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

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        <div xml:id="echoid-div641" type="section" level="1" n="462">
          <head xml:id="echoid-head489" xml:space="preserve">PRIMVM CONSECTARIVM</head>
          <head xml:id="echoid-head490" xml:space="preserve">è 27 propoſitione 1 Libri S*TATICÆ*.</head>
          <p>
            <s xml:id="echoid-s4710" xml:space="preserve">SI in figura 27 propoſitionis 1 lib. </s>
            <s xml:id="echoid-s4711" xml:space="preserve">in E
              <lb/>
            loco ponderis obliquè attollentis ſub-
              <lb/>
            ſtituatur firmitudinis punctum quale
              <lb/>
            hic vides, perſpicuum eſt hoc affici
              <lb/>
            preſſu ponderi G æquali, atque iſtiuſmodi obliqui-
              <lb/>
            tate niti, qualem oſtendit obliqua linea L E.</s>
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          <figure number="214">
            <image file="527.01.161-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.161-01"/>
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          <head xml:id="echoid-head491" xml:space="preserve">2 C*ONSECTARIVM*.</head>
          <p>
            <s xml:id="echoid-s4713" xml:space="preserve">Item ſi in eadem figura 27 propoſ. </s>
            <s xml:id="echoid-s4714" xml:space="preserve">LE, MF continuatæ concurrant,' pun
              <lb/>
            ctum concurſus per 25 propoſ. </s>
            <s xml:id="echoid-s4715" xml:space="preserve">incidet in pendulam
              <lb/>
              <figure xlink:label="fig-527.01.161-02" xlink:href="fig-527.01.161-02a" number="215">
                <image file="527.01.161-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.161-02"/>
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            gravitatis ejus diametrum. </s>
            <s xml:id="echoid-s4716" xml:space="preserve">Quamobrem ut cognoſ-
              <lb/>
            catur quanta obliqua preſſio puncto E infideat; </s>
            <s xml:id="echoid-s4717" xml:space="preserve">du-
              <lb/>
            cito pendulam diametrum à centro P quæ occur-
              <lb/>
            rat continuatæ M F in Q, hinc ab Q per E rectam
              <lb/>
            Q R ut R ſit in A M. </s>
            <s xml:id="echoid-s4718" xml:space="preserve">quæ cum ita ſint, preſſio erit
              <lb/>
            ab R verſus E. </s>
            <s xml:id="echoid-s4719" xml:space="preserve">Atqui ut etiam quanta ea ſit cognoſ-
              <lb/>
            cas, uſurpato E R tanquam lineam obliquè tollen-
              <lb/>
            tem, & </s>
            <s xml:id="echoid-s4720" xml:space="preserve">ES tanquam tollentem rectè, unde reliqua
              <lb/>
            erunt in proclivi.</s>
            <s xml:id="echoid-s4721" xml:space="preserve"/>
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        <div xml:id="echoid-div644" type="section" level="1" n="464">
          <head xml:id="echoid-head492" xml:space="preserve">3 C*ONSECTARIVM*.</head>
          <p>
            <s xml:id="echoid-s4722" xml:space="preserve">Sed ut rationem ponderum è funibus dependentium explicemus, eſto co-
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            lumna AB, cujus centrum C, eq̀ue duobus firmi-
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              <figure xlink:label="fig-527.01.161-03" xlink:href="fig-527.01.161-03a" number="216">
                <image file="527.01.161-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.161-03"/>
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            tudinis punctis D, E ſuſpenſum, eductis ex cen-
              <lb/>
            tro C duabus lineis C D, CE, quare iſtæ per 5 defin.
              <lb/>
            </s>
            <s xml:id="echoid-s4723" xml:space="preserve">ſunt columnæ gravitatis diametri, ideoq́ue H I paral-
              <lb/>
            lela contra C E inter C D, C F educta erit C I per 13
              <lb/>
            defin. </s>
            <s xml:id="echoid-s4724" xml:space="preserve">linea rectà attollens, C H autem obliquè, unde
              <lb/>
            efficitur ut C I ad C H ſic pondus illius recta attol-
              <lb/>
            lens ad pondus hujus attollens obliquè. </s>
            <s xml:id="echoid-s4725" xml:space="preserve">Sed pondus re-
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            ctà tollens quod pertinetad C I, totius columnæ pon-
              <lb/>
            deri æquatur; </s>
            <s xml:id="echoid-s4726" xml:space="preserve">itaque ut C I ad C H, ſic totius columnæ
              <lb/>
            pondus, ad pondus quod pertinetad D. </s>
            <s xml:id="echoid-s4727" xml:space="preserve">Eademq́ue via
              <lb/>
            concludetur pondus pertinens ad E ductâ ab I in C E
              <lb/>
            rectâ IK contra D C parallelâ; </s>
            <s xml:id="echoid-s4728" xml:space="preserve">atque tum erit ut rectà
              <lb/>
            tollens C I ad tollentem obliquè C K, ſic totius columnæ pondus, ad pon-
              <lb/>
            dus ſubnixum ipſi E.</s>
            <s xml:id="echoid-s4729" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4730" xml:space="preserve">Verùm quia C K perpetuò eſt æqualis HI, nihil eſt neceſſe ducere hanc
              <lb/>
            poſtremam I K, omnesq́ue neceſſarii cogniti termini inſunt tribus trianguli
              <lb/>
            H I C lateribus: </s>
            <s xml:id="echoid-s4731" xml:space="preserve">unde ita fari licet.</s>
            <s xml:id="echoid-s4732" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4733" xml:space="preserve">Vt CI ad C H, ſic pondus columnæ ad pondus pertingens ad D. </s>
            <s xml:id="echoid-s4734" xml:space="preserve">Item
              <lb/>
            ut C I ad I H, ſic pondus columnæ ad id quod pertinet ad E. </s>
            <s xml:id="echoid-s4735" xml:space="preserve">Et denique ut
              <lb/>
            CH ad HI, fic pondus quod ab D ad pondus quod ab E ſuſtinetur.</s>
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