve">HBCF; </s>
            <s xml:id="echoid-s3463" xml:space="preserve">quibus poſitis
              <lb/>
            fundo DE quoque, propter aquam finitimam GHFE
              <lb/>
            (cum utrobiq; </s>
            <s xml:id="echoid-s3464" xml:space="preserve">ſit parratio) plus pó deris incumbet quàm
              <lb/>
              <figure xlink:label="fig-527.01.119-01" xlink:href="fig-527.01.119-01a" number="164">
                <image file="527.01.119-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.119-01"/>
              </figure>
            ſit aquæ AGED, perinde quoque baſi FC plusinſi-
              <lb/>
            det ponderis quam aquæ HBCF; </s>
            <s xml:id="echoid-s3465" xml:space="preserve">quare toti fundo
              <lb/>
            DC majus quoddam pondus inſidet quam aquæ totius
              <lb/>
            ABCD, quod tamen, cum ABCD corpus rectan-
              <lb/>
            gulum ſit, abſurdum ſuerit. </s>
            <s xml:id="echoid-s3466" xml:space="preserve">Eadem ratione evinces fun-
              <lb/>
            do EF non minus pondus ſuſtentari quam ſit aquæ GHFE; </s>
            <s xml:id="echoid-s3467" xml:space="preserve">quare tantun-
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            dem duntaxat ponderis neceſſario ipſi incumbet.</s>
            <s xml:id="echoid-s3468" xml:space="preserve"/>
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        <div xml:id="echoid-div494" type="section" level="1" n="356">
          <head xml:id="echoid-head373" xml:space="preserve">1 C*ONSECTARIVM.*</head>
          <p>
            <s xml:id="echoid-s3469" xml:space="preserve">Immittito in aquam ABCD hujus propoſitionis corpus ſolidum IKLM,
              <lb/>
            materiæ levioris quam aqua, quodque ideo ipſi innatet parte NOLM
              <lb/>
            immersâ, reliquâ NOKI ſupereminente, ut in ſubjecta ſigura apparet. </s>
            <s xml:id="echoid-s3470" xml:space="preserve">Iam
              <lb/>
            ſolidum IKLM per 5 propoſ. </s>
            <s xml:id="echoid-s3471" xml:space="preserve">gravitate æquale eſt tan-
              <lb/>
              <figure xlink:label="fig-527.01.119-02" xlink:href="fig-527.01.119-02a" number="165">
                <image file="527.01.119-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.119-02"/>
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            tæ aqueæ moli, quanta eſt pars ſui demerſa NOLM;
              <lb/>
            </s>
            <s xml:id="echoid-s3472" xml:space="preserve">quare ſolidum IKLM cum reliqua ipſum ambiente
              <lb/>
            aqua pondere æquat corpus aqueum magnitudinis
              <lb/>
            ABCD. </s>
            <s xml:id="echoid-s3473" xml:space="preserve">Itaque etiamnum aſſerimus ſecundùm pro-
              <lb/>
            poſitionis ſententiam, ſundo EF inniti pondus æquale
              <lb/>
            corpori aqueo magnitudinis columnæ, cujus baſis ſit
              <lb/>
            EF, altitudo perpendicularis GE à ſumma ſuperficie
              <lb/>
            aquæ AB adimum fundum EF demiſſa. </s>
            <s xml:id="echoid-s3474" xml:space="preserve">Vnde efficitur à materia qualibct
              <lb/>
            aquæ innatante fundum nec magis nec minus affici, quam ab aqua in eadem
              <lb/>
            altitudine conſtituta.</s>
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