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

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            caſu niſi quadratis velocitatis vires proportionales ſint .</s>
            <s xml:id="echoid-s6566" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">47. El. v.</note>
          <p>
            <s xml:id="echoid-s6567" xml:space="preserve">Deducimus ex his non intereſſe neque reſpectu impreſ-
              <lb/>
              <note position="left" xlink:label="note-0238-02" xlink:href="note-0238-02a" xml:space="preserve">
                <emph style="sc">TAB. XXIII</emph>
              .
                <lb/>
              fig. 3.</note>
            ſionum, quibus corpus agitatur, neque reſpectu virium, ne-
              <lb/>
            que velocitatum, utrum corpus per AB feratur celeritate
              <lb/>
            AB, an per AD & </s>
            <s xml:id="echoid-s6568" xml:space="preserve">AE celeritatibus hiſce lineis proportio-
              <lb/>
            nalibus, quæ inter ſe angulum rectum continent. </s>
            <s xml:id="echoid-s6569" xml:space="preserve">Quare
              <lb/>
            motus per AB, juxta directionem ut AD, nil continet præ-
              <lb/>
              <note position="left" xlink:label="note-0238-03" xlink:href="note-0238-03a" xml:space="preserve">603.</note>
            ter motum velocitate AD.</s>
            <s xml:id="echoid-s6570" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6571" xml:space="preserve">Deducimus etiam motum corporis reſolvi poſſe in duos
              <lb/>
              <note position="left" xlink:label="note-0238-04" xlink:href="note-0238-04a" xml:space="preserve">604.</note>
            alios innumeris modis, quod fiet, ſi linea, in directione motus da-
              <lb/>
            ti poſita, & </s>
            <s xml:id="echoid-s6572" xml:space="preserve">longitudine celeritatem deſignans, ſit hypotenu-
              <lb/>
            ſa trianguli rectanguli; </s>
            <s xml:id="echoid-s6573" xml:space="preserve">nam hujus reliqua duo latera ſitu
              <lb/>
            motuum quæ ſitorum directiones dabunt, & </s>
            <s xml:id="echoid-s6574" xml:space="preserve">longitudinibus ſuis
              <lb/>
            reſpective velocitates horum expriment: </s>
            <s xml:id="echoid-s6575" xml:space="preserve">eruntque vires juxta
              <lb/>
            has directiones quadratis velocitatum proportionales.</s>
            <s xml:id="echoid-s6576" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6577" xml:space="preserve">Ut nunc determinemus, qua vi corpus per AE ſit agitandum,
              <lb/>
              <note position="left" xlink:label="note-0238-05" xlink:href="note-0238-05a" xml:space="preserve">605.</note>
            ut ei communicetur celeritas AE, in caſu in quo motus hic cum
              <lb/>
              <note position="left" xlink:label="note-0238-06" xlink:href="note-0238-06a" xml:space="preserve">
                <emph style="sc">TAB. XXIII</emph>
              .
                <lb/>
              fig. 4.</note>
            primo motu pro parte conſpirat; </s>
            <s xml:id="echoid-s6578" xml:space="preserve">motum per A Ein duos reſol-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0238-07" xlink:href="note-0238-07a" xml:space="preserve">246.</note>
            vo per A f & </s>
            <s xml:id="echoid-s6579" xml:space="preserve">A g, ângulum rectum continentes, & </s>
            <s xml:id="echoid-s6580" xml:space="preserve">ducitur E g parallelâ A f. </s>
            <s xml:id="echoid-s6581" xml:space="preserve">Per A f tantum corpori vis communicanda eſt,
              <lb/>
            qua corpus ſi quieſceret hac celeritate poſſet ferri, & </s>
            <s xml:id="echoid-s6582" xml:space="preserve">quæ
              <lb/>
            proportionalis eſt quadrato A f ; </s>
            <s xml:id="echoid-s6583" xml:space="preserve">per A g autem vis
              <note symbol="*" position="left" xlink:label="note-0238-08" xlink:href="note-0238-08a" xml:space="preserve">601. 447.</note>
            municanda eſt, qua celeritas AD quantitate A g augeatur,
              <lb/>
            id eſt fiat A h, quæ vis proportionalis eſt differentiæ qua-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0238-09" xlink:href="note-0238-09a" xml:space="preserve">591.</note>
            dratorum A h, AD . </s>
            <s xml:id="echoid-s6584" xml:space="preserve">Hæ vires ſimul communicandæ e- runt juxta AE ut corpus hac celeritate poſſit ferri; </s>
            <s xml:id="echoid-s6585" xml:space="preserve">& </s>
            <s xml:id="echoid-s6586" xml:space="preserve">vis
              <lb/>
            integra corporis proportionalis eſt quadrato lineæ AD, dif-
              <lb/>
            ferentiæ quadratorum linearum A h & </s>
            <s xml:id="echoid-s6587" xml:space="preserve">AD, & </s>
            <s xml:id="echoid-s6588" xml:space="preserve">quadrato
              <lb/>
            A f; </s>
            <s xml:id="echoid-s6589" xml:space="preserve">primis duobus ex hiſce tribus quantitatibus in unam
              <lb/>
            ſummam collectis, habemus quadratum lineæ A h, cui ſi
              <lb/>
            addatur quadratum lineæ A f, aut h B, habemus quadra-
              <lb/>
            tum lineæ AB; </s>
            <s xml:id="echoid-s6590" xml:space="preserve">cui proportionalem eſſe vim corpori inſi-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0238-10" xlink:href="note-0238-10a" xml:space="preserve">447.
                <lb/>
              *246.</note>
            tam ex ante demonſtratis ſequitur , cum conſtet
              <note position="left" xlink:label="note-0238-11" xlink:href="note-0238-11a" xml:space="preserve">606.</note>
            celeritate AB ferri .</s>
            <s xml:id="echoid-s6591" xml:space="preserve">
              <note position="left" xlink:label="note-0238-12" xlink:href="note-0238-12a" xml:space="preserve">
                <emph style="sc">TAB. XXIII</emph>
              .
                <lb/>
              fig. 5.</note>
            </s>
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          <p>
            <s xml:id="echoid-s6592" xml:space="preserve">Simotum per AE eodem modo in duos reſolvamus per A f & </s>
            <s xml:id="echoid-s6593" xml:space="preserve">
              <lb/>
            A g , motu hoc ſecundo retardatur motus per AD; </s>
            <s xml:id="echoid-s6594" xml:space="preserve">unde
              <note symbol="*" position="left" xlink:label="note-0238-13" xlink:href="note-0238-13a" xml:space="preserve">604.</note>
            tur, ut corpus per AE, celeritate hac lineâ deſignatâ feratur, </s>
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