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

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              <pb o="80" file="0120" n="128" rhead="CHRISTIANI HUGENII"/>
            quanta acquiritur deſcendendo per arcum Cycloi-
              <lb/>
              <note position="left" xlink:label="note-0120-01" xlink:href="note-0120-01a" xml:space="preserve">
                <emph style="sc">De motu</emph>
                <lb/>
                <emph style="sc">IN</emph>
                <emph style="sc">Cy-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
              .</note>
            dis B G, fore ad tempus quo percurretur recta
              <lb/>
            O P, celeritate æquabili dimidia ejus quæ acqui-
              <lb/>
            ritur deſcendendo per totam tangentem B I, ſicut
              <lb/>
            eſt tangens S T ad partem axis Q R.</s>
            <s xml:id="echoid-s1761" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1762" xml:space="preserve">Deſcribatur enim ſuper axe A D ſemicirculus D V A ſe-
              <lb/>
            cans rectam B F in V, & </s>
            <s xml:id="echoid-s1763" xml:space="preserve">Σ G in Φ, & </s>
            <s xml:id="echoid-s1764" xml:space="preserve">jungatur A V ſe-
              <lb/>
            cans rectas O Q, P R, G Σ in E K & </s>
            <s xml:id="echoid-s1765" xml:space="preserve">Λ. </s>
            <s xml:id="echoid-s1766" xml:space="preserve">Jungantur item
              <lb/>
            H F, H A, H X & </s>
            <s xml:id="echoid-s1767" xml:space="preserve">A Φ; </s>
            <s xml:id="echoid-s1768" xml:space="preserve">quæ poſtrema ſecet rectas O Q,
              <lb/>
            P R in punctis Δ & </s>
            <s xml:id="echoid-s1769" xml:space="preserve">Π.</s>
            <s xml:id="echoid-s1770" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1771" xml:space="preserve">Habet ergo dictum tempus per M N ad tempus per O P,
              <lb/>
            rationem eam quæ componitur ex ratione ipſarum linearum
              <lb/>
            M N ad O P, & </s>
            <s xml:id="echoid-s1772" xml:space="preserve">ex ratione celeritatum quibus ipſæ per-
              <lb/>
            curruntur, contrarie ſumpta , hoc eſt, & </s>
            <s xml:id="echoid-s1773" xml:space="preserve">ex ratione
              <note symbol="*" position="left" xlink:label="note-0120-02" xlink:href="note-0120-02a" xml:space="preserve">Prop. 5.
                <lb/>
              Galil. de
                <lb/>
              motu æ-
                <lb/>
              quab.</note>
            diæ celeritatis ex B I ſive ex F A, ad celeritatem ex B G, ſive
              <lb/>
            ex F Σ . </s>
            <s xml:id="echoid-s1774" xml:space="preserve">Atqui tota celeritas ex F A ad celeritatem ex F
              <note symbol="*" position="left" xlink:label="note-0120-03" xlink:href="note-0120-03a" xml:space="preserve">Prop. 8.
                <lb/>
              huj.</note>
            eſt in ſubduplicata ratione longitudinum F A ad F Σ ,
              <note symbol="*" position="left" xlink:label="note-0120-04" xlink:href="note-0120-04a" xml:space="preserve">Prop. 3.
                <lb/>
              huj.</note>
            proinde eadem quæ F A ad F H Ergo dimidia celeritas ex
              <lb/>
            F A ad celeritatem ex F Σ erit ut F X ad F H. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">Itaque tem-
              <lb/>
            pus dictum per M N ad tempus per O P habebit rationem
              <lb/>
            compoſitam ex rationibus M N ad O P, & </s>
            <s xml:id="echoid-s1776" xml:space="preserve">F X ad F H.
              <lb/>
            </s>
            <s xml:id="echoid-s1777" xml:space="preserve">Harum vero prior ratio, nempe M N ad O P, eadem oſten-
              <lb/>
            detur quæ F H ad H Σ.</s>
            <s xml:id="echoid-s1778" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1779" xml:space="preserve">Eſt enim tangens Cycloidis B I parallela rectæ V A, ſi-
              <lb/>
            militerque tangens M G N parallela rectæ Φ A; </s>
            <s xml:id="echoid-s1780" xml:space="preserve">ac proinde
              <lb/>
            recta M N æqualis Δ Π, & </s>
            <s xml:id="echoid-s1781" xml:space="preserve">O P æqualis E K. </s>
            <s xml:id="echoid-s1782" xml:space="preserve">Ergo dicta
              <lb/>
            ratio rectæ M N ad O P eadem eſt quæ Δ Π ad E K; </s>
            <s xml:id="echoid-s1783" xml:space="preserve">hoc
              <lb/>
            eſt, Δ A ad E A; </s>
            <s xml:id="echoid-s1784" xml:space="preserve">hoc eſt, Φ A ad Λ A; </s>
            <s xml:id="echoid-s1785" xml:space="preserve">hoc eſt V A ad
              <lb/>
            Φ A . </s>
            <s xml:id="echoid-s1786" xml:space="preserve">Eſt autem ut V A ad A Φ ita F A ad A H; </s>
            <s xml:id="echoid-s1787" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0120-05" xlink:href="note-0120-05a" xml:space="preserve">Lemma
                <lb/>
              @ræced,</note>
            quia quadratum V A æquale eſt rectangulo D A F, & </s>
            <s xml:id="echoid-s1788" xml:space="preserve">qua-
              <lb/>
            dratum A Φ æquale rectangulo D A Σ, quæ rectangula ſunt
              <lb/>
            inter ſe ut F A ad Σ A, hoc eſt ut quadratum F A ad qua-
              <lb/>
            dratum A H, erit proinde & </s>
            <s xml:id="echoid-s1789" xml:space="preserve">quadratum V A ad quadra-
              <lb/>
            tum Φ A ut quadratum F A ad quadratum A H; </s>
            <s xml:id="echoid-s1790" xml:space="preserve"/>
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