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

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        <div xml:id="echoid-div233" type="section" level="1" n="168">
          <p>
            <s xml:id="echoid-s1511" xml:space="preserve">
              <pb o="48" file="527.01.048" n="48" rhead="1 L*IBER* S*TATICÆ*"/>
            obliqua. </s>
            <s xml:id="echoid-s1512" xml:space="preserve">Siilla huic annuit; </s>
            <s xml:id="echoid-s1513" xml:space="preserve">annuet & </s>
            <s xml:id="echoid-s1514" xml:space="preserve">hæcilli: </s>
            <s xml:id="echoid-s1515" xml:space="preserve">ſin
              <note symbol="*" position="left" xlink:label="note-527.01.048-01" xlink:href="note-527.01.048-01a" xml:space="preserve">Ann@@ere &
                <lb/>
              abnudere pa-
                <lb/>
              ralleliſm
                <unsure/>
              o op-
                <lb/>
              ponuntur.</note>
            abnuet.</s>
            <s xml:id="echoid-s1516" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1517" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1518" xml:space="preserve">AB columna duabus lineis eſto ſuſtentata, CD quidem ad
              <lb/>
            horizontem perpendiculari, EF vero (ſi poſſit) ad eandem obliquâ, & </s>
            <s xml:id="echoid-s1519" xml:space="preserve">GH
              <lb/>
            columnæ pendula gravitatis diametrus. </s>
            <s xml:id="echoid-s1520" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1521" xml:space="preserve">Veritas propofitio-
              <lb/>
            nis à nobis demonſtrari debet. </s>
            <s xml:id="echoid-s1522" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s1523" xml:space="preserve">CD, & </s>
            <s xml:id="echoid-s1524" xml:space="preserve">EF infinitum
              <lb/>
            continuantor mutuo ſe in I interſecantes.</s>
            <s xml:id="echoid-s1525" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div235" type="section" level="1" n="169">
          <head xml:id="echoid-head181" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1526" xml:space="preserve">Quocunque in ſitu columna de lineis CD, EF fuerit ſuſpenſa, eundem
              <unsure/>
              <lb/>
            in quovis puncto firmo continuatarũ linearum ſervabit, quod anguli I CE & </s>
            <s xml:id="echoid-s1527" xml:space="preserve">
              <lb/>
            IEC non mutentur. </s>
            <s xml:id="echoid-s1528" xml:space="preserve">Poſito igitur, I firmum pun-
              <lb/>
              <figure xlink:label="fig-527.01.048-01" xlink:href="fig-527.01.048-01a" number="82">
                <image file="527.01.048-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.048-01"/>
              </figure>
            ctum eſſe duarum linearum commune, columna
              <lb/>
            ex eo ſuſpenſa datum ſitum retinebit, & </s>
            <s xml:id="echoid-s1529" xml:space="preserve">IC pen-
              <lb/>
            dula gravitatis diametrus erit. </s>
            <s xml:id="echoid-s1530" xml:space="preserve">Atqui illud neuti-
              <lb/>
            quam fieri poteſt, quod GH iſti parallela, ea ipſa
              <lb/>
            ſit. </s>
            <s xml:id="echoid-s1531" xml:space="preserve">Eadem demonſtratio fuerit, rectà EF in oppo-
              <lb/>
            ſitam partem inclinatâ. </s>
            <s xml:id="echoid-s1532" xml:space="preserve">Si igitur IC horizonti eſt
              <lb/>
            perpendicularis reliqua EF eidem nó poteſt eſſe
              <lb/>
            obliqua, neceſſariò igitur perpendicularis etiam
              <lb/>
            fuerit: </s>
            <s xml:id="echoid-s1533" xml:space="preserve">Et per conſequens ſi EF horizonti eft
              <lb/>
            obliqua, etiam reliqua obliqua fuerit.</s>
            <s xml:id="echoid-s1534" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1535" xml:space="preserve">Porro, quia EF, A verſus annuit, etiam reliquam, quæ in dato ſitu co-
              <lb/>
            lumnam ſervat, EF verſus annuere neceſſe eſt. </s>
            <s xml:id="echoid-s1536" xml:space="preserve">Ab ea enim (ſi poteſt) decli-
              <lb/>
            net, ut CK, ſecans EI continuatam in K, perpendicularis per K, ob dictam
              <lb/>
            cauſam, columnæ pendula gravitatis diametrus erit, quod magis abſurdũ eft,
              <lb/>
            quam eandem illam per I cadere. </s>
            <s xml:id="echoid-s1537" xml:space="preserve">Neque hic igitur reliqua linea, columnam
              <lb/>
            in dato ſitu ſervans, ab EF declinat, neque parallela eſt, quod antea demon-
              <lb/>
            ftratum eſt, in latum autem decedere manifeſtè abſurdum eſt. </s>
            <s xml:id="echoid-s1538" xml:space="preserve">Quapropter ne-
              <lb/>
            ceſſariò EF verſus annuit. </s>
            <s xml:id="echoid-s1539" xml:space="preserve">Si vero EF in oppoſitam partem abiret, conſimi-
              <lb/>
            liter etiam reliquam ab illa abire, & </s>
            <s xml:id="echoid-s1540" xml:space="preserve">abnuere demonſtrabitur.</s>
            <s xml:id="echoid-s1541" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1542" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1543" xml:space="preserve">Siigitur, &</s>
            <s xml:id="echoid-s1544" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1545" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div237" type="section" level="1" n="170">
          <head xml:id="echoid-head182" xml:space="preserve">18 PROBLEMA. 27 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1546" xml:space="preserve">Si columna, & </s>
            <s xml:id="echoid-s1547" xml:space="preserve">duo pondera obliquè extollentia ſitu
              <lb/>
            æquilibria ſunt, erit quemadmodum linea obliquè extol-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-527.01.048-02" xlink:href="note-527.01.048-02a" xml:space="preserve">Pondus o
                <unsure/>
              bls-
                <lb/>
              quium & re-
                <lb/>
              ctum intelli-
                <lb/>
              ge rectè &
                <lb/>
              obliquè extol-
                <lb/>
              lens.</note>
            lans, ad lineam rectè extollĕtem: </s>
            <s xml:id="echoid-s1548" xml:space="preserve">ita ponderum quodq́ue obliquum ad ſuum pondus rectum.</s>
            <s xml:id="echoid-s1549" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1550" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1551" xml:space="preserve">AB columna, CD ejus axis eſto, & </s>
            <s xml:id="echoid-s1552" xml:space="preserve">in iſto E, F puncta, quo-
              <lb/>
            rum pondera, columnam in dato ſitu detinentia, ſunt G, H, quidem obliquè,
              <lb/>
            I, K verò rectè extollentia, & </s>
            <s xml:id="echoid-s1553" xml:space="preserve">lineæ EL, FM obliquè, EN & </s>
            <s xml:id="echoid-s1554" xml:space="preserve">FO rectè ex-
              <lb/>
            tollentes. </s>
            <s xml:id="echoid-s1555" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1556" xml:space="preserve">Quemadmodum LE ad EN: </s>
            <s xml:id="echoid-s1557" xml:space="preserve">ita eſſe G ad I,
              <lb/>
            & </s>
            <s xml:id="echoid-s1558" xml:space="preserve">quemadmodum MF ad FO: </s>
            <s xml:id="echoid-s1559" xml:space="preserve">ita eſſe H ad K, demonſtrabimus.</s>
            <s xml:id="echoid-s1560" xml:space="preserve"/>
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