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

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        <div xml:id="echoid-div170" type="section" level="1" n="131">
          <pb o="35" file="527.01.035" n="35" rhead="*DE* S*TATICÆ ELEMENTIS*."/>
        </div>
        <div xml:id="echoid-div173" type="section" level="1" n="132">
          <head xml:id="echoid-head144" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1034" xml:space="preserve">Si ſacoma quaternûm globorum D, R, Q,-P, non æquaretur antiſacoma-
              <lb/>
            ti binorum, E F. </s>
            <s xml:id="echoid-s1035" xml:space="preserve">alterutri graviores erunt: </s>
            <s xml:id="echoid-s1036" xml:space="preserve">ſunto autem (ſi fieri poteſt) quatuor
              <lb/>
            iſti D, R, Q, P; </s>
            <s xml:id="echoid-s1037" xml:space="preserve">Atqui O, N, M, L, æquiponderant quatuor G, H, I, K. </s>
            <s xml:id="echoid-s1038" xml:space="preserve">Latus
              <lb/>
            igitur octo globorum D, R, Q, P, O, N, M, L, ponderoſius eſt latere ſex glo-
              <lb/>
            borum E, F, G, H, I, K. </s>
            <s xml:id="echoid-s1039" xml:space="preserve">Quia vero gravius præpõderat leviori, octo deorſum
              <lb/>
            volventur, ſex vero reliqui ſurſum. </s>
            <s xml:id="echoid-s1040" xml:space="preserve">Deſcenderit D, in O, & </s>
            <s xml:id="echoid-s1041" xml:space="preserve">E, F, G, H ſint,
              <lb/>
            loco P, Q, R, D, denique I, K, loco E, F. </s>
            <s xml:id="echoid-s1042" xml:space="preserve">Atqui hoc ſi ſit, globorum ſeries
              <lb/>
            ſive corona eundem ſitum cum priore habebit, eadem q́ue de cauſa octo glo-
              <lb/>
            bi ſiniſtri ponderoſiores erunt ſex dextris, ideoq́ue rurſus octo illi deſcen-
              <lb/>
            dent, ſex iſti adſcendent, ipſiq́ue globi ex ſeſe continuum & </s>
            <s xml:id="echoid-s1043" xml:space="preserve">æternum motum
              <lb/>
            efficient, quod eſt falſum. </s>
            <s xml:id="echoid-s1044" xml:space="preserve">Pars igitur coronæ D, R, Q, P, O, N, M, L, parti
              <lb/>
            E, F, G, H, I, K, ſitu æquilibris eſt. </s>
            <s xml:id="echoid-s1045" xml:space="preserve">Si verò ab æquilibribus æquilibria tollantur
              <lb/>
            reliqua manent æquilibria. </s>
            <s xml:id="echoid-s1046" xml:space="preserve">illinc igitur O, N, M, L, hinc vero G, H, I, K, qui
              <lb/>
            æquantur O, N, M, L ſublatis, reliqui D, R, P, Q, reliquis E, F ſitu æquilibres
              <lb/>
            erunt. </s>
            <s xml:id="echoid-s1047" xml:space="preserve">Atqui duobus iſtis quatuor illis æquilibribus, E duplo ponderoſior erit
              <lb/>
            ſitu, quam D. </s>
            <s xml:id="echoid-s1048" xml:space="preserve">Quemadmodum igitur latus B A 2 ad latus B C 1, ita ſaco-
              <lb/>
            ma globi E ad antiſacoma globi D. </s>
            <s xml:id="echoid-s1049" xml:space="preserve">C*ONCLUSIO*. </s>
            <s xml:id="echoid-s1050" xml:space="preserve">Si igitur trianguli
              <lb/>
            planum horizonti ſit perpendiculare &</s>
            <s xml:id="echoid-s1051" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1052" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div174" type="section" level="1" n="133">
          <head xml:id="echoid-head145" xml:space="preserve">1 C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s1053" xml:space="preserve">Si A B C triangulum ſit, ut ante, ejusq́ue latus A B duplum lateris B C,
              <lb/>
            inq́ue A B jaceat globus D, in B C verò globus E, ſubduplus ponderi D, & </s>
            <s xml:id="echoid-s1054" xml:space="preserve">
              <lb/>
            in F fixus ſit punctus quâ linea ſive funiculus DFE
              <lb/>
              <figure xlink:label="fig-527.01.035-01" xlink:href="fig-527.01.035-01a" number="55">
                <image file="527.01.035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.035-01"/>
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            (è centro ſcilicet D, per F, in centrum E uſque)
              <lb/>
            motus radit F fixum punctum, ut D F ab A B,
              <lb/>
            & </s>
            <s xml:id="echoid-s1055" xml:space="preserve">F E à B C æquidiſtans ſit: </s>
            <s xml:id="echoid-s1056" xml:space="preserve">quia quatuor globi
              <lb/>
            P, Q, R, D, ſitu æquilibres fuerunt duobus E, F,
              <lb/>
            etiam globus D ſitu æquilibris erit globo E. </s>
            <s xml:id="echoid-s1057" xml:space="preserve">Vt
              <lb/>
            enim P, Q, R, D ad E, F: </s>
            <s xml:id="echoid-s1058" xml:space="preserve">ita D ad E. </s>
            <s xml:id="echoid-s1059" xml:space="preserve">Igitur quem-
              <lb/>
            admodum latus A B, ad B C: </s>
            <s xml:id="echoid-s1060" xml:space="preserve">ita globus D ad globum E.</s>
            <s xml:id="echoid-s1061" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div176" type="section" level="1" n="134">
          <head xml:id="echoid-head146" xml:space="preserve">2 C*ONSECTARIUM*.</head>
          <figure number="56">
            <image file="527.01.035-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.035-02"/>
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          <p>
            <s xml:id="echoid-s1062" xml:space="preserve">SI latus trianguli B C, cui A B duplum eſt, re-
              <lb/>
            ctum ad A C collocetur, ut expreſſum hîcvi-
              <lb/>
            des; </s>
            <s xml:id="echoid-s1063" xml:space="preserve">globus D duplus ad globum E, cum E ſitu
              <lb/>
            æquilibris erit, utenim A B ad B C: </s>
            <s xml:id="echoid-s1064" xml:space="preserve">ita globus D
              <lb/>
            ad globum E.</s>
            <s xml:id="echoid-s1065" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div177" type="section" level="1" n="135">
          <head xml:id="echoid-head147" xml:space="preserve">3 C*ONSECTARIUM*.</head>
          <figure number="57">
            <image file="527.01.035-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.035-03"/>
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          <p>
            <s xml:id="echoid-s1066" xml:space="preserve">SI loco puncti F trochlea ita collocetur,
              <lb/>
            ut linea D F, obliquè extollens, ad A B
              <lb/>
            ſit parallela, & </s>
            <s xml:id="echoid-s1067" xml:space="preserve">proglobo E pondus ſit con-
              <lb/>
            tingĕti quidem figura, ſed eodem cum illo
              <lb/>
            po dere, erit cum D ſitu æquilibre. </s>
            <s xml:id="echoid-s1068" xml:space="preserve">Ideoq́;
              <lb/>
            </s>
            <s xml:id="echoid-s1069" xml:space="preserve">quemadmodum A B ad B C: </s>
            <s xml:id="echoid-s1070" xml:space="preserve">ita globus
              <lb/>
            D ad pondus E.</s>
            <s xml:id="echoid-s1071" xml:space="preserve"/>
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