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

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              <pb o="109" file="0161" n="175" rhead="HOROLOG. OSCILLATOR."/>
            ſtabit ab A; </s>
            <s xml:id="echoid-s2457" xml:space="preserve">interſectio vero rectarum B D, F E, quæ eſt
              <lb/>
              <note position="right" xlink:label="note-0161-01" xlink:href="note-0161-01a" 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>
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                <emph style="sc">NE</emph>
              .</note>
            G, cadet ultra punctum D in recta B D. </s>
            <s xml:id="echoid-s2458" xml:space="preserve">Nam concurrere
              <lb/>
            ipſas B D, F E neceſſe eſt, cum curvæ B F ad partem ca-
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            vam inſiſtant rectis angulis.</s>
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          <p>
            <s xml:id="echoid-s2460" xml:space="preserve">Quanto autem punctum F ipſi B propinquius fuerit, tanto
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            propius quoque puncta D, G & </s>
            <s xml:id="echoid-s2461" xml:space="preserve">E convenire apparet; </s>
            <s xml:id="echoid-s2462" xml:space="preserve">ideo-
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            que, ſi interſtitium B F infinite parvum intelligatur, tria
              <lb/>
            dicta puncta pro uno eodemque erunt habenda; </s>
            <s xml:id="echoid-s2463" xml:space="preserve">ac præterea,
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            ductâ rectâ B H, quæ curvam in B tangat, eadem quoque
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            pro tangente in F cenſebitur. </s>
            <s xml:id="echoid-s2464" xml:space="preserve">Sit B O parallela K L, & </s>
            <s xml:id="echoid-s2465" xml:space="preserve">
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            in hanc perpendiculares cadant B K, F L: </s>
            <s xml:id="echoid-s2466" xml:space="preserve">ſecetque F L
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            rectam B O in P, & </s>
            <s xml:id="echoid-s2467" xml:space="preserve">ſint puncta notata M, N, in quibus
              <lb/>
            rectæ, B D, F E, occurrant ipſi K L. </s>
            <s xml:id="echoid-s2468" xml:space="preserve">Quia igitur ratio
              <lb/>
            B G ad G M eſt eadem quæ B O ad M N, data hac dabi-
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            tur & </s>
            <s xml:id="echoid-s2469" xml:space="preserve">illa; </s>
            <s xml:id="echoid-s2470" xml:space="preserve">& </s>
            <s xml:id="echoid-s2471" xml:space="preserve">quia recta B M datur magnitudine ac po-
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            ſitione, dabitur & </s>
            <s xml:id="echoid-s2472" xml:space="preserve">punctum G in producta B M, ſive D
              <lb/>
            in curva C D E, quia G & </s>
            <s xml:id="echoid-s2473" xml:space="preserve">D in unum convenire diximus.
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            </s>
            <s xml:id="echoid-s2474" xml:space="preserve">Datur autem ratio B O ad M N, ſimpliciter quidem in
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            Cycloide, ubi primùm omnium illam inveſtigavimus, inve-
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            nimuſque duplam; </s>
            <s xml:id="echoid-s2475" xml:space="preserve">in aliis vero curvis, quas hactenus exa-
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            minavimus, per duarum datarum rationum compoſitionem. </s>
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            Nam quia ratio B O ad M N componitur ex rationibus B O
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            ad B P, ſive N H ad L H, & </s>
            <s xml:id="echoid-s2477" xml:space="preserve">ex B P ſive K L ad M N; </s>
            <s xml:id="echoid-s2478" xml:space="preserve">
              <lb/>
            patet, ſi rationes hæ utræque dentur etiam ex iis compoſi-
              <lb/>
            tam rationem B O ad M N datum iri. </s>
            <s xml:id="echoid-s2479" xml:space="preserve">Illas vero dari in o-
              <lb/>
            mnibus curvis geometricis, in ſequentibus patebit; </s>
            <s xml:id="echoid-s2480" xml:space="preserve">ac proin-
              <lb/>
            de iis ſemper curvas adſignari poſſe, quarum evolutione de-
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            ſcribantur, quæque ideo ad rectas lineas ſint reducibiles.</s>
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            <s xml:id="echoid-s2482" xml:space="preserve">Ponatur primò parabola eſſe A B F, cujus vertex A,
              <lb/>
              <note position="right" xlink:label="note-0161-02" xlink:href="note-0161-02a" xml:space="preserve">TAB. XVI.
                <lb/>
              Fig. 2.</note>
            axis A Q. </s>
            <s xml:id="echoid-s2483" xml:space="preserve">Cum igitur lineæ B M, F N, ſint parabolæ ad
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            angulos rectos; </s>
            <s xml:id="echoid-s2484" xml:space="preserve">ductæque ſint ad axem A Q perpendicula-
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            res B K, F L; </s>
            <s xml:id="echoid-s2485" xml:space="preserve">erunt, ex proprietate parabolæ, ſingulæ
              <lb/>
            M K, N L dimidio lateri recto æquales; </s>
            <s xml:id="echoid-s2486" xml:space="preserve">& </s>
            <s xml:id="echoid-s2487" xml:space="preserve">ablata commu-
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            ni L M, æquales inter ſe K L, M N. </s>
            <s xml:id="echoid-s2488" xml:space="preserve">Hinc, quum ratio
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            B G ad G M componatur ex rationibus N H ad H L, & </s>
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            K L ad M N, uti dictum fuit, ſitque earum poſterior </s>
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