Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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          <p>
            <s xml:id="echoid-s1679" xml:space="preserve">
              <pb o="35" file="0073" n="77" rhead="MATHEMATICA. LIB. 1. CAP. IX."/>
            mam dividenda erit, ad detegendam memoratam diſtantiam centri gravitatis a
              <lb/>
            plano.</s>
            <s xml:id="echoid-s1680" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1681" xml:space="preserve">Ex hiſce deducimus methodum, qua inveſtigatur centrum gravitatis; </s>
            <s xml:id="echoid-s1682" xml:space="preserve">quæ-
              <lb/>
              <note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">162.</note>
            rendo bujus diſtantiam a tribus planis . </s>
            <s xml:id="echoid-s1683" xml:space="preserve">Quæ eadem methodus ad corpus
              <note position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve">163.</note>
            que peculiare applicari poteſt, referendo adhujus partes, quæ de corporibus ſunt de-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0073-03" xlink:href="note-0073-03a" xml:space="preserve">160</note>
            monſtrata.</s>
            <s xml:id="echoid-s1684" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1685" xml:space="preserve">Si Corpora, quorum commune gravitatis centrum quæritur, ſua peculiaria
              <lb/>
              <note position="right" xlink:label="note-0073-04" xlink:href="note-0073-04a" xml:space="preserve">164.</note>
            gravitatis centra in eodem plano babeant, determinatur quæſitum centrum, dete-
              <lb/>
            gendo bujus diſtantiam â duabus lineis , utcunque in eodem hoc plano ductis.</s>
            <s xml:id="echoid-s1686" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0073-05" xlink:href="note-0073-05a" xml:space="preserve">159.</note>
            </s>
          </p>
          <p style="it">
            <s xml:id="echoid-s1687" xml:space="preserve">Quando peculiaria gravitatis centra in eâdem lineâ dantur, detegitur commune
              <lb/>
              <note position="right" xlink:label="note-0073-06" xlink:href="note-0073-06a" xml:space="preserve">165.</note>
            gravitatis centrum operatione unicâ, qua nempe ipſius diſtantia à puncto quocun-
              <lb/>
            que, in eâdem illâ lineâ ſumto, determinatur.</s>
            <s xml:id="echoid-s1688" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div270" type="section" level="1" n="92">
          <head xml:id="echoid-head139" xml:space="preserve">SCHOLIUM 2.</head>
          <head xml:id="echoid-head140" style="it" xml:space="preserve">Arithmetica Mechanica.</head>
          <p>
            <s xml:id="echoid-s1689" xml:space="preserve">Regulæ quatuor Arithmeticæ, Additic, Subtractio, Multiplicatio, & </s>
            <s xml:id="echoid-s1690" xml:space="preserve">Diviſio, ope
              <lb/>
            libræ ſuperius memoratæ , cujus brachia in partes æquales ſunt diviſa
              <note symbol="*" position="right" xlink:label="note-0073-07" xlink:href="note-0073-07a" xml:space="preserve">130.</note>
            cile inſtitui poſſunt, operationumque demonſtratio ex ante memoratis quam
              <lb/>
            facillimè deducitur; </s>
            <s xml:id="echoid-s1691" xml:space="preserve">ſatis ideò erit ipſas regulas exemplis illuſtrare.</s>
            <s xml:id="echoid-s1692" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1693" xml:space="preserve">Habeatur pondus quodcunque pro unitate; </s>
            <s xml:id="echoid-s1694" xml:space="preserve">uncia Ex gr.</s>
            <s xml:id="echoid-s1695" xml:space="preserve">; decima pars un-
              <lb/>
            ciæ eodem modo poſſet adhiberi.</s>
            <s xml:id="echoid-s1696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1697" xml:space="preserve">Sit numerus 364 libræ applicandus; </s>
            <s xml:id="echoid-s1698" xml:space="preserve">tres uncias centeſimæ applico divi-
              <lb/>
              <note position="right" xlink:label="note-0073-08" xlink:href="note-0073-08a" xml:space="preserve">166.</note>
            ſioni, & </s>
            <s xml:id="echoid-s1699" xml:space="preserve">unciam unam diviſioni 64
              <emph style="super">tæ</emph>
            .</s>
            <s xml:id="echoid-s1700" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1701" xml:space="preserve">Gravetur brachium libræ urcunque; </s>
            <s xml:id="echoid-s1702" xml:space="preserve">quem numerum valeat actio hæc, de-
              <lb/>
              <note position="right" xlink:label="note-0073-09" xlink:href="note-0073-09a" xml:space="preserve">167.</note>
            terminamus, ſuſpendendo in centeſimâ diviſione brachii oppoſiti pondus,
              <lb/>
            quod augeatur additâ ſucceſſivè unciâ atque unciâ; </s>
            <s xml:id="echoid-s1703" xml:space="preserve">ponamus novem uncias
              <lb/>
            nondum æquilibrium dare, decem autem excedere; </s>
            <s xml:id="echoid-s1704" xml:space="preserve">relictis novem mo-
              <lb/>
            tu unius juxta brachium quæro æquilibrium, detur hoc ubi pondus ad 47 di-
              <lb/>
            viſionem pervenit, actio quæſita valebit 947.</s>
            <s xml:id="echoid-s1705" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1706" xml:space="preserve">ADDITIO. </s>
            <s xml:id="echoid-s1707" xml:space="preserve">Sint addenda 34, 54, 268, 407, 45. </s>
            <s xml:id="echoid-s1708" xml:space="preserve">65. </s>
            <s xml:id="echoid-s1709" xml:space="preserve">Separatim numeros
              <lb/>
              <note position="right" xlink:label="note-0073-10" xlink:href="note-0073-10a" xml:space="preserve">168.</note>
            hos applico eidem brachio libræ ; </s>
            <s xml:id="echoid-s1710" xml:space="preserve">quæro hujus actionis valorem ; </s>
            <s xml:id="echoid-s1711" xml:space="preserve">& </s>
            <s xml:id="echoid-s1712" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0073-11" xlink:href="note-0073-11a" xml:space="preserve">166.</note>
            go 873, ſummam quæſitam.
              <lb/>
            </s>
            <s xml:id="echoid-s1713" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0073-12" xlink:href="note-0073-12a" xml:space="preserve">167.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s1714" xml:space="preserve">SUBTRACTIO. </s>
            <s xml:id="echoid-s1715" xml:space="preserve">Ex ſumma numerorum 567, 258, ſubtrahenda ſunt 489
              <lb/>
              <note position="right" xlink:label="note-0073-13" xlink:href="note-0073-13a" xml:space="preserve">169.</note>
            & </s>
            <s xml:id="echoid-s1716" xml:space="preserve">56. </s>
            <s xml:id="echoid-s1717" xml:space="preserve">Numeros primos uni applico brachio ; </s>
            <s xml:id="echoid-s1718" xml:space="preserve">ſubtrahendos alteri applico
              <note symbol="*" position="right" xlink:label="note-0073-14" xlink:href="note-0073-14a" xml:space="preserve">166.</note>
            & </s>
            <s xml:id="echoid-s1719" xml:space="preserve">quæro quantum valeat actio, qua actio in brachium unum alteram
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0073-15" xlink:href="note-0073-15a" xml:space="preserve">166.</note>
            actionem ſuperat , & </s>
            <s xml:id="echoid-s1720" xml:space="preserve">detego differentiam quæſitam 280.</s>
            <s xml:id="echoid-s1721" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0073-16" xlink:href="note-0073-16a" xml:space="preserve">167.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s1722" xml:space="preserve">MULTIPLICATIO. </s>
            <s xml:id="echoid-s1723" xml:space="preserve">Detur numerus 67, multiplicandus per 15. </s>
            <s xml:id="echoid-s1724" xml:space="preserve">Pon-
              <lb/>
              <note position="right" xlink:label="note-0073-17" xlink:href="note-0073-17a" xml:space="preserve">170.</note>
            dus 15. </s>
            <s xml:id="echoid-s1725" xml:space="preserve">ſuſpendo diviſioni 67 & </s>
            <s xml:id="echoid-s1726" xml:space="preserve">quæro valorem , quo productum
              <note symbol="*" position="right" xlink:label="note-0073-18" xlink:href="note-0073-18a" xml:space="preserve">167.</note>
            detego 1005.</s>
            <s xml:id="echoid-s1727" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1728" xml:space="preserve">DIVISIO. </s>
            <s xml:id="echoid-s1729" xml:space="preserve">Sit 1005. </s>
            <s xml:id="echoid-s1730" xml:space="preserve">numerus dividendus per 15, Numerum dividendum
              <lb/>
              <note position="right" xlink:label="note-0073-19" xlink:href="note-0073-19a" xml:space="preserve">171.</note>
            applico libræ , & </s>
            <s xml:id="echoid-s1731" xml:space="preserve">movendo pondus quindecim juxta brachium, quæro
              <note symbol="*" position="right" xlink:label="note-0073-20" xlink:href="note-0073-20a" xml:space="preserve">166.</note>
            librium, quod datur ubi pondus ad 67 diviſionem, quotientem deſignantem,
              <lb/>
            pervenit.</s>
            <s xml:id="echoid-s1732" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1733" xml:space="preserve">Præſtat in hiſce duabus ultimis operationibus, minori pondere pro unita-
              <lb/>
            te uti.</s>
            <s xml:id="echoid-s1734" xml:space="preserve"/>
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