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

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        <div xml:id="echoid-div147" type="section" level="1" n="115">
          <pb o="29" file="527.01.029" n="29" rhead="*DE* S*TATICÆ ELEMENTIS*."/>
        </div>
        <div xml:id="echoid-div149" type="section" level="1" n="116">
          <head xml:id="echoid-head125" xml:space="preserve">8 PROBLEMA. 14 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s855" xml:space="preserve">Datis, columnâ, inque ejus axe duobus punctis, uno
              <lb/>
            fixo, altero in longiore ſegmento mobili: </s>
            <s xml:id="echoid-s856" xml:space="preserve">invenire pondus
              <lb/>
            rectè attollens ex puncto mobili, quod datam columnam
              <lb/>
            in dato ſitu conſervet, retineatque.</s>
            <s xml:id="echoid-s857" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s858" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s859" xml:space="preserve">A B C D columna, ſecta utin 1 propoſit. </s>
            <s xml:id="echoid-s860" xml:space="preserve">initio, 6 ℔ pendeat,
              <lb/>
            punctum ejus firmum R, mobile autem in longiore axis R Q ſegmento, V
              <lb/>
            eſto, in breviore enim ſieri neutiquam poteſt, ut ullum pondus rectè attollens
              <lb/>
            axem in dato ſitu detineat.</s>
            <s xml:id="echoid-s861" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s862" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s863" xml:space="preserve">Pondus recte attollens nobis eſt inveniendum, quod in
              <lb/>
            ſuo ſitu columnam ſervet.</s>
            <s xml:id="echoid-s864" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div150" type="section" level="1" n="117">
          <head xml:id="echoid-head126" xml:space="preserve">PRAGMATIA.</head>
          <p>
            <s xml:id="echoid-s865" xml:space="preserve">Linea Q R continuanda
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              <figure xlink:label="fig-527.01.029-01" xlink:href="fig-527.01.029-01a" number="44">
                <image file="527.01.029-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.029-01"/>
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            eſt in Y, ut R Y æquet R V:
              <lb/>
            </s>
            <s xml:id="echoid-s866" xml:space="preserve">hinc pondus Z invenien-
              <lb/>
            dum, quod de Y ſuſpen-
              <lb/>
            ſum columnæ ſit ſitu æqui-
              <lb/>
            libre: </s>
            <s xml:id="echoid-s867" xml:space="preserve">illud ipſum, quia R
              <lb/>
            eſt punctum firmum, per 3
              <lb/>
            propoſit 4 ℔ pendebit. </s>
            <s xml:id="echoid-s868" xml:space="preserve">Dico
              <lb/>
            itaque Æ quæſitum pondus
              <lb/>
            rectè attollens 4 ℔ eſſe.</s>
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          </p>
        </div>
        <div xml:id="echoid-div152" type="section" level="1" n="118">
          <head xml:id="echoid-head127" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s870" xml:space="preserve">Quandoquidem radius R V ponderis Æ rectè attollentis æquatur radio
              <lb/>
            R Y ponderis Z. </s>
            <s xml:id="echoid-s871" xml:space="preserve">ipſaq́ue pondera Æ & </s>
            <s xml:id="echoid-s872" xml:space="preserve">Z æqualia, iſtorum quoque poten-
              <lb/>
            tias, ex 13 propoſit. </s>
            <s xml:id="echoid-s873" xml:space="preserve">æquari conſequens eſt. </s>
            <s xml:id="echoid-s874" xml:space="preserve">Atqui potentia Z eſt (amoto Æ)
              <lb/>
            columnam in ſuo ſitu retinere: </s>
            <s xml:id="echoid-s875" xml:space="preserve">itaque & </s>
            <s xml:id="echoid-s876" xml:space="preserve">potentia Æ (amoto Z) eadem eſt,
              <lb/>
            quod nobis fuit demonſtrandum.</s>
            <s xml:id="echoid-s877" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s878" xml:space="preserve">C*ONCLUSIO*. </s>
            <s xml:id="echoid-s879" xml:space="preserve">Datis igitur, columnâ, & </s>
            <s xml:id="echoid-s880" xml:space="preserve">in axe duobus punctis, altero
              <lb/>
            fixo, reliquo ſegmenti longioris mobili: </s>
            <s xml:id="echoid-s881" xml:space="preserve">rectum pondus attollens invenimus
              <lb/>
            quod in puncto mobili columnam in dato ſitu conſervat, quod fuit quæ-
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            ſitum.</s>
            <s xml:id="echoid-s882" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div153" type="section" level="1" n="119">
          <head xml:id="echoid-head128" xml:space="preserve">NOTATO</head>
          <p style="it">
            <s xml:id="echoid-s883" xml:space="preserve">Compendio concludi poſſe quemadmodum V R 3, ad R T 2: </s>
            <s xml:id="echoid-s884" xml:space="preserve">ita columna 6 ℔ ad
              <lb/>
            quem terminum quartum? </s>
            <s xml:id="echoid-s885" xml:space="preserve">concluditur pro Æ 4 ℔, utpaulò ante, cujus cauſa 15
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s886" xml:space="preserve">patebit.</s>
            <s xml:id="echoid-s887" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div154" type="section" level="1" n="120">
          <head xml:id="echoid-head129" xml:space="preserve">1 C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s888" xml:space="preserve">QVandoquidem univerſa columna ex conceſſo 6 ℔ pendet, quarum 4 ℔
              <lb/>
            Æ attollit, neceſſariò ſequitur in puncto R, hoc eſt, faſtigio coni, vel py-
              <lb/>
            ramidis OE reliquas 2 ℔ quieſcere.</s>
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