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

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          <p>
            <s xml:id="echoid-s3518" xml:space="preserve">
              <pb o="156" file="0222" n="243" rhead="CHRISTIANI HUGENII"/>
            dulo longitudinis ſubſesquialteræ. </s>
            <s xml:id="echoid-s3519" xml:space="preserve">Conſiderando nempe li-
              <lb/>
              <note position="left" xlink:label="note-0222-01" xlink:href="note-0222-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            neam ejusmodi, ac ſi eſſet rectangulum minimæ latitudinis.</s>
            <s xml:id="echoid-s3520" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3521" xml:space="preserve">Quod ſi figura triangulum fuerit, vertice ſurſum conver-
              <lb/>
            ſo, fit D H {3/4} diametri. </s>
            <s xml:id="echoid-s3522" xml:space="preserve">Si deorſum, {1/2} diametri.</s>
            <s xml:id="echoid-s3523" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3524" xml:space="preserve">Quod autem propoſitione 16 demonſtratum fuit, id ad hu-
              <lb/>
            jusmodi figuræ planæ motum ita pertinere ſciendum. </s>
            <s xml:id="echoid-s3525" xml:space="preserve">Nem-
              <lb/>
            pe, ſi aliam atque aliam poſitionem demus figuræ B C D,
              <lb/>
            invertendo eam circa axem B A C, ut vel horizonti paral-
              <lb/>
            lela jaceat, vel oblique inclinetur, manente eodem agitatio-
              <lb/>
            nis axe F E, etiam longitudo penduli iſochroni F K eadem
              <lb/>
            manebit. </s>
            <s xml:id="echoid-s3526" xml:space="preserve">Hoc enim ex propoſitione illa manifeſtum eſt.</s>
            <s xml:id="echoid-s3527" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3528" xml:space="preserve">Porro quando figura plana, circa axem ad planum figu-
              <lb/>
              <note position="left" xlink:label="note-0222-02" xlink:href="note-0222-02a" xml:space="preserve">TAB. XXIII.
                <lb/>
              Fig. 1. & 2.</note>
            ræ erectum, agitatur; </s>
            <s xml:id="echoid-s3529" xml:space="preserve">quam vocavimus agitationem in latus;
              <lb/>
            </s>
            <s xml:id="echoid-s3530" xml:space="preserve">velut ſi figura B C D moveatur circa axem, qui per pun-
              <lb/>
            ctum F intelligitur ad planum D B C erectus; </s>
            <s xml:id="echoid-s3531" xml:space="preserve">hic jam ha-
              <lb/>
            benda eſt ſumma quadratorum a diſtantiis particularum
              <lb/>
            omnium ab recta quæ per centrum gravitatis A intelligitur
              <lb/>
            axi oſcillationis parallela; </s>
            <s xml:id="echoid-s3532" xml:space="preserve">ſecundum ea quæ prop. </s>
            <s xml:id="echoid-s3533" xml:space="preserve">18. </s>
            <s xml:id="echoid-s3534" xml:space="preserve">ex-
              <lb/>
            poſita fuere. </s>
            <s xml:id="echoid-s3535" xml:space="preserve">Hoc eſt ſumma quadratorum a diſtantiis ab ipſo
              <lb/>
            A centro gravitatis, quoniam figura plana eſt. </s>
            <s xml:id="echoid-s3536" xml:space="preserve">Sive etiam
              <lb/>
            ſummæ quadratorum a diſtantiis tam ab recta B A C quam
              <lb/>
            ab recta D A. </s>
            <s xml:id="echoid-s3537" xml:space="preserve">Conſtat enim quadratum rectæ O A, quam
              <lb/>
            pono eſſe diſtantiam unius cujusdam particulæ a centro A,
              <lb/>
            æquari quadratis diſtantiarum O N, O V, quibus eadem
              <lb/>
            particula abeſt a rectis B A C, D A . </s>
            <s xml:id="echoid-s3538" xml:space="preserve">Atqui ſumma
              <note symbol="*" position="left" xlink:label="note-0222-03" xlink:href="note-0222-03a" xml:space="preserve">Per 47.
                <lb/>
              lib. 1.
                <lb/>
              Elem.</note>
            dratorum a diſtantiis ab recta B A C æquatur rectangulo
              <lb/>
            D A H, ſi D H ſit ſubcentrica cunei ſuper figura abſciſſi
              <lb/>
            per tangentem D D, parallelam B A . </s>
            <s xml:id="echoid-s3539" xml:space="preserve">item ſumma
              <note symbol="*" position="left" xlink:label="note-0222-04" xlink:href="note-0222-04a" xml:space="preserve">Prop. 10.
                <lb/>
              huj.</note>
            dratorum a diſtantiis ab recta D A æquatur rectangulo B A L,
              <lb/>
            ſi B L ſit ſubcentrica cunei abſciſſi per tangentem B D pa-
              <lb/>
            rallelam A D. </s>
            <s xml:id="echoid-s3540" xml:space="preserve">Oportetque dari, præter figuræ centrum gra-
              <lb/>
            vitatis A, ſubcentricamque H D cunei prioris, etiam ſub-
              <lb/>
            centricam L B cunei poſterioris. </s>
            <s xml:id="echoid-s3541" xml:space="preserve">Ita enim nota erunt rectan-
              <lb/>
            gula D A H, B A L, quæ ſimul ſumpta faciunt hic ſpa-
              <lb/>
            tium applicandum, quod deinceps etiam rectangulum oſcil-
              <lb/>
            lationis vocabitur. </s>
            <s xml:id="echoid-s3542" xml:space="preserve">Quod nempe, applicatum ad </s>
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