Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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        <div xml:id="echoid-div77" type="section" level="1" n="32">
          <p>
            <s xml:id="echoid-s1398" xml:space="preserve">
              <pb o="66" file="0100" n="105" rhead="CHRISTIANI HUGENII"/>
            vel per C F. </s>
            <s xml:id="echoid-s1399" xml:space="preserve">Ergo in B duntaxat eam qua potuiſſet aſcen-
              <lb/>
              <note position="left" xlink:label="note-0100-01" xlink:href="note-0100-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            dere per B F, hoc eſt, eandem quam acquireret deſcendendo
              <lb/>
            per F B. </s>
            <s xml:id="echoid-s1400" xml:space="preserve">Atqui in B habet velocitatem qua poteſt aſcende-
              <lb/>
            re uſque in A. </s>
            <s xml:id="echoid-s1401" xml:space="preserve">Ergo illa velocitate quam acquirit grave de-
              <lb/>
            ſcendendo per F B, poſſet aſcendere per B A, hoc eſt, al-
              <lb/>
            tius quam unde diſceſſerat, quod fieri non poteſt.</s>
            <s xml:id="echoid-s1402" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1403" xml:space="preserve">Eſt autem eadem prorſus demonſtratio quotcunque plana
              <lb/>
            fuerint per quæ mobile aſcendat. </s>
            <s xml:id="echoid-s1404" xml:space="preserve">Unde & </s>
            <s xml:id="echoid-s1405" xml:space="preserve">ſi infinita fuerit
              <lb/>
            planorum multitudo, hoc eſt, ſi ſuperficies aliqua curva
              <lb/>
            ponatur, per hanc quoque ad eam ex qua venit altitudinem
              <lb/>
            mobile aſſurget.</s>
            <s xml:id="echoid-s1406" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div80" type="section" level="1" n="33">
          <head xml:id="echoid-head55" xml:space="preserve">PROPOSITIO X.</head>
          <p style="it">
            <s xml:id="echoid-s1407" xml:space="preserve">SI mobile cadat perpendiculariter, vel per quam-
              <lb/>
            libet ſuperficiem deſcendat, ac rurſus impetu
              <lb/>
            concepto per quamlibet aliam feratur ſurſum, ha-
              <lb/>
            bebit aſcendendo ac deſcendendo in punctis æque al-
              <lb/>
            tis eandem ſemper velocitatem.</s>
            <s xml:id="echoid-s1408" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1409" xml:space="preserve">Ut ſi mobile ex altitudine A B decidens, motum deinde
              <lb/>
              <note position="left" xlink:label="note-0100-02" xlink:href="note-0100-02a" xml:space="preserve">TAB. IV.
                <lb/>
              Fig. 3.</note>
            continuet per ſuperficiem B C D, in qua punctum C ſit
              <lb/>
            pari altitudine atque in A B eſt punctum E. </s>
            <s xml:id="echoid-s1410" xml:space="preserve">Dico in C ean-
              <lb/>
            dem velocitatem ineſſe mobili atque in E fuerat.</s>
            <s xml:id="echoid-s1411" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1412" xml:space="preserve">Quum enim in C ea velocitas ſuperſit mobili qua porro
              <lb/>
            aſcendat usque ad D punctum, æque altum ac A : </s>
            <s xml:id="echoid-s1413" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0100-03" xlink:href="note-0100-03a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            que & </s>
            <s xml:id="echoid-s1414" xml:space="preserve">ex deſcenſu per A E velocitatem eam acquirat qua,
              <lb/>
            converſo motu, aſcenſurum ſit per C D ; </s>
            <s xml:id="echoid-s1415" xml:space="preserve">Patet cum
              <note symbol="*" position="left" xlink:label="note-0100-04" xlink:href="note-0100-04a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            venit ad C aſcendendo, eandem ipſum habere velocitatem,
              <lb/>
            quam habebat in E deſcendendo; </s>
            <s xml:id="echoid-s1416" xml:space="preserve">quod erat demonſtran-
              <lb/>
            dum.</s>
            <s xml:id="echoid-s1417" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div83" type="section" level="1" n="34">
          <head xml:id="echoid-head56" xml:space="preserve">PROPOSITIO XI.</head>
          <p style="it">
            <s xml:id="echoid-s1418" xml:space="preserve">SI mobile per ſuperficiem aliquam deorſum ten-
              <lb/>
            dat, ac deinde converſo motu ſurſum per </s>
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