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

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        <div xml:id="echoid-div72" type="section" level="1" n="30">
          <pb o="64" file="0096" n="100" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s1354" xml:space="preserve">Sint plana inclinata A C, A D quorum eadem elevatio
              <lb/>
              <note position="left" xlink:label="note-0096-01" xlink:href="note-0096-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            A B. </s>
            <s xml:id="echoid-s1355" xml:space="preserve">dico tempus deſcenſus per planum A C ad tempus
              <lb/>
              <note position="left" xlink:label="note-0096-02" xlink:href="note-0096-02a" xml:space="preserve">TAB. V.
                <lb/>
              Fig. 5.</note>
            deſcenſus per A D eſſe ut longitudo A C ad A D. </s>
            <s xml:id="echoid-s1356" xml:space="preserve">Eſt enim
              <lb/>
            tempus per A C æquale tempori motus æquabilis per ean-
              <lb/>
            dem A C, cum celeritate dimidia ejus quæ acquiritur caſu
              <lb/>
            per A C . </s>
            <s xml:id="echoid-s1357" xml:space="preserve">Similiter tempus per A D eſt æquale
              <note symbol="*" position="left" xlink:label="note-0096-03" xlink:href="note-0096-03a" xml:space="preserve">Prop. 1.
                <lb/>
              huj.</note>
            motus æquabilis per ipſam A D, cum dimidia celeritate ejus
              <lb/>
            quæ acquiritur caſu per A D. </s>
            <s xml:id="echoid-s1358" xml:space="preserve">Eſt autem hæc dimidia celeri-
              <lb/>
            tas illi dimidiæ celerirati æqualis , ideoque dictum
              <note symbol="*" position="left" xlink:label="note-0096-04" xlink:href="note-0096-04a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            motus æquabilis per A C, ad tempus motus æquabilis per A D,
              <lb/>
            erit ut A C ad A D. </s>
            <s xml:id="echoid-s1359" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1360" xml:space="preserve">tempora ſingulis iſtis æqualia,
              <lb/>
            nimirum tempus deſcenſus per A C, ad tempus deſcenſus
              <lb/>
            per A D, eandem rationem habebunt, nempe quam A C
              <lb/>
            ad A D. </s>
            <s xml:id="echoid-s1361" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1362" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1363" xml:space="preserve">Eodem modo oſtendetur & </s>
            <s xml:id="echoid-s1364" xml:space="preserve">tempus deſcenſus per A C, ad
              <lb/>
            tempus caſus per A B perpendicularem, eſſe ut A C ad
              <lb/>
            A B longitudine.</s>
            <s xml:id="echoid-s1365" xml:space="preserve"/>
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        <div xml:id="echoid-div74" type="section" level="1" n="31">
          <head xml:id="echoid-head53" xml:space="preserve">PROPOSITIO VIII.</head>
          <p style="it">
            <s xml:id="echoid-s1366" xml:space="preserve">SI ex altitudine eadem deſcendat mobile conti-
              <lb/>
            nuato motu per quotlibet ac quælibet plana con-
              <lb/>
            tigua, utcunque inclinata; </s>
            <s xml:id="echoid-s1367" xml:space="preserve">ſemper eandem in fine
              <lb/>
            velocitatem acquiret, quæ nimirum æqualis erit ei
              <lb/>
            quam acquireret cadendo perpendiculariter ex pa-
              <lb/>
            ri altitudine.</s>
            <s xml:id="echoid-s1368" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1369" xml:space="preserve">Sint plana contigua A B, B C, C D, quorum terminus
              <lb/>
              <note position="left" xlink:label="note-0096-05" xlink:href="note-0096-05a" xml:space="preserve">TAB VI.
                <lb/>
              Fig. 1.</note>
            A, ſupra horizontalem lineam D F per infimum terminum
              <lb/>
            D ductam, altitudinem habeat quanta eſt perpendicularis E F.
              <lb/>
            </s>
            <s xml:id="echoid-s1370" xml:space="preserve">deſcendatque mobile per plana illa ab A uſque in D. </s>
            <s xml:id="echoid-s1371" xml:space="preserve">Di-
              <lb/>
            co in D eam velocitatem habiturum quam, ex E cadens, ha-
              <lb/>
            beret in F.</s>
            <s xml:id="echoid-s1372" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1373" xml:space="preserve">Producta enim C B occurrat rectæ A E in G. </s>
            <s xml:id="echoid-s1374" xml:space="preserve">Itemque
              <lb/>
            D C producta occurrat eidem A E in E. </s>
            <s xml:id="echoid-s1375" xml:space="preserve">Quoniam </s>
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