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

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        <div xml:id="echoid-div78" type="section" level="1" n="66">
          <pb o="17" file="527.01.017" n="17" rhead="*DE STATICÆ* ELEMENTIS."/>
        </div>
        <div xml:id="echoid-div79" type="section" level="1" n="67">
          <head xml:id="echoid-head76" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s422" xml:space="preserve">Gravioris põderis A, in primo paradigma-
              <lb/>
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            te, ea eſt ratio ad levius B, quę longioris radii
              <lb/>
            E D ad breviorem E C. </s>
            <s xml:id="echoid-s423" xml:space="preserve">E F itaque per 9
              <lb/>
            definitionem anſa erit. </s>
            <s xml:id="echoid-s424" xml:space="preserve">Reliquorum exem-
              <lb/>
            plorum eadem demonſtratio fuerit, quibus
              <lb/>
            brevitatis cauſa ſuperſedemus.</s>
            <s xml:id="echoid-s425" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s426" xml:space="preserve">*CONCLVSIO.</s>
            <s xml:id="echoid-s427" xml:space="preserve">* Cognitis igitur ponde-
              <lb/>
            ribus datis anſam illorum invenerimus.</s>
            <s xml:id="echoid-s428" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div81" type="section" level="1" n="68">
          <head xml:id="echoid-head77" xml:space="preserve">NOTATO.</head>
          <p style="it">
            <s xml:id="echoid-s429" xml:space="preserve">Si ad γ, 2 paradigmatis pondus, 1 ℔ adderetur, & </s>
            <s xml:id="echoid-s430" xml:space="preserve">ex V 1 ℔ ſuſpenderetur, at
              <lb/>
            hîc infra ponitur, ex antecedentibus manifeſtum
              <lb/>
              <figure xlink:label="fig-527.01.017-02" xlink:href="fig-527.01.017-02a" number="23">
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            eſt X N anſam nibilo minus manere, & </s>
            <s xml:id="echoid-s431" xml:space="preserve">quæcung
              <lb/>
            ex ea dependĕt ſitu æquilibria eſſe. </s>
            <s xml:id="echoid-s432" xml:space="preserve">Idem N X ma-
              <lb/>
            nebit ſi Z 1 ℔ pendeat ex T, & </s>
            <s xml:id="echoid-s433" xml:space="preserve">γ 14 ℔ valeat;
              <lb/>
            </s>
            <s xml:id="echoid-s434" xml:space="preserve">aut Z 1 ℔ ex S, & </s>
            <s xml:id="echoid-s435" xml:space="preserve">γ ſit ℔ 15: </s>
            <s xml:id="echoid-s436" xml:space="preserve">itidem Z 1 ℔ ex
              <lb/>
            R, & </s>
            <s xml:id="echoid-s437" xml:space="preserve">γ ſit 16 ℔, aut ex P, & </s>
            <s xml:id="echoid-s438" xml:space="preserve">γ ſit 17 ℔. </s>
            <s xml:id="echoid-s439" xml:space="preserve">& </s>
            <s xml:id="echoid-s440" xml:space="preserve">
              <lb/>
            ita deinceps ſi jugum longius fuerit, perpetuo 1 ℔
              <lb/>
            ad γ addendo, pro longitudine cujus{q́ue} partis
              <lb/>
            æquantis X V, quò Z promovetur. </s>
            <s xml:id="echoid-s441" xml:space="preserve">Vnde quali-
              <lb/>
            tates & </s>
            <s xml:id="echoid-s442" xml:space="preserve">affectiones Stater æ cognoſcuntur, ut ple-
              <lb/>
            nius in Statices praxi tr actabitur.</s>
            <s xml:id="echoid-s443" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div83" type="section" level="1" n="69">
          <head xml:id="echoid-head78" xml:space="preserve">2 PROBLEMA. 3 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s444" xml:space="preserve">Datis ponderibus ſitu æquipondiis, altero cognito, al-
              <lb/>
            tero incognito, unà cum ansâ: </s>
            <s xml:id="echoid-s445" xml:space="preserve">incognitum cognitum
              <lb/>
            reddere.</s>
            <s xml:id="echoid-s446" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div84" type="section" level="1" n="70">
          <head xml:id="echoid-head79" xml:space="preserve">1 Exemplum.</head>
          <p>
            <s xml:id="echoid-s447" xml:space="preserve">*DATVM.</s>
            <s xml:id="echoid-s448" xml:space="preserve">* A & </s>
            <s xml:id="echoid-s449" xml:space="preserve">B duo pondera ſitu æquipondia ſunto
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            quorum A ex C ſuſpenſum 3 ℔ pendeat, B verò ſuſpenſum
              <lb/>
            ex D ignorator, E F anſa. </s>
            <s xml:id="echoid-s450" xml:space="preserve">*QVAESITVM.</s>
            <s xml:id="echoid-s451" xml:space="preserve">* Pondus B
              <lb/>
            innoteſcat.</s>
            <s xml:id="echoid-s452" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div86" type="section" level="1" n="71">
          <head xml:id="echoid-head80" xml:space="preserve">PRAGMATIA.</head>
          <p>
            <s xml:id="echoid-s453" xml:space="preserve">In rationem radii E D ad radium E C inquirendum eſt,
              <lb/>
            ſit autem ex hypotheſi, ut 3 ad 1, dico igitur quemadmodum
              <lb/>
            E D 3, ad E C 1: </s>
            <s xml:id="echoid-s454" xml:space="preserve">ita & </s>
            <s xml:id="echoid-s455" xml:space="preserve">3 ℔ ad quem? </s>
            <s xml:id="echoid-s456" xml:space="preserve">proportione conclu-
              <lb/>
            ditur 1 ℔.</s>
            <s xml:id="echoid-s457" xml:space="preserve"/>
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        <div xml:id="echoid-div87" type="section" level="1" n="72">
          <head xml:id="echoid-head81" style="it" xml:space="preserve">2 Exemplum.</head>
          <p>
            <s xml:id="echoid-s458" xml:space="preserve">*DATVM.</s>
            <s xml:id="echoid-s459" xml:space="preserve">* Quemadmodum 2 propoſitionis 2 exemplo, columna A B C D
              <lb/>
            pro altero pondere 6 ℔ pendeat, reliquum pondus incognitũ, & </s>
            <s xml:id="echoid-s460" xml:space="preserve">inde ſuſpen-
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            ſum Y ſit, anſa autĕ X N. </s>
            <s xml:id="echoid-s461" xml:space="preserve">*QVAESITVM.</s>
            <s xml:id="echoid-s462" xml:space="preserve">* In põdus X inquirendũ nobis eſt.</s>
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