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

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            <s xml:id="echoid-s2132" xml:space="preserve">
              <pb o="96" file="0142" n="153" rhead="CHRISTIANI HUGENII"/>
            culus genitor A H D, cui occurrat B H, baſi parallela, in
              <lb/>
              <note position="left" xlink:label="note-0142-01" xlink:href="note-0142-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
                <lb/>
                <emph style="sc">RUM CUR-</emph>
                <lb/>
                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO-</emph>
                <lb/>
                <emph style="sc">NE.</emph>
              </note>
            H, & </s>
            <s xml:id="echoid-s2133" xml:space="preserve">jungatur H A. </s>
            <s xml:id="echoid-s2134" xml:space="preserve">Quia ergo B K tangit cycloidem in B,
              <lb/>
            conſtat eam parallelam eſſe rectæ H A . </s>
            <s xml:id="echoid-s2135" xml:space="preserve">Itaque A H B K parallelogrammum eſt, ac proinde A K æqualis H B, hoc
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0142-02" xlink:href="note-0142-02a" xml:space="preserve">Propoſ. 15.
                <lb/>
              partis 2.</note>
            eſt, arcui A H. </s>
            <s xml:id="echoid-s2136" xml:space="preserve">Sit porro jam deſcriptus circulus K
              <note symbol="*" position="left" xlink:label="note-0142-03" xlink:href="note-0142-03a" xml:space="preserve">Propoſ. 14.
                <lb/>
              partis 2.</note>
            genitori circulo, hoc eſt ipſi A H D, æqualis, qui tangat
              <lb/>
            baſin A G in K, rectam vero B K productam ſecet in pun-
              <lb/>
            cto E. </s>
            <s xml:id="echoid-s2137" xml:space="preserve">Quia ergo ipſi A H parallela eſt B K E, ac proin-
              <lb/>
            de angulus E K A æqualis K A H, manifeſtum eſt B K
              <lb/>
            productam abſcindere à circulo K M arcum æqualem ei
              <lb/>
            quem à circulo A H D abſcindit recta A H. </s>
            <s xml:id="echoid-s2138" xml:space="preserve">Itaque arcus
              <lb/>
            K E æqualis eſt arcui A H, hoc eſt rectæ H B, hoc eſt
              <lb/>
            rectæ K A. </s>
            <s xml:id="echoid-s2139" xml:space="preserve">Hinc vero ſequitur, ex cycloidis proprietate,
              <lb/>
            cum circulus genitor M K tangebat regulam in K, punctum
              <lb/>
            deſcribens fuiſſe in E. </s>
            <s xml:id="echoid-s2140" xml:space="preserve">Itaque recta K E occurrit cycloidi in
              <lb/>
            E ad angulos rectos . </s>
            <s xml:id="echoid-s2141" xml:space="preserve">Eſt autem K E ipſa B K producta.</s>
            <s xml:id="echoid-s2142" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0142-04" xlink:href="note-0142-04a" xml:space="preserve">Propoſ. 15.
                <lb/>
              partis 2.</note>
            Ergo patet productam B K occurrere cycloidiad angulos re-
              <lb/>
            ctos. </s>
            <s xml:id="echoid-s2143" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s2144" xml:space="preserve"/>
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          <head xml:id="echoid-head85" xml:space="preserve">PROPOSITIO VI.</head>
          <p style="it">
            <s xml:id="echoid-s2145" xml:space="preserve">SEmicycloidis evolutione, à vertice cœpta, alia
              <lb/>
            ſemicyclois deſcribitur evolutæ æqualis & </s>
            <s xml:id="echoid-s2146" xml:space="preserve">ſimi-
              <lb/>
            lis, cujus baſis eſt in ea recta quæ cycloidem evolu-
              <lb/>
            tam in vertice contingit.</s>
            <s xml:id="echoid-s2147" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2148" xml:space="preserve">Sit ſemicyclois A B C, cui ſuperimpoſita ſit alia ſimilis
              <lb/>
              <note position="left" xlink:label="note-0142-05" xlink:href="note-0142-05a" xml:space="preserve">TAB. XVI.
                <lb/>
              Fig. 1.</note>
            A E F, quemadmodum in propoſitione præcedenti. </s>
            <s xml:id="echoid-s2149" xml:space="preserve">Dico,
              <lb/>
            ſi linea flexilis, circa ſemicycloidem A B C applicata, evol-
              <lb/>
            vatur, incipiendo ab A, eam deſcribere extremitate ſua i-
              <lb/>
            pſam ſemicycloidem A E F. </s>
            <s xml:id="echoid-s2150" xml:space="preserve">Quia enim ex puncto A egredi-
              <lb/>
            untur ſemicycloides A B C, A E F, in unam partem in-
              <lb/>
            flexæ, & </s>
            <s xml:id="echoid-s2151" xml:space="preserve">ambæ in eandem cavæ, ac præterea ita comparatæ,
              <lb/>
            ut omnes tangentes ſemicycloidis A B C occurrant ſemicy-
              <lb/>
            cloidi A E F ad angulos rectos, ſequitur hanc evolutione
              <lb/>
            illius, à termino A incepta, deſcribi . </s>
            <s xml:id="echoid-s2152" xml:space="preserve">quod erat
              <note symbol="*" position="left" xlink:label="note-0142-06" xlink:href="note-0142-06a" xml:space="preserve">Propoſ. 4.
                <lb/>
              huj.</note>
            ſtrandum.</s>
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