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

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          <pb o="13" file="527.01.013" n="13" rhead="*DE* S*TATICÆ ELEMENTIS*."/>
        </div>
        <div xml:id="echoid-div54" type="section" level="1" n="48">
          <head xml:id="echoid-head56" xml:space="preserve">DEMONSTRATIO.</head>
          <head xml:id="echoid-head57" xml:space="preserve">1 MEMBRVM.</head>
          <p>
            <s xml:id="echoid-s274" xml:space="preserve">MH ex dato æquatur MG. </s>
            <s xml:id="echoid-s275" xml:space="preserve">utrique KM addito KH æquabitur MG
              <lb/>
            & </s>
            <s xml:id="echoid-s276" xml:space="preserve">KM. </s>
            <s xml:id="echoid-s277" xml:space="preserve">ſubductoq́ue deinde hinc GK, inde KI (ex dato autem GK & </s>
            <s xml:id="echoid-s278" xml:space="preserve">KI
              <lb/>
            æqualia ſunt) KM & </s>
            <s xml:id="echoid-s279" xml:space="preserve">KM reliqua æqualia erunt IH reliquo, eorundemq́ue
              <lb/>
            dimidia æqualia fuerint.</s>
            <s xml:id="echoid-s280" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div55" type="section" level="1" n="49">
          <head xml:id="echoid-head58" xml:space="preserve">2 MEMBRVM.</head>
          <p>
            <s xml:id="echoid-s281" xml:space="preserve">MI ad KM & </s>
            <s xml:id="echoid-s282" xml:space="preserve">IL addito tota ML & </s>
            <s xml:id="echoid-s283" xml:space="preserve">IK æqualia erunt.</s>
            <s xml:id="echoid-s284" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div56" type="section" level="1" n="50">
          <head xml:id="echoid-head59" xml:space="preserve">3 MEMBRVM.</head>
          <p>
            <s xml:id="echoid-s285" xml:space="preserve">Vt GI ad ſui dimidium KI: </s>
            <s xml:id="echoid-s286" xml:space="preserve">ſic IH ad ſui dimidium IL. </s>
            <s xml:id="echoid-s287" xml:space="preserve">& </s>
            <s xml:id="echoid-s288" xml:space="preserve">proportio-
              <lb/>
            ne alternatâ, ut GI ad IH: </s>
            <s xml:id="echoid-s289" xml:space="preserve">ita KI ad IL, atqui KI æquatur ML juxta 2
              <lb/>
            membrum, & </s>
            <s xml:id="echoid-s290" xml:space="preserve">IL ſegmento MK, juxta primum, ideoq́ue ut GI ad IH: </s>
            <s xml:id="echoid-s291" xml:space="preserve">ita
              <lb/>
            ML ad MK. </s>
            <s xml:id="echoid-s292" xml:space="preserve">Atqui ut GI ad IH: </s>
            <s xml:id="echoid-s293" xml:space="preserve">ita corpus five gravitas EFDA ad
              <lb/>
            EFCB, itaque ut ponderoſior gravitas EFDA, ad leviorem EFCB: </s>
            <s xml:id="echoid-s294" xml:space="preserve">ita
              <lb/>
            longior radius ML, ad breviorem MK.</s>
            <s xml:id="echoid-s295" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s296" xml:space="preserve">OCcurrerit hic non nemo. </s>
            <s xml:id="echoid-s297" xml:space="preserve">Propoſitionĕ deſegmentis ejuſdem columnæ,
              <lb/>
            & </s>
            <s xml:id="echoid-s298" xml:space="preserve">quidem æquabilis gravitatis à meeſſe demõſtratam, ignorari tamen an
              <lb/>
            veritas in aliis, & </s>
            <s xml:id="echoid-s299" xml:space="preserve">variis ſegmentis ſigurarum irregularium, & </s>
            <s xml:id="echoid-s300" xml:space="preserve">materiæ inæqua-
              <lb/>
            bilis cadem futura ſit: </s>
            <s xml:id="echoid-s301" xml:space="preserve">quapropter propoſitionis generalitatem ita dein-
              <lb/>
            ceps demonſtrabimus. </s>
            <s xml:id="echoid-s302" xml:space="preserve">Iugum KL primi modi immotum manere ima-
              <lb/>
            ginemur, ſegmentum autem EFDA demitti, lineâ è gravitatis centro edu-
              <lb/>
            ctâ ſuſpenſum è puncto K, reliquumq́ue ſe-
              <lb/>
              <figure xlink:label="fig-527.01.013-01" xlink:href="fig-527.01.013-01a" number="13">
                <image file="527.01.013-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.013-01"/>
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            gmentum EFCB conſimiliter depreſſum
              <lb/>
            è gravitatis centro L ſuſpendi, ſegmen-
              <lb/>
            tumq́ue EFCB ab EFDA diſtare, & </s>
            <s xml:id="echoid-s303" xml:space="preserve">ſi-
              <lb/>
            tum corũ eſſe qualem diagramma exhibet.
              <lb/>
            </s>
            <s xml:id="echoid-s304" xml:space="preserve">Quando corpus primi modi ex anſa MN
              <lb/>
            penderet, ſegmenta EFCB & </s>
            <s xml:id="echoid-s305" xml:space="preserve">EFDA
              <lb/>
            ſitu æquipondia erant: </s>
            <s xml:id="echoid-s306" xml:space="preserve">neque in ſecundo
              <lb/>
            pondus EFDA depreſſius altero, plus mi-
              <lb/>
            núsve gravitatis quam in primo adſert jugo
              <lb/>
            KL, ex 3 poſtulati ſententiâ. </s>
            <s xml:id="echoid-s307" xml:space="preserve">Neque EFCB pondus ſecundi modi plus gra-
              <lb/>
            vitatis jugo adfert quam prius. </s>
            <s xml:id="echoid-s308" xml:space="preserve">Quapropter gravitates tam primi, quàm ſecun-
              <lb/>
            di modi eædem manent, jugiq́ue ſitus idem qui erat prius. </s>
            <s xml:id="echoid-s309" xml:space="preserve">ideoq́ue EFDA
              <lb/>
            & </s>
            <s xml:id="echoid-s310" xml:space="preserve">EFCB ſitu æquilibria. </s>
            <s xml:id="echoid-s311" xml:space="preserve">ſegmentaq́ue columnæ tam diviſa, quam conjun-
              <lb/>
            cta fitu æquipondia, atque radii eandem rationem, quam habuerunt, reti-
              <lb/>
            nent.</s>
            <s xml:id="echoid-s312" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s313" xml:space="preserve">Hoc probato, corpora EFDA & </s>
            <s xml:id="echoid-s314" xml:space="preserve">EFCB ſe-
              <lb/>
              <figure xlink:label="fig-527.01.013-02" xlink:href="fig-527.01.013-02a" number="14">
                <image file="527.01.013-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.013-02"/>
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            cundi modi aliter premendo ſingendoq́ue figure-
              <lb/>
            mus (materiam ceream, argillaceam, aliamve tra-
              <lb/>
            ctabilem eſſe ponamus) ut EFDA & </s>
            <s xml:id="echoid-s315" xml:space="preserve">EFCB
              <lb/>
            modi ſecundi, EFDA & </s>
            <s xml:id="echoid-s316" xml:space="preserve">EFCB fiant tertii;
              <lb/>
            </s>
            <s xml:id="echoid-s317" xml:space="preserve">KL jugum eundem poſitum ſervare, radiosq́ue
              <lb/>
            ML, & </s>
            <s xml:id="echoid-s318" xml:space="preserve">KM eandem rationem manifeſtum eſt,
              <lb/>
            ideoq́ue EFDA & </s>
            <s xml:id="echoid-s319" xml:space="preserve">EFCB ſitu æquilibria ma-
              <lb/>
            nere conſequens eſt, quia manente materiâ, muta-
              <lb/>
            tio ſormæ mutationem gravitatis non adfert.</s>
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