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

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              <pb o="159" file="0227" n="249" rhead="HOROLOG. OSCILLATOR."/>
            ex B, centro circuli ſui, fit pendulum ipſi iſochronum {3 pr/4b},
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              <note position="right" xlink:label="note-0227-01" xlink:href="note-0227-01a" 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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            hoc eſt, trium quartarum rectæ, quæ ſit ad radium B F ut
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            arcus C F D ad ſubtenſam C D. </s>
            <s xml:id="echoid-s3585" xml:space="preserve">Hæc autem inveniuntur
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            cognitis ſubcentricis cuneorum; </s>
            <s xml:id="echoid-s3586" xml:space="preserve">tum illius qui ſuper ſectore
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            toto abſcinditur, plano ducto per B K parallelam ſubtenſæ
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            C D, cujus cunei ſubcentricam ſuper B K invenimus eſſe
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            {3/8} y
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            - {3/8} a + {3 p r/8 b}, vocando a ſinum verſum E F; </s>
            <s xml:id="echoid-s3587" xml:space="preserve">tum illius.
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            </s>
            <s xml:id="echoid-s3588" xml:space="preserve">qui ſuper dimidio ſectore B F C abſcinditur plano per
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            B F, cujus nempe cunei ſubcentricam ſuper B F invenimus
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            {3/8} b - {3 b r/8 a} + {3 p r/8 a}.</s>
            <s xml:id="echoid-s3589" xml:space="preserve"/>
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            <s xml:id="echoid-s3590" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s3591" xml:space="preserve">alia via, ſectoris centrum oſcillationis, facilius in-
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              <note position="right" xlink:label="note-0227-02" xlink:href="note-0227-02a" xml:space="preserve">TAB.XXIII.
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              Fig. 6.</note>
            venitur, quæ eſt hujusmodi. </s>
            <s xml:id="echoid-s3592" xml:space="preserve">Intelligatur ſectoris B C D
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            pars minima ſector B C P, qui trianguli loco haberi poteſt.
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            </s>
            <s xml:id="echoid-s3593" xml:space="preserve">Quadrata autem, à diſtantiis particularum ejus à puncto B,
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            æqualia ſunt quadratis diſtantiarum ab recta B R, bifariam
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            ſectorem dividente, una cum quadratis diſtantiarum ab recta
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            B Q, quæ ipſi B R eſt ad angulos rectos. </s>
            <s xml:id="echoid-s3594" xml:space="preserve">Sed, horum
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            quadratorum ad illa, ratio quavis data eſt major, quoniam
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            angulus C B P minimus; </s>
            <s xml:id="echoid-s3595" xml:space="preserve">ideoque illa pro nullis habenda
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            ſunt.</s>
            <s xml:id="echoid-s3596" xml:space="preserve"/>
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            <s xml:id="echoid-s3597" xml:space="preserve">Poſitâ vero B O duarum tertiarum B R, hoc eſt, poſito
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            O centro gravitatis trianguli B C P; </s>
            <s xml:id="echoid-s3598" xml:space="preserve">& </s>
            <s xml:id="echoid-s3599" xml:space="preserve">B N trium quar-
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            tarum B R: </s>
            <s xml:id="echoid-s3600" xml:space="preserve">ut nempe N ſit centrum gravitatis cunei, ſu-
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            per triangulo B C P abſciſſi plano per B Q. </s>
            <s xml:id="echoid-s3601" xml:space="preserve">His poſitis,
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            conſtat quadrata, à diſtantiis particularum trianguli B C P
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            ab recta B Q, æquari rectangulo N B O multiplici ſecun-
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            dum particularum ejuſdem trianguli numerum. </s>
            <s xml:id="echoid-s3602" xml:space="preserve">Itaque rectan-
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            gulum N B O, ita multiplex, æquale cenſendum quadratis
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            diſtantiarum à puncto B particularum trianguli B C P. </s>
            <s xml:id="echoid-s3603" xml:space="preserve">Sunt
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            autem quadrata diſtantiarum harum, ad quadrata diſtantia-
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            rum totius ſectoris B C D, ſicut ſector B C P ad ſectorem
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            B C D, hoc eſt, ſicut numerus particularum ſectoris B C P,
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            ad numerum particularum ſectoris B C D; </s>
            <s xml:id="echoid-s3604" xml:space="preserve">hoc enim facile
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            intelligitur, eo quod ſector B C D dividatur in ſectores qua-
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            lis B C P. </s>
            <s xml:id="echoid-s3605" xml:space="preserve">Ergo rectangulum N B O, multiplex </s>
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