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

Table of handwritten notes

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              <pb o="129" file="0189" n="207" rhead="HOROLOG. OSCILLATOR."/>
            que arcus percurri, ac proinde pendulum F G, pendulo
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              <note position="right" xlink:label="note-0189-01" xlink:href="note-0189-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
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                <emph style="sc">OSCILLA-</emph>
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                <emph style="sc">TIONIS.</emph>
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            compoſito ex A, B, C, iſochronum eſſe. </s>
            <s xml:id="echoid-s2935" xml:space="preserve">Oſtendetur au-
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            tem hoc modo.</s>
            <s xml:id="echoid-s2936" xml:space="preserve"/>
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            <s xml:id="echoid-s2937" xml:space="preserve">Sit primo, ſi poteſt, major celeritas puncti L, ubi in P
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            pervenit, quam ponderis G in O. </s>
            <s xml:id="echoid-s2938" xml:space="preserve">Conſtatautem, dum pun-
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            ctum L percurrit arcum L P, ſimul centrum gravitatis E
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            percurrere arcum ſimilem E Q. </s>
            <s xml:id="echoid-s2939" xml:space="preserve">Ducantur à punctis Q, P, O,
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            perpendiculares ſurſum, quæ occurrant ſubtenſis arcuum
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            E I, L N, G M, in R, S, Y. </s>
            <s xml:id="echoid-s2940" xml:space="preserve">& </s>
            <s xml:id="echoid-s2941" xml:space="preserve">S P vocetur y. </s>
            <s xml:id="echoid-s2942" xml:space="preserve">Unde,
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            cum ſit ut L D, x, ad E D, d, ita S P, y, ad R Q; </s>
            <s xml:id="echoid-s2943" xml:space="preserve">erit
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            R Q æqualis {d y/x}. </s>
            <s xml:id="echoid-s2944" xml:space="preserve">Jam quia pondus G eam celeritatem ha-
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            bet in O, qua valet ad eandem unde deſcendit altitudinem
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            aſcendere, nempe per arcum O M, vel perpendicularem
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            O Y ipſi P S æqualem; </s>
            <s xml:id="echoid-s2945" xml:space="preserve">punctum igitur L, ubi in P per-
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            venerit, majorem ibi celeritatem habebit, quam qua aſcen-
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            ditur ad altitudinem P S. </s>
            <s xml:id="echoid-s2946" xml:space="preserve">Dum vero L tranſit in P, ſimul
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            pondera A, B, C, ſimiles arcus percurrunt ipſi L P, nimirum
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            A T, B V, C X. </s>
            <s xml:id="echoid-s2947" xml:space="preserve">Eſtque puncti L celeritas in P, ad celeri-
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            tatem ponderis A in T, quum vinculo eodem contineantur,
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            ſicut diſtantia D L ad D A. </s>
            <s xml:id="echoid-s2948" xml:space="preserve">Sed ut quadratum celeritatis
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            puncti L, quam habet in P, ad quadratum celeritatis pun-
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            cti A in T, ita eſt altitudo ad quam illa celeritate
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            aſcendi poteſt, ad altitudinem quò hac celeritate aſcendi
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            poteſt . </s>
            <s xml:id="echoid-s2949" xml:space="preserve">Ergo etiam, ut quadratum diſtantiæ D L,
              <note symbol="*" position="right" xlink:label="note-0189-02" xlink:href="note-0189-02a" xml:space="preserve">Prop. 3.
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              & 4. part. @.</note>
            eſt x x, ad quadratum diſtantiæ D A, quod eſt e e, ita eſt
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            altitudo quo aſcenditur celeritate puncti L, quum eſt in P,
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            (quæ altitudo major dicta eſt quam P S ſive y,) ad altitu-
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            dinem quo aſcenditur celeritate ponderis A in T; </s>
            <s xml:id="echoid-s2950" xml:space="preserve">ſi nempe
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            poſtquam in T pervenit, relicto pendulo, ſeorſim motum
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            ſuum ſurſum converteret. </s>
            <s xml:id="echoid-s2951" xml:space="preserve">Quæ proinde altitudo major erit
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            quam {e e y/x x}.</s>
            <s xml:id="echoid-s2952" xml:space="preserve"/>
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            <s xml:id="echoid-s2953" xml:space="preserve">Eadem ratione, erit altitudo ad quam aſcenderet pondus
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            B, celeritate acquiſita per arcum B V, major quam {f f y/x x}. </s>
            <s xml:id="echoid-s2954" xml:space="preserve">Et
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            altitudo ad quam aſcenderet pondus C, celeritate acquiſita
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            per arcum C X, major quam {g g y/x x}. </s>
            <s xml:id="echoid-s2955" xml:space="preserve">Unde, ductis ſingulis </s>
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