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

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          <pb o="114" file="527.01.114" n="114" rhead="4 L*IBER* S*TATICÆ*"/>
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        <div xml:id="echoid-div462" type="section" level="1" n="332">
          <head xml:id="echoid-head348" xml:space="preserve">PROPOSITIONES.</head>
          <head xml:id="echoid-head349" xml:space="preserve">1 THEOREMA. 1 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s3258" xml:space="preserve">Aquam datam, datum ſibi intra aquam locum ſervare.</s>
            <s xml:id="echoid-s3259" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3260" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s3261" xml:space="preserve">Aqua data vaſe ſuperficiario contenta collocator in aqua B C.
              <lb/>
            </s>
            <s xml:id="echoid-s3262" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3263" xml:space="preserve">Aquam A eo loco ſubſiſtere.</s>
            <s xml:id="echoid-s3264" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div463" type="section" level="1" n="333">
          <head xml:id="echoid-head350" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3265" xml:space="preserve">A igitur (ſi ullo modo per naturam ſieri poſſit) locum ſibi tributum non fer-
              <lb/>
            vato, ac delabatur in D; </s>
            <s xml:id="echoid-s3266" xml:space="preserve">quibus poſitis aqua quæ ipſi A ſucceffit eandem ob
              <lb/>
            cauſam deſluet in D, eademq́ue ab alia iſtinc expelletur, atque adeo aqua bæc
              <lb/>
            (cum ubique eadem ratio ſit) motũ inſtituet perpetuurn, quod
              <lb/>
            abſurdum fuerit. </s>
            <s xml:id="echoid-s3267" xml:space="preserve">Similiter demonſtratur A nec adſcendere
              <lb/>
              <figure xlink:label="fig-527.01.114-01" xlink:href="fig-527.01.114-01a" number="154">
                <image file="527.01.114-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.114-01"/>
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            neque in latus moveri. </s>
            <s xml:id="echoid-s3268" xml:space="preserve">Proinde manifeſtum jam eſt, ſi A ſtatua-
              <lb/>
            tur alicubi intra aquam in D, E, F vel G iſtic in loco ſibi tribu-
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            to ſeſe ſiſtere.</s>
            <s xml:id="echoid-s3269" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3270" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s3271" xml:space="preserve">Itaque data aqua quemlibet datum ſibilo-
              <lb/>
            cum ſervat. </s>
            <s xml:id="echoid-s3272" xml:space="preserve">Quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s3273" xml:space="preserve"/>
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        <div xml:id="echoid-div465" type="section" level="1" n="334">
          <head xml:id="echoid-head351" xml:space="preserve">2 THE OREMA. 2 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s3274" xml:space="preserve">Solidum corpus materia leviore quam ſit aqua non
              <lb/>
            omnino mergitur, ſed eminet aliqua ſui parte.</s>
            <s xml:id="echoid-s3275" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3276" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s3277" xml:space="preserve">Solidum corpus A materiam habeat leviorem aquâ B C, cujus
              <lb/>
            ſumma ſuperficies B D. </s>
            <s xml:id="echoid-s3278" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3279" xml:space="preserve">A aquæ impoſitum non universè
              <lb/>
            mergi ſed aliqua parte eminere demonſtrandum eſto.</s>
            <s xml:id="echoid-s3280" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3281" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s3282" xml:space="preserve">EF vas ſuperſiciarium, cujus pars G F demerſa & </s>
            <s xml:id="echoid-s3283" xml:space="preserve">
              <lb/>
            plena aquæ æqualis ſimilisq́ue ſit ipſi A, itaque aquæ ejus ſuperſicies G H erit
              <lb/>
            in plano B D, quia ſuperſiciarium vas E F gravitatis levitatisq́ue ſit expers.</s>
            <s xml:id="echoid-s3284" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div466" type="section" level="1" n="335">
          <head xml:id="echoid-head352" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3285" xml:space="preserve">Cum igitur A ex hypotheſi materiam habeat leviorem aquâ G F, & </s>
            <s xml:id="echoid-s3286" xml:space="preserve">hæc
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            dato corpori A ſit æ qualis, G F neceſſariò ipſi A præponderabit, jam in vaſe
              <lb/>
            ſuperſiciario locoaquæ ſubſtituitor corpus A ipſi congruum, nam ex fabrica
              <lb/>
            parti G F æquale eſt & </s>
            <s xml:id="echoid-s3287" xml:space="preserve">ſimile; </s>
            <s xml:id="echoid-s3288" xml:space="preserve">cumq́ue A corpus levius ſit aqua effusâ pro-
              <lb/>
            pterea vas ſuperficiarium E F per 3 poſtul non tam alte
              <lb/>
              <figure xlink:label="fig-527.01.114-02" xlink:href="fig-527.01.114-02a" number="155">
                <image file="527.01.114-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.114-02"/>
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            mergetur ab A atque ab F G: </s>
            <s xml:id="echoid-s3289" xml:space="preserve">atqui quantò minus altè
              <lb/>
            corpus ſuperſiciarium E F ſubſidit, tantum corporis A
              <lb/>
            ſupra aquam extare neceſſe eſt.</s>
            <s xml:id="echoid-s3290" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3291" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s3292" xml:space="preserve">Quamobrem corpus ſolidum ma-
              <lb/>
            teriæ levioris quàm aqua non totum mergitur, ſed ali-
              <lb/>
            qua ſui parte ſupereminet. </s>
            <s xml:id="echoid-s3293" xml:space="preserve">Quod demonſtraſſe oportuit.</s>
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