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

Table of Notes

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        <div xml:id="echoid-div353" type="section" level="1" n="251">
          <head xml:id="echoid-head265" xml:space="preserve">9 PROBLEMA. 21 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2420" xml:space="preserve">Dato ſolido epipedoëdro quocunque; </s>
            <s xml:id="echoid-s2421" xml:space="preserve">gravitatis centrum
              <lb/>
            invenire.</s>
            <s xml:id="echoid-s2422" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2423" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2424" xml:space="preserve">Eſto epipedoëdrum A quotcunque planis ſuperficiebus com-
              <lb/>
            prehenſum. </s>
            <s xml:id="echoid-s2425" xml:space="preserve">Q*VÆSITVM*. </s>
            <s xml:id="echoid-s2426" xml:space="preserve">Gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2427" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div354" type="section" level="1" n="252">
          <head xml:id="echoid-head266" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s2428" xml:space="preserve">Solidum ipſum tribuito in pyramides componentes, quam fieri poterit pau-
              <lb/>
            ciſſimas. </s>
            <s xml:id="echoid-s2429" xml:space="preserve">Summa autem eo caſu difficultas hucredit, utſi neceſſum ſit ſolidum
              <lb/>
            ipſum in totpyramides dirimatur quot hedris clauditur, pun-
              <lb/>
              <figure xlink:label="fig-527.01.074-01" xlink:href="fig-527.01.074-01a" number="120">
                <image file="527.01.074-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.074-01"/>
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            cto quocunque intra corpus pro vertice aſſumpto; </s>
            <s xml:id="echoid-s2430" xml:space="preserve">quibus cõ-
              <lb/>
            ſtitutis, pyramidum centra ſigillatim per 17 propoſ. </s>
            <s xml:id="echoid-s2431" xml:space="preserve">invenian-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s2432" xml:space="preserve">deinde duorum pyramidum centris rectâ linea connexis,
              <lb/>
            jugum hoc ſecetur ratione ipſorũ pyramidum, ut tamen mi-
              <lb/>
            nus ſegmentum ponderoſiori pyramidi ſit vicinum, deinde
              <lb/>
            centrum hoc inventum cum tertiæ pyramidis centro conjungatur, quarũ com-
              <lb/>
            mune centrum cum quarto connectes, atque eò in reliquis omnibus ordine
              <lb/>
            continuato, noviſſima jugi ſectio exhibebit optatum dati ſolidi gravitatis cen-
              <lb/>
            trum; </s>
            <s xml:id="echoid-s2433" xml:space="preserve">cujus demonſtratio ipſo operis ſucceſſu manifeſta eſt.</s>
            <s xml:id="echoid-s2434" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2435" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2436" xml:space="preserve">Itaque, dato qualicunque ſolido planis hedris compre-
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            henſo, gravitatis centrum invenimus. </s>
            <s xml:id="echoid-s2437" xml:space="preserve">Quod feciſſe oport
              <unsure/>
            uit.</s>
            <s xml:id="echoid-s2438" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div356" type="section" level="1" n="253">
          <head xml:id="echoid-head267" xml:space="preserve">13 PROBLEMA. 22 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2439" xml:space="preserve">Conoïdalis gravitatis centrum eſt in axe.</s>
            <s xml:id="echoid-s2440" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2441" xml:space="preserve">Conoïdalis recti centrum gravitatis eſſe in axe, per ſe & </s>
            <s xml:id="echoid-s2442" xml:space="preserve">communi quaſi no-
              <lb/>
            titiâ manifeſtum eſt, quamobrem duntaxat eo caſu cum axis baſi obliquus erit
              <lb/>
            demonſtrationem formabimus.</s>
            <s xml:id="echoid-s2443" xml:space="preserve"/>
          </p>
          <figure number="121">
            <image file="527.01.074-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.074-02"/>
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          <p>
            <s xml:id="echoid-s2444" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2445" xml:space="preserve">ABC conoïdale, baſis BC,
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            axis AD dictæ baſi obliquus.</s>
            <s xml:id="echoid-s2446" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2447" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2448" xml:space="preserve">Gravitatis centrum in
              <lb/>
            AD conſiſtere demonſtrandum.</s>
            <s xml:id="echoid-s2449" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2450" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s2451" xml:space="preserve">Conoïdale inter-
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            ſecetur planis duobus FF, GH baſi pa-
              <lb/>
            rallelis quæ axem AD incîdant in I & </s>
            <s xml:id="echoid-s2452" xml:space="preserve">K,
              <lb/>
            deinde ducantur rectæ EL, FM, GN,
              <lb/>
            HO, quare LM, NO, GH exipsâ ſe-
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            ctione ellipſes erunt ſimiles baſi BC: </s>
            <s xml:id="echoid-s2453" xml:space="preserve">& </s>
            <s xml:id="echoid-s2454" xml:space="preserve">
              <lb/>
            EM, GO cylindri baſis ellipticæ</s>
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        <div xml:id="echoid-div357" type="section" level="1" n="254">
          <head xml:id="echoid-head268" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2455" xml:space="preserve">LD ſemidiameter ellipſis LM, æquatur ſemidiametro DM, æquatur item
              <lb/>
            ipſis EI, IF; </s>
            <s xml:id="echoid-s2456" xml:space="preserve">Igitur ID axis fuerit cylindri EM in quo ejus gravitatis cen-
              <lb/>
            trum conſiſtit; </s>
            <s xml:id="echoid-s2457" xml:space="preserve">pari ratione cylindri GO gravitatis centrum erit in axe KI.
              <lb/>
            </s>
            <s xml:id="echoid-s2458" xml:space="preserve">quamobrem centrum ſolidi ex utroque compoſiti erit in KD, atque adeò in
              <lb/>
            axe AD. </s>
            <s xml:id="echoid-s2459" xml:space="preserve">ſed quò crebriores cylindri in conoïdale inſcribentur, eò </s>
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