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

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            <s xml:id="echoid-s6536" xml:space="preserve">
              <pb o="165" file="0237" n="258" rhead="MATHEMATICA. LIB. I. CAP XXV."/>
            dem demonſtratio in acceleratione quacunque corporis ex
              <lb/>
            duabus actionibus locum habet.</s>
            <s xml:id="echoid-s6537" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6538" xml:space="preserve">Si in corpus motum, actio detur juxta directionem di-
              <lb/>
            verſam a directione motus primi, mutationem in directione
              <lb/>
            dari ſuperius vidimus , & </s>
            <s xml:id="echoid-s6539" xml:space="preserve">quæ velocitates in hiſce
              <note symbol="*" position="right" xlink:label="note-0237-01" xlink:href="note-0237-01a" xml:space="preserve">245.</note>
            fpectant examinavimus , de viribus nunc agendum. </s>
            <s xml:id="echoid-s6540" xml:space="preserve">
              <note position="right" xlink:label="note-0237-02" xlink:href="note-0237-02a" xml:space="preserve">246.</note>
            tur corpus per AD, celeritate, quam hac lineâ deſigna-
              <lb/>
            mus, & </s>
            <s xml:id="echoid-s6541" xml:space="preserve">vis nova hoc pellat per AE, celeritate, quam hac
              <lb/>
              <note position="right" xlink:label="note-0237-03" xlink:href="note-0237-03a" xml:space="preserve">
                <emph style="sc">TAB. XXIII</emph>
              .
                <lb/>
              fig. 314. 5.</note>
            linea deſignamus; </s>
            <s xml:id="echoid-s6542" xml:space="preserve">corpus duabus celeritatibus latum, mo-
              <lb/>
            vetur per AB . </s>
            <s xml:id="echoid-s6543" xml:space="preserve">Non tamen in ſingulis hiſce caſibus
              <note position="right" xlink:label="note-0237-04" xlink:href="note-0237-04a" xml:space="preserve">600.</note>
            preſſione æ quali æ qualis communicatur velocitas lateralis;
              <lb/>
            </s>
            <s xml:id="echoid-s6544" xml:space="preserve">
              <note position="right" xlink:label="note-0237-05" xlink:href="note-0237-05a" xml:space="preserve">246.</note>
            ponimus AB & </s>
            <s xml:id="echoid-s6545" xml:space="preserve">AE in tribus figuris reſpectivè æquales.
              <lb/>
            </s>
            <s xml:id="echoid-s6546" xml:space="preserve">In fig. </s>
            <s xml:id="echoid-s6547" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6548" xml:space="preserve">motus ſecundus, pro parte cum motu primo con-
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            ſpirat, ita ut in hoc motu contineatur acceleratio motus
              <lb/>
            per AD. </s>
            <s xml:id="echoid-s6549" xml:space="preserve">Eodem modo retardatio velocitatis per AD con-
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            tinetur in motu per AE in fig. </s>
            <s xml:id="echoid-s6550" xml:space="preserve">5. </s>
            <s xml:id="echoid-s6551" xml:space="preserve">Idcirco impreſſiones, qui-
              <lb/>
            bus corpora per AE pelluntur, ut velocitatem hac lineâ
              <lb/>
            deſignatam corporibus ſingulis communicent, non ſunt æ-
              <lb/>
            quales inter ſe , neque impreſſioni, qua corpori
              <note symbol="*" position="right" xlink:label="note-0237-06" xlink:href="note-0237-06a" xml:space="preserve">443.</note>
            hæc poſſet communicari velocitas .</s>
            <s xml:id="echoid-s6552" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">440.</note>
          <p>
            <s xml:id="echoid-s6553" xml:space="preserve">In ſolo caſu fig. </s>
            <s xml:id="echoid-s6554" xml:space="preserve">3, in quo angulus EAD eſt rectus, motus
              <lb/>
              <note position="right" xlink:label="note-0237-08" xlink:href="note-0237-08a" xml:space="preserve">601.</note>
            lateralis neque conſpirat neque contrarie agit cum motu per
              <lb/>
            AD, & </s>
            <s xml:id="echoid-s6555" xml:space="preserve">impreſſio, qua corpus movetur, in corpus agit quaſi
              <lb/>
            quieſceret; </s>
            <s xml:id="echoid-s6556" xml:space="preserve">idcirco in hoc caſu vis corpori communicata pro-
              <lb/>
            portionalis eſt quadrato ſuæ velocitatis , & </s>
            <s xml:id="echoid-s6557" xml:space="preserve">cùm impreſſio non poſſit vim per AE minuere, corporis vis integra pro-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0237-09" xlink:href="note-0237-09a" xml:space="preserve">447.</note>
            portionalis eſt ambobus quadratis linearum AD & </s>
            <s xml:id="echoid-s6558" xml:space="preserve">AE, quod
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            congruit cum demonſtratis: </s>
            <s xml:id="echoid-s6559" xml:space="preserve">nam fertur corpus celeritate
              <note symbol="*" position="right" xlink:label="note-0237-10" xlink:href="note-0237-10a" xml:space="preserve">246.</note>
            cujus quadratum valet memorata duo quadrata .</s>
            <s xml:id="echoid-s6560" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">[47. El I.</note>
          <p>
            <s xml:id="echoid-s6561" xml:space="preserve">Ex his virium menſura ſi hæc ignota eſſet, detegi poſſet. </s>
            <s xml:id="echoid-s6562" xml:space="preserve">Cor-
              <lb/>
              <note position="right" xlink:label="note-0237-12" xlink:href="note-0237-12a" xml:space="preserve">601.</note>
            pori, quod habet vim quæ reſpondet celeritati AD, communi-
              <lb/>
            catur vis quæ velocitati AE reſpondet, quæ cum corpori com-
              <lb/>
            municetur quaſi quieſceret, vim primam mutare non poteſt; </s>
            <s xml:id="echoid-s6563" xml:space="preserve">va-
              <lb/>
            let ideò corporis vis integra ſummam harum virium, dum
              <lb/>
            ipſius velocitas eſt AB; </s>
            <s xml:id="echoid-s6564" xml:space="preserve">ergo vis quæ huic reſpondet velocitati,
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            memoratæ ſummæ æqualis eſt. </s>
            <s xml:id="echoid-s6565" xml:space="preserve">Quod ſieri non poterit in </s>
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