Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605
page |< < (57) of 197 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div256" type="section" level="1" n="183">
          <pb o="57" file="527.01.057" n="57" rhead="DE INVENIENDO GRAVITATIS CENTRO."/>
        </div>
        <div xml:id="echoid-div257" type="section" level="1" n="184">
          <head xml:id="echoid-head197" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1679" xml:space="preserve">Quadrangulo delineâ HI ſuſpenſo, ſe-
              <lb/>
              <figure xlink:label="fig-527.01.057-01" xlink:href="fig-527.01.057-01a" number="91">
                <image file="527.01.057-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.057-01"/>
              </figure>
            gmentum H I D A ſegmĕto H I C B æqui-
              <lb/>
            libre pendebit, quia æqualia ſunt, ſimilia, & </s>
            <s xml:id="echoid-s1680" xml:space="preserve">
              <lb/>
            ſimiliter ſita. </s>
            <s xml:id="echoid-s1681" xml:space="preserve">H I igitur in parallelogrammo
              <lb/>
            A B C D gravitatis diameter eſt, eandemq́;
              <lb/>
            </s>
            <s xml:id="echoid-s1682" xml:space="preserve">ob cauſam & </s>
            <s xml:id="echoid-s1683" xml:space="preserve">F G. </s>
            <s xml:id="echoid-s1684" xml:space="preserve">Atqui iſtæ in E mutuo
              <lb/>
            ſe interſecantes gravitatis centrum in ſeſe
              <lb/>
            habent. </s>
            <s xml:id="echoid-s1685" xml:space="preserve">Quapropter E illud eſſe conclu-
              <lb/>
            ditur.</s>
            <s xml:id="echoid-s1686" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div259" type="section" level="1" n="185">
          <head xml:id="echoid-head198" xml:space="preserve">3 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1687" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1688" xml:space="preserve">A B C D E ordinatum ſive circulo inſcriptũ quinquangulum
              <lb/>
            eſto, & </s>
            <s xml:id="echoid-s1689" xml:space="preserve">figuræ centrum F. </s>
            <s xml:id="echoid-s1690" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1691" xml:space="preserve">F gravitatis centrum quoq; </s>
            <s xml:id="echoid-s1692" xml:space="preserve">eſſe
              <lb/>
            demonſtrandum eſt. </s>
            <s xml:id="echoid-s1693" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s1694" xml:space="preserve">Ab A in medium latus D C recta
              <lb/>
            A G; </s>
            <s xml:id="echoid-s1695" xml:space="preserve">conſimiliter à B in medium latus E D recta B H ducatur.</s>
            <s xml:id="echoid-s1696" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div260" type="section" level="1" n="186">
          <head xml:id="echoid-head199" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1697" xml:space="preserve">Quinquangulo de A G ſuſpenſo, ſegmentũ A G D E ſegmento A G C B
              <lb/>
            æquilibre erit. </s>
            <s xml:id="echoid-s1698" xml:space="preserve">ſunt enim æqualia, ſimilia, & </s>
            <s xml:id="echoid-s1699" xml:space="preserve">ſimiliter ſi-
              <lb/>
              <figure xlink:label="fig-527.01.057-02" xlink:href="fig-527.01.057-02a" number="92">
                <image file="527.01.057-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.057-02"/>
              </figure>
            ta. </s>
            <s xml:id="echoid-s1700" xml:space="preserve">A G igitur nec non B H in codem quinquangulo
              <lb/>
            gravitatis diametereſt. </s>
            <s xml:id="echoid-s1701" xml:space="preserve">Atqui mutuò ſe in F figuræ cen-
              <lb/>
            tro interſecant, & </s>
            <s xml:id="echoid-s1702" xml:space="preserve">illarum quæq́ue gravitatis centrum in
              <lb/>
            ſe habet. </s>
            <s xml:id="echoid-s1703" xml:space="preserve">F igitur illud ipſum eſt. </s>
            <s xml:id="echoid-s1704" xml:space="preserve">Eadem demonſtratio
              <lb/>
            aliarum omnium fuerit, quæcunque figuræ, centrum
              <lb/>
            habebunt, cujuſmodi ſunt ſexangulum, Circulus, & </s>
            <s xml:id="echoid-s1705" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1706" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1707" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1708" xml:space="preserve">In omni igitur plano figuræ cen-
              <lb/>
            trum, gravitatis quoque centrum eſt, quod nobis de-
              <lb/>
            monſtrandum fuit.</s>
            <s xml:id="echoid-s1709" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div262" type="section" level="1" n="187">
          <head xml:id="echoid-head200" xml:space="preserve">2 THEOREMA. 2 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1710" xml:space="preserve">Trianguli cujusq́ue gravitatis centrum eſt in rectâ ab
              <lb/>
            angulo in oppoſitum latus medium ductâ.</s>
            <s xml:id="echoid-s1711" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1712" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1713" xml:space="preserve">A B C contingentis figuræ triangulum eſto, ab ejusq́ue angu-
              <lb/>
            lo, A in D medium oppoſiti lateris B C punctum, recta A D ducta.</s>
            <s xml:id="echoid-s1714" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1715" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1716" xml:space="preserve">Gravitatis centrum dati trianguli in rectâ A D eſſe, de-
              <lb/>
            monſtrandum eſt. </s>
            <s xml:id="echoid-s1717" xml:space="preserve">PRAEPARATIO. </s>
            <s xml:id="echoid-s1718" xml:space="preserve">Rectæ E F, G H, I K ad B C paral-
              <lb/>
            lelæ ducuntor, ſecantes A D in L, M, N. </s>
            <s xml:id="echoid-s1719" xml:space="preserve">ducuntor conſimiliter E O, G P,
              <lb/>
            I Q, K R, H S, F T ad A D parallelæ.</s>
            <s xml:id="echoid-s1720" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div263" type="section" level="1" n="188">
          <head xml:id="echoid-head201" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1721" xml:space="preserve">Quandoquidem E F ad B C parallela eſt, idemq́ue E O & </s>
            <s xml:id="echoid-s1722" xml:space="preserve">F T ad L D,
              <lb/>
            quadrang ulum E F T O parallelogrammum erit, in quo E L, L F, O D & </s>
            <s xml:id="echoid-s1723" xml:space="preserve">
              <lb/>
            D T æqualia ſunt, ideoq́ue gravitatis centrum in D L per 1 hujus propoſit.
              <lb/>
            </s>
            <s xml:id="echoid-s1724" xml:space="preserve">eandemq́ue ob cauſam parallelogrammi G H S P gravitatis centrum in L M.</s>
            <s xml:id="echoid-s1725" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum