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

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          <pb o="31" file="527.01.031" n="31" rhead="*DE* S*TATICÆ ELEMENTIS*."/>
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        <div xml:id="echoid-div157" type="section" level="1" n="122">
          <head xml:id="echoid-head131" xml:space="preserve">7 THEOREMA. 15 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s903" xml:space="preserve">Duorum punctorum in axe columnæ altero fixo, alte-
              <lb/>
            ro mobili: </s>
            <s xml:id="echoid-s904" xml:space="preserve">Pondus rectèattollĕs ex mobili cum columnâ
              <lb/>
            ſitu æquipondium, illam habet rationem ad columnam,
              <lb/>
            quæ eſt ſegmenti axis quod inter centrum gravitatis & </s>
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              <lb/>
            punctum fixum eſt, ad ſegmentum ejuſdem quod inter
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            fixum & </s>
            <s xml:id="echoid-s906" xml:space="preserve">mobile intercipitur.</s>
            <s xml:id="echoid-s907" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div158" type="section" level="1" n="123">
          <head xml:id="echoid-head132" xml:space="preserve">DECLARATIO.</head>
          <p>
            <s xml:id="echoid-s908" xml:space="preserve">Figuras è 14 propoſit. </s>
            <s xml:id="echoid-s909" xml:space="preserve">repetamus, è quibus patet ita eſſe T R ad R V:
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            </s>
            <s xml:id="echoid-s910" xml:space="preserve">quemadmodum Æ 4 ℔ ad columnam 6 ℔. </s>
            <s xml:id="echoid-s911" xml:space="preserve">Sed ut cauſam hujus Mathema-
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            iicèaperiamus, ſciendum eſt, ita eſſe R T ad R Y: </s>
            <s xml:id="echoid-s912" xml:space="preserve">ut pondus Z ad pondus
              <lb/>
            columnæ, per 1 propoſit. </s>
            <s xml:id="echoid-s913" xml:space="preserve">Atqui Æ æquale eſt Z, & </s>
            <s xml:id="echoid-s914" xml:space="preserve">R V ex conceſſo æquale
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            eſt R Y, itaque ut Æ ad columnam: </s>
            <s xml:id="echoid-s915" xml:space="preserve">ita T R ad R V. </s>
            <s xml:id="echoid-s916" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s917" xml:space="preserve">Duo-
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            rum igitur punctorum altero fixo, altero mobili, &</s>
            <s xml:id="echoid-s918" xml:space="preserve">c.</s>
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          </p>
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        <div xml:id="echoid-div159" type="section" level="1" n="124">
          <head xml:id="echoid-head133" xml:space="preserve">8 THEOREMA. 16 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s920" xml:space="preserve">Duorum punctorum in axe columnæ, altero fixo, al-
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            tero mobili: </s>
            <s xml:id="echoid-s921" xml:space="preserve">Pondus rectèattollens è puncto mobili ſer-
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            vans columnam in uno aliquo ſitu, in quovis alio ſervare
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            poterit.</s>
            <s xml:id="echoid-s922" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s923" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s924" xml:space="preserve">Columnam 14 propoſitionis cum ſuis póderibus, in fixo pun-
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            cto R non nihil vertamus mutemusq́ue, maneatq́ue Æ pondus rectum ex-
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            tollens, cæteráque ſint bujuſmodi, quemadmodum hîc exhibentur.</s>
            <s xml:id="echoid-s925" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s926" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s927" xml:space="preserve">Demonſtrandum nobis eſt, Æ pondus rectè attollens
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            columnam in dato ſitu ſervare.</s>
            <s xml:id="echoid-s928" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div160" type="section" level="1" n="125">
          <head xml:id="echoid-head134" xml:space="preserve">DEMONSTRATIO.</head>
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            <s xml:id="echoid-s929" xml:space="preserve">Amoto Æ, Z vero 4 ℔ ap-
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              <figure xlink:label="fig-527.01.031-01" xlink:href="fig-527.01.031-01a" number="49">
                <image file="527.01.031-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.031-01"/>
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            penſo, columna ex 10 propoſ.
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            </s>
            <s xml:id="echoid-s930" xml:space="preserve">in dato manebit ſitu. </s>
            <s xml:id="echoid-s931" xml:space="preserve">Atqui
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            Æ in puncto V, & </s>
            <s xml:id="echoid-s932" xml:space="preserve">Z in pun-
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            cto Y vim potentiamq́ue pa-
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            rilem columnæ adferunt ex
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            13 propoſit. </s>
            <s xml:id="echoid-s933" xml:space="preserve">Amoto itaque Z,
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            Æ appenſum eodem in ſitu
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            columnam tenebit.</s>
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            <s xml:id="echoid-s935" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s936" xml:space="preserve">Duorum
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            igitur punctorum in axe, alte-
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            ro fixo, altero mobili, rectè attollens pondus mobili appenſum in uno aliquo
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            ſitu columnam ſervans, in quovis alio ſervare poterit.</s>
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