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

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              <pb o="167" file="0239" n="260" rhead="MATHEMATICA. LIB. I. CAP. XXV."/>
            communicandam eſſe vim, quæ proportionalis ſit quadrato
              <lb/>
            A f, & </s>
            <s xml:id="echoid-s6595" xml:space="preserve">impreſſionem, qua agitatur, ulterius tantum valere
              <lb/>
            debere, ut quantitate A g poſſit minuere velocitatem AD,
              <lb/>
            in hoc caſu corpus juxta directionem AD tantum ſuperſti-
              <lb/>
            tem habebit vim proportionalem quadrato A b , cui ſi
              <note symbol="*" position="right" xlink:label="note-0239-01" xlink:href="note-0239-01a" xml:space="preserve">598.</note>
            datur vis proportionalis quadrato A f, habemus vim
              <note symbol="*" position="right" xlink:label="note-0239-02" xlink:href="note-0239-02a" xml:space="preserve">601.</note>
            tionalem quadrato AB; </s>
            <s xml:id="echoid-s6596" xml:space="preserve">quod iterum cum ante demonſtra-
              <lb/>
            tis congruit .</s>
            <s xml:id="echoid-s6597" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">246 447.</note>
          <p>
            <s xml:id="echoid-s6598" xml:space="preserve">Propoſitionem hanc, vim ſequi proportionem quadrati
              <lb/>
              <note position="right" xlink:label="note-0239-04" xlink:href="note-0239-04a" xml:space="preserve">607.</note>
            velocitatis, non poſſe referri ad illam cum qua alia in ea-
              <lb/>
            dem linea agit, facile ex ante demonſtratis ſequitur ,
              <note symbol="*" position="right" xlink:label="note-0239-05" xlink:href="note-0239-05a" xml:space="preserve">598. 599</note>
            de causâ ubi vim in duas reſolvimus, hæ quadratis veloci-
              <lb/>
            tatum proportionales non erunt, niſi ambarum directiones
              <lb/>
            angulum rectum contineant ne aliter pro parte conſpirent
              <lb/>
            aut contrarie agant . </s>
            <s xml:id="echoid-s6599" xml:space="preserve">Ex quibus deducimus vim
              <note symbol="*" position="right" xlink:label="note-0239-06" xlink:href="note-0239-06a" xml:space="preserve">601.</note>
            tam non iterum poſſe reſolvi. </s>
            <s xml:id="echoid-s6600" xml:space="preserve">Motus per AB reſolvitur
              <lb/>
            in duos motus ejuſdem corporis per AD & </s>
            <s xml:id="echoid-s6601" xml:space="preserve">AE, & </s>
            <s xml:id="echoid-s6602" xml:space="preserve">vires
              <lb/>
              <note position="right" xlink:label="note-0239-07" xlink:href="note-0239-07a" xml:space="preserve">
                <emph style="sc">TAB. XXIII</emph>
              .
                <lb/>
              fig 54.</note>
            quadratis velociratum ſunt proportionales; </s>
            <s xml:id="echoid-s6603" xml:space="preserve">ſed ſi motus per
              <lb/>
            AE iterum in duos per AF & </s>
            <s xml:id="echoid-s6604" xml:space="preserve">AG angulum rectum con-
              <lb/>
            tinentes ſeparetur, non erunt hæ ultimæ quadratis veloci-
              <lb/>
            tatum proportionales, & </s>
            <s xml:id="echoid-s6605" xml:space="preserve">non poterit hîc applicari n. </s>
            <s xml:id="echoid-s6606" xml:space="preserve">604,
              <lb/>
            in quo agitur de viribus, quæ non modo inter ſe non con-
              <lb/>
            fpirant, neque contrarie agunt, ſed quæ cum tertiâ nil
              <lb/>
            commune habent. </s>
            <s xml:id="echoid-s6607" xml:space="preserve">Hîc autem ipſe motus corporis per
              <lb/>
            AB in tres motus reſolvitur per AD, AF & </s>
            <s xml:id="echoid-s6608" xml:space="preserve">AG, in qui-
              <lb/>
            bus AF & </s>
            <s xml:id="echoid-s6609" xml:space="preserve">AD pro parte conſpirant, AD & </s>
            <s xml:id="echoid-s6610" xml:space="preserve">AG partim
              <lb/>
            contrariè agunt; </s>
            <s xml:id="echoid-s6611" xml:space="preserve">& </s>
            <s xml:id="echoid-s6612" xml:space="preserve">reſolutio quæ ad velocitates poteſtappli-
              <lb/>
            cari, cùm demonſtratio n. </s>
            <s xml:id="echoid-s6613" xml:space="preserve">246. </s>
            <s xml:id="echoid-s6614" xml:space="preserve">eadem ſit, ſive motus in re-
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            folutione conſpirent, ſive contrarie agunt, ad vires non poſſe
              <lb/>
            referri ex ante demonſtratis clarum eſt .</s>
            <s xml:id="echoid-s6615" xml:space="preserve">
              <note position="right" xlink:label="note-0239-08" xlink:href="note-0239-08a" xml:space="preserve">440. 443.</note>
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          <p>
            <s xml:id="echoid-s6616" xml:space="preserve">In n. </s>
            <s xml:id="echoid-s6617" xml:space="preserve">605. </s>
            <s xml:id="echoid-s6618" xml:space="preserve">606. </s>
            <s xml:id="echoid-s6619" xml:space="preserve">motum per AB compoſitum habemus ex
              <lb/>
              <note position="right" xlink:label="note-0239-09" xlink:href="note-0239-09a" xml:space="preserve">608.</note>
            duobus, quorum unum in alios reſolvimus, ſed ita, ut poſt
              <lb/>
              <note position="right" xlink:label="note-0239-10" xlink:href="note-0239-10a" xml:space="preserve">
                <emph style="sc">TAB. XXIII</emph>
              .
                <lb/>
              fig. 4. 5.</note>
            reſolutionem omnes motus darentur in duabus lineis, angu-
              <lb/>
            lum rectum continentibus: </s>
            <s xml:id="echoid-s6620" xml:space="preserve">quare motus in ſingulis lineis,
              <lb/>
            ſeparatim conſiderari potuere, quod nunquam fieri poteſt
              <lb/>
            ubi motus varii in pluribus quàm duabus lineis dantur, </s>
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