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

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          <p>
            <s xml:id="echoid-s541" xml:space="preserve">
              <pb o="20" file="527.01.020" n="20" rhead="*I LIBER STATICÆ*"/>
            eſto, ut ſecunda figura exhibet, & </s>
            <s xml:id="echoid-s542" xml:space="preserve">I H producatur in O, A B ſecans in P, ſe-
              <lb/>
            gmentumq́ue columnæ P O C B contra P O D A æquilibre pendeat, atqui
              <lb/>
            illud iſto & </s>
            <s xml:id="echoid-s543" xml:space="preserve">majus & </s>
            <s xml:id="echoid-s544" xml:space="preserve">ponderoſius eſt (C F G D A enim æquatur F G C B,
              <lb/>
            triangulum autem FHI deſectum de F G C B minus eſt triangulo O H G
              <lb/>
            de F G C B deſecto, ideo & </s>
            <s xml:id="echoid-s545" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s546" xml:space="preserve">ponderoſius itaque ſeleviori æquilibre erit,
              <lb/>
            quod planè abſurdum eſt. </s>
            <s xml:id="echoid-s547" xml:space="preserve">Quapropter K L
              <lb/>
              <figure xlink:label="fig-527.01.020-01" xlink:href="fig-527.01.020-01a" number="28">
                <image file="527.01.020-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.020-01"/>
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            ad horizontem M N parallelus eſt, ut in
              <lb/>
            primo diagrammate.</s>
            <s xml:id="echoid-s548" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s549" xml:space="preserve">Illud quoque tanquam Statices generale
              <lb/>
            theorema habendum eſt.</s>
            <s xml:id="echoid-s550" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s551" xml:space="preserve">Gravitatis centrum pendentis corporis in pen-
              <lb/>
            dulâ gravitatis diametro eſſe.</s>
            <s xml:id="echoid-s552" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s553" xml:space="preserve">Atqui gravitatis centrum E ſecundi dia-
              <lb/>
            grammatis non eſt in I O pendulâ gravitatis
              <lb/>
            diametro. </s>
            <s xml:id="echoid-s554" xml:space="preserve">Impoſſibile igitur.</s>
            <s xml:id="echoid-s555" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s556" xml:space="preserve">*CONCLVSIO.</s>
            <s xml:id="echoid-s557" xml:space="preserve">* Columnâigitur ſecta, & </s>
            <s xml:id="echoid-s558" xml:space="preserve">c.</s>
            <s xml:id="echoid-s559" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div104" type="section" level="1" n="85">
          <head xml:id="echoid-head94" xml:space="preserve">3 THEOREMA. 7 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s560" xml:space="preserve">Si punctum firmitudinis centrum gravitatis ſit penden-
              <lb/>
            tis columnæ, quemcunque ei ſitum dederis, ſervat.</s>
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          <p>
            <s xml:id="echoid-s562" xml:space="preserve">*DATVM*. </s>
            <s xml:id="echoid-s563" xml:space="preserve">A B C D columna eſto, ejusq́;
              <lb/>
            </s>
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              <figure xlink:label="fig-527.01.020-02" xlink:href="fig-527.01.020-02a" number="29">
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            centrum E firmum fixumq́ue, quo de linea
              <lb/>
            E F ſit ſuſpenſa, axis G H ad horizontem I K
              <lb/>
            parallelus. </s>
            <s xml:id="echoid-s565" xml:space="preserve">*QVAESITVM.</s>
            <s xml:id="echoid-s566" xml:space="preserve">* Columnam
              <lb/>
            A B C D, quemcunqueſitum dederis, reti-
              <lb/>
            nere demonſtrandum eſt.</s>
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        <div xml:id="echoid-div106" type="section" level="1" n="86">
          <head xml:id="echoid-head95" xml:space="preserve">DEMONSTRATIO.</head>
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            <s xml:id="echoid-s568" xml:space="preserve">Datæ columnæ (E puncto immoto) alium
              <lb/>
            affingamus ſitum, quam prius, ut ſecundâ
              <lb/>
            hæc figurâ exhibetur, producaturq́ue F E, ut in L uſque, ſecans A B in M,
              <lb/>
            eq́ue ſuo ſitu, ſi quidem poſſit, emoveatur, & </s>
            <s xml:id="echoid-s569" xml:space="preserve">ſegmentum M L D A, vel
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            M L C B nutet deſcendatq́ue. </s>
            <s xml:id="echoid-s570" xml:space="preserve">Atqui duo iſta ſegmenta magnitudine æqua-
              <lb/>
            lia ſunt, ideoq́ue æquilibria, æquilibrium
              <lb/>
              <figure xlink:label="fig-527.01.020-03" xlink:href="fig-527.01.020-03a" number="30">
                <image file="527.01.020-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.020-03"/>
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            igitur alterum ponderoſius eſſe altero conſe-
              <lb/>
            quens erit, quod prorſus abſurdum eſt. </s>
            <s xml:id="echoid-s571" xml:space="preserve">Co-
              <lb/>
            lumna igitur ſitum ſuum obtinet, aut alium
              <lb/>
            quemvis, quicunque ei tributus fuerit.</s>
            <s xml:id="echoid-s572" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s573" xml:space="preserve">*CONCLVSIO.</s>
            <s xml:id="echoid-s574" xml:space="preserve">* Si itaque firmitudinis
              <lb/>
            punctum columnæ centrum fuerit, quemli-
              <lb/>
            bet datum ſitum ſervabit.</s>
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          </p>
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        <div xml:id="echoid-div108" type="section" level="1" n="87">
          <head xml:id="echoid-head96" xml:space="preserve">4 THEOREMA. 8 PROPOSITIO.</head>
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            <s xml:id="echoid-s576" xml:space="preserve">Sicolumna per gravitatis punctum ſit ſecta à plano </s>
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