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

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          <pb o="148" file="0216" n="235" rhead="PHYSICES ELEMENTA"/>
          <p>
            <s xml:id="echoid-s5857" xml:space="preserve">Jugum Bilancis figuram habet quæ in AB repræſentatur, in ipſis locis A & </s>
            <s xml:id="echoid-s5858" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0216-01" xlink:href="note-0216-01a" xml:space="preserve">548.</note>
            B excavatur, ut hoc in fig. </s>
            <s xml:id="echoid-s5859" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5860" xml:space="preserve">videri poteſt, de cætero ubique eſt ejuſdem
              <lb/>
              <note position="left" xlink:label="note-0216-02" xlink:href="note-0216-02a" xml:space="preserve">TAB. XX.
                <lb/>
              fig. 5.</note>
            craſſitiei.</s>
            <s xml:id="echoid-s5861" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5862" xml:space="preserve">Propter figuram irregularem, admodum difficilis foret computatio; </s>
            <s xml:id="echoid-s5863" xml:space="preserve">ideo,
              <lb/>
            ſervato jugi pondere, mutatam concepi figuram; </s>
            <s xml:id="echoid-s5864" xml:space="preserve">remotis partibus quibuſdam
              <lb/>
            à centro, & </s>
            <s xml:id="echoid-s5865" xml:space="preserve">admotis aliis, poſuique figuram illam eſſe, quæ repræſentatur in
              <lb/>
            fig. </s>
            <s xml:id="echoid-s5866" xml:space="preserve">6.</s>
            <s xml:id="echoid-s5867" xml:space="preserve">, in qua tota longitudo illa eſt, quæ in Bilance inter puncta ſuſpen-
              <lb/>
            ſionis datur; </s>
            <s xml:id="echoid-s5868" xml:space="preserve">ex qua mutatione exiguus tantum error in computatione dari
              <lb/>
            poteſt.</s>
            <s xml:id="echoid-s5869" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5870" xml:space="preserve">Hujus figuræ ſuperficies, cum jugum ejuſdem ſit craſſitudinis ubique, re-
              <lb/>
            præſentare poteſt jugi pondus in omnibus partibus. </s>
            <s xml:id="echoid-s5871" xml:space="preserve">Figura hæc AB conſt@t
              <lb/>
            ex parallelogrammo & </s>
            <s xml:id="echoid-s5872" xml:space="preserve">duobus triangulis: </s>
            <s xml:id="echoid-s5873" xml:space="preserve">junctis triangulis, figura reducitur ad
              <lb/>
            illam quæ in fig. </s>
            <s xml:id="echoid-s5874" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5875" xml:space="preserve">exhibetur, qua adſumtâ computationem inibo.</s>
            <s xml:id="echoid-s5876" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5877" xml:space="preserve">Hunc uſum computatio hæc habere poterit, quod inde patebit, cum
              <lb/>
            demonſtratis circa percuffionem experimenta noſtra congruere. </s>
            <s xml:id="echoid-s5878" xml:space="preserve">Fundamentum
              <lb/>
            autem ipſius computationis habetur in n. </s>
            <s xml:id="echoid-s5879" xml:space="preserve">543.</s>
            <s xml:id="echoid-s5880" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5881" xml:space="preserve">Ante omnia ſingula puncta ſuperficiei ADEB, pondus jugi repræſentan-
              <lb/>
              <note position="left" xlink:label="note-0216-03" xlink:href="note-0216-03a" xml:space="preserve">TAB. XX.
                <lb/>
              fig. 7.</note>
            tis, per quadrata diſtantiarum ſuarum a centro motus reſpective multiplicari
              <lb/>
            debent. </s>
            <s xml:id="echoid-s5882" xml:space="preserve">Hoc ſine errore ſenſibili fiet, ſi loco diſtantiarum a centro, di-
              <lb/>
            ſtantiæ a lineâ CF uſurpentur, quo computatio facilior evadit.</s>
            <s xml:id="echoid-s5883" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5884" xml:space="preserve">Si nunc operatio pro parallelogrammo inſtituatur, ſingulæ lineæ parallelæ & </s>
            <s xml:id="echoid-s5885" xml:space="preserve">
              <lb/>
            æquales lineæ DA, per quadratum ſuæ diſtantiæ à CF multiplicandæ ſunt,
              <lb/>
            id eſt, ſingula hæc quadrata per eandem quantitatem AB aut CG multiplica-
              <lb/>
            ri debent, id eſt, ſumma quadratorum per CG multiplicanda eſt; </s>
            <s xml:id="echoid-s5886" xml:space="preserve">ſumma au-
              <lb/>
            tem quadratorum eſt pyramis, cujus baſis eſt quadratum AC & </s>
            <s xml:id="echoid-s5887" xml:space="preserve">altitudo ea-
              <lb/>
            dem AC, quæ pyramis valet {1/3} AC
              <emph style="super">c</emph>
            . </s>
            <s xml:id="echoid-s5888" xml:space="preserve">Multiplicata hac per CG
              <note symbol="*" position="left" xlink:label="note-0216-04" xlink:href="note-0216-04a" xml:space="preserve">7. El. XII.</note>
            {1/3} CG x AC x AC
              <emph style="super">q</emph>
            ſummam productorum ſingulorum punctorum paralle-
              <lb/>
            logrammi DC, multiplicatorum per quadrata diſtantiarum ſuarum a
              <lb/>
            CG.</s>
            <s xml:id="echoid-s5889" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5890" xml:space="preserve">Similis ſumma pro ſingulis punctis trianguli DCG æqualis eſt, {1/12} GF
              <lb/>
            x AC x AC
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s5891" xml:space="preserve">Hoc facile detegent ſubtilioris Geometriæ gnari, & </s>
            <s xml:id="echoid-s5892" xml:space="preserve">aliis il-
              <lb/>
            lud explicare inutiliter laborarem. </s>
            <s xml:id="echoid-s5893" xml:space="preserve">Duplicando producta hæc habebimus ſi-
              <lb/>
            milem ſummam pro integra figura ADFEB; </s>
            <s xml:id="echoid-s5894" xml:space="preserve">& </s>
            <s xml:id="echoid-s5895" xml:space="preserve">eſt {2/3} CG x AC x AC
              <emph style="super">q</emph>
              <lb/>
            + {1/6} GF x AC x AC
              <emph style="super">q</emph>
            , = b x AC
              <emph style="super">q</emph>
            ; </s>
            <s xml:id="echoid-s5896" xml:space="preserve">ponendo b = {2/3} CG x AC + {1/6} GF x
              <lb/>
            AC.</s>
            <s xml:id="echoid-s5897" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5898" xml:space="preserve">His poſitis dicatur a altitudo a qua globus dimittitur, & </s>
            <s xml:id="echoid-s5899" xml:space="preserve">velocitas ca-
              <lb/>
              <note position="left" xlink:label="note-0216-05" xlink:href="note-0216-05a" xml:space="preserve">549.</note>
            dendo acquiſita, qua globus in lancem Mincurrit, & </s>
            <s xml:id="echoid-s5900" xml:space="preserve">quæ radici quadratæ
              <lb/>
            hujus altitudinis proportionalis eſt , poterit √ a deſignare.</s>
            <s xml:id="echoid-s5901" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">255</note>
          <p>
            <s xml:id="echoid-s5902" xml:space="preserve">Multiplicando hanc velocitatem per globum G (fig 4.) </s>
            <s xml:id="echoid-s5903" xml:space="preserve">& </s>
            <s xml:id="echoid-s5904" xml:space="preserve">per quadratum di-
              <lb/>
            ſtantiæ AC, & </s>
            <s xml:id="echoid-s5905" xml:space="preserve">dividendo hoc productum per ſummam omnium corporum
              <lb/>
            in experimento motorum, reſpectivè multiplicatorum per quadrata diſtantia-
              <lb/>
            rum ſuarum a centro motus, habemus velocitatem puncti A poſt ictum .</s>
            <s xml:id="echoid-s5906" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">543.</note>
          <p>
            <s xml:id="echoid-s5907" xml:space="preserve">Partem hujus ſummæ jam determinavimus, quoad jugum nempe, quod ſu-
              <lb/>
            pereſt habemus multiplicando pondera lancium L & </s>
            <s xml:id="echoid-s5908" xml:space="preserve">M, ut & </s>
            <s xml:id="echoid-s5909" xml:space="preserve">P, Q, & </s>
            <s xml:id="echoid-s5910" xml:space="preserve">G (fig.
              <lb/>
            </s>
            <s xml:id="echoid-s5911" xml:space="preserve">4.) </s>
            <s xml:id="echoid-s5912" xml:space="preserve">per quadratum diſtantiæ AC, nam omnia hæc corpora conſiderari poſſunt
              <lb/>
            quaſi darentur in ipſis punctis ſupenſionis A & </s>
            <s xml:id="echoid-s5913" xml:space="preserve">B. </s>
            <s xml:id="echoid-s5914" xml:space="preserve">Summam ponderum
              <note symbol="*" position="left" xlink:label="note-0216-08" xlink:href="note-0216-08a" xml:space="preserve">128.</note>
            </s>
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