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

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            <s xml:id="echoid-s6799" xml:space="preserve">
              <pb o="173" file="0249" n="272" rhead="MATHEMATICA. LIB. I. CAP. XXVII."/>
            dem tempore moveatur corpus per AH & </s>
            <s xml:id="echoid-s6800" xml:space="preserve">AE, velocitatibus
              <lb/>
            hiſce lineis proportionalibus; </s>
            <s xml:id="echoid-s6801" xml:space="preserve">an in linea AP moveatur eo-
              <lb/>
            dem tempore velocitatibus AI & </s>
            <s xml:id="echoid-s6802" xml:space="preserve">AL. </s>
            <s xml:id="echoid-s6803" xml:space="preserve">In utroque caſu
              <lb/>
            revera movetur corpus per AP, velocitate AP; </s>
            <s xml:id="echoid-s6804" xml:space="preserve">quæ ergo
              <lb/>
            valet ambas velocitates AL, AI, quod & </s>
            <s xml:id="echoid-s6805" xml:space="preserve">aliunde conſtat:
              <lb/>
            </s>
            <s xml:id="echoid-s6806" xml:space="preserve">Nam AL & </s>
            <s xml:id="echoid-s6807" xml:space="preserve">IP ſunt æquales propter triangula ſimilia & </s>
            <s xml:id="echoid-s6808" xml:space="preserve">
              <lb/>
            æqualia AEL, HIP habentia latera reſpectivè parallela,
              <lb/>
            quorum AE & </s>
            <s xml:id="echoid-s6809" xml:space="preserve">HP ſunt æqualia .</s>
            <s xml:id="echoid-s6810" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0249-01" xlink:href="note-0249-01a" xml:space="preserve">34. El 17</note>
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          </p>
          <p>
            <s xml:id="echoid-s6811" xml:space="preserve">Jam cum motus per A L contineatur in motu per AE
              <lb/>
            quo agit in planum GC, & </s>
            <s xml:id="echoid-s6812" xml:space="preserve">motus per AI contineatur in
              <lb/>
            motu per AH, quo in aliud planum corpus agit; </s>
            <s xml:id="echoid-s6813" xml:space="preserve">ſequitur
              <lb/>
            actiones in plana eſſe vires quibus corpus eodem tempore
              <lb/>
            fertur velocitatibus AL & </s>
            <s xml:id="echoid-s6814" xml:space="preserve">AI: </s>
            <s xml:id="echoid-s6815" xml:space="preserve">vires verò hæ ſunt ut ipſæ
              <lb/>
            velocitates , & </s>
            <s xml:id="echoid-s6816" xml:space="preserve">integra vis corporis, quæ quadrato
              <note symbol="*" position="right" xlink:label="note-0249-02" xlink:href="note-0249-02a" xml:space="preserve">599.</note>
            tatis AP proportionalis eſt , ſecari debet in duas
              <note symbol="*" position="right" xlink:label="note-0249-03" xlink:href="note-0249-03a" xml:space="preserve">447.</note>
            quæ ſint inter ſe ut AL & </s>
            <s xml:id="echoid-s6817" xml:space="preserve">AI; </s>
            <s xml:id="echoid-s6818" xml:space="preserve">partes hæ ſunt rectangula
              <lb/>
            AP per AL, & </s>
            <s xml:id="echoid-s6819" xml:space="preserve">AP per AI.</s>
            <s xml:id="echoid-s6820" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6821" xml:space="preserve">Si, poſito angulo GCF obtuſo, directio motus AP cum
              <lb/>
              <note position="right" xlink:label="note-0249-04" xlink:href="note-0249-04a" xml:space="preserve">620</note>
            crure uno, ut CF, angulum etiam efficiat obtuſum, in
              <lb/>
              <note position="right" xlink:label="note-0249-05" xlink:href="note-0249-05a" xml:space="preserve">
                <emph style="sc">TAB. XXV.</emph>
                <lb/>
              fig. 3.</note>
            hoc ultimum planum tantum actionem exerit corpus, pro-
              <lb/>
            portionalem quadrato lineæ AD, perpendiculari ad FC,
              <lb/>
            & </s>
            <s xml:id="echoid-s6822" xml:space="preserve">ictu non integram amittit vim, ſed per CF motum
              <lb/>
            poſt impactionem continuat, velocitate linea DC proportio-
              <lb/>
            nali.</s>
            <s xml:id="echoid-s6823" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6824" xml:space="preserve">Hæc ex reſolutione motus ſequuntur. </s>
            <s xml:id="echoid-s6825" xml:space="preserve">Nam
              <note symbol="*" position="right" xlink:label="note-0249-06" xlink:href="note-0249-06a" xml:space="preserve">604</note>
            demonſtrabimus nullam in planum GC dari actionem.</s>
            <s xml:id="echoid-s6826" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6827" xml:space="preserve">In caſu fig. </s>
            <s xml:id="echoid-s6828" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6829" xml:space="preserve">ubi angulus; </s>
            <s xml:id="echoid-s6830" xml:space="preserve">quem AP cum CF efficit, eſt
              <lb/>
            acutus, actio in planum GC minuitur, aucto angulo hoc,
              <lb/>
            ſi hic rectus ſit, ut in fig 3. </s>
            <s xml:id="echoid-s6831" xml:space="preserve">datâ corporis directione a P,
              <lb/>
            parallelogrammi AEPH diagonalis AP coincidit cum latere
              <lb/>
            AH, & </s>
            <s xml:id="echoid-s6832" xml:space="preserve">latus aliud AE, ideoque AL, evaneſcunt, & </s>
            <s xml:id="echoid-s6833" xml:space="preserve">cum
              <lb/>
            hiſce actio in planum GC etiam tollitur ; </s>
            <s xml:id="echoid-s6834" xml:space="preserve">quæ ergo
              <note symbol="*" position="right" xlink:label="note-0249-07" xlink:href="note-0249-07a" xml:space="preserve">619.</note>
            inclinatione viæ corporis ad planum hoc etiam nulla e-
              <lb/>
            rit.</s>
            <s xml:id="echoid-s6835" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6836" xml:space="preserve">In determinandis quæſpectant directam colliſionem trium
              <lb/>
            corporum, illi ſimili utimur methodo quam circa duorum </s>
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