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

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          <p>
            <s xml:id="echoid-s3744" xml:space="preserve">
              <pb o="165" file="0237" n="261" rhead="HOROLOG. OSCILLATOR."/>
            quæ velut luxatione illarum efficiuntur, ut trianguli ſcaleni,
              <lb/>
              <note position="right" xlink:label="note-0237-01" xlink:href="note-0237-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            & </s>
            <s xml:id="echoid-s3745" xml:space="preserve">parabolæ non rectæ, centra oſcillationis haberi. </s>
            <s xml:id="echoid-s3746" xml:space="preserve">Ut ſi,
              <lb/>
              <note position="right" xlink:label="note-0237-02" xlink:href="note-0237-02a" xml:space="preserve">TAB.XXVII.
                <lb/>
              Fig. 1.</note>
            exempli gratia, triangulum B A C iſoſceles, cujus axis
              <lb/>
            A D, à puncto E ſuſpenſum intelligatur; </s>
            <s xml:id="echoid-s3747" xml:space="preserve">ſit vero & </s>
            <s xml:id="echoid-s3748" xml:space="preserve">aliud
              <lb/>
            triangulum ſcalenum F A G, axem eundem habens A D, & </s>
            <s xml:id="echoid-s3749" xml:space="preserve">
              <lb/>
            baſin F G æqualem baſi B C; </s>
            <s xml:id="echoid-s3750" xml:space="preserve">etiam hoc triangulum, ex E
              <lb/>
            ſuſpenſum, priori B A C iſochronum eſſe dico.</s>
            <s xml:id="echoid-s3751" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3752" xml:space="preserve">Quia enim virga, ſeu linea gravis, F G, affixa virgæ ſi-
              <lb/>
            ne pondere E D in D, ſitu obliquo, ſuſpenſaque ex E,
              <lb/>
            iſochrona eſt virgæ B C, ſimiliter in D affixæ ; </s>
            <s xml:id="echoid-s3753" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0237-03" xlink:href="note-0237-03a" xml:space="preserve">Prop. 16.
                <lb/>
              huj.</note>
            evenit in virgis cæteris trianguli útriusque, quæ axem A D
              <lb/>
            ſecant in iisdem punctis, atque inter ſe æquales ſunt: </s>
            <s xml:id="echoid-s3754" xml:space="preserve">ne-
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            ceſſe eſt tota triangula, quæ ex lineis, ſeu virgis iisdem
              <lb/>
            compoſita intelligi poſſunt, iſochrona eſſe. </s>
            <s xml:id="echoid-s3755" xml:space="preserve">In aliis figuris ſi-
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            milis eſt demonſtratio.</s>
            <s xml:id="echoid-s3756" xml:space="preserve"/>
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        <div xml:id="echoid-div342" type="section" level="1" n="121">
          <head xml:id="echoid-head147" xml:space="preserve">PROPOSITIO XXII.</head>
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            <s xml:id="echoid-s3757" xml:space="preserve">QUomodo, in ſolidis figuris, oſcillationis centra
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            inveniantur.</s>
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            <s xml:id="echoid-s3759" xml:space="preserve">In ſolidis porro figuris facile quoque, per ante demon-
              <lb/>
              <note position="right" xlink:label="note-0237-04" xlink:href="note-0237-04a" xml:space="preserve">TAB. XXV.
                <lb/>
              Fig. 5.</note>
            ſtrata, centrum oſcillationis invenire licebit. </s>
            <s xml:id="echoid-s3760" xml:space="preserve">Si enim ſit ſc-
              <lb/>
            lidum A B C, ſuſpenſum ab axe, qui, per punctum E,
              <lb/>
            intelligitur hujus paginæ plano ad rectos angulos; </s>
            <s xml:id="echoid-s3761" xml:space="preserve">centrum
              <lb/>
            autem gravitatis ſit F: </s>
            <s xml:id="echoid-s3762" xml:space="preserve">ductis jam per F planis E F D, G F H,
              <lb/>
            quorum poſterius ſit horizonti parallelum, alterum vero per
              <lb/>
            axem E transeat; </s>
            <s xml:id="echoid-s3763" xml:space="preserve">inventisque, per propoſitionem 14, ſum-
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            mis quadratorum à diſtantiis particularum ſolidi A B C à
              <lb/>
            plano G F H, itemque à plano E F D; </s>
            <s xml:id="echoid-s3764" xml:space="preserve">hoc eſt, inven-
              <lb/>
            tis rectangulis utrisque, quæ, multiplicia ſecundum numc-
              <lb/>
            rum dictarum particularum, æqualia ſint dictis quadratcrum
              <lb/>
            ſummis; </s>
            <s xml:id="echoid-s3765" xml:space="preserve">rectangula hæc applicata ad diſtantiam E F, qua
              <lb/>
            nempe axis ſuſpenſionis diſtat à centro gravitatis, dabunt
              <lb/>
            intervallum F K, quo centrum agitationis K inferius eſt
              <lb/>
            centro gravitatis F. </s>
            <s xml:id="echoid-s3766" xml:space="preserve">Hoc enim patet ex propoſitione 18. </s>
            <s xml:id="echoid-s3767" xml:space="preserve">Da-
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            bimus autem & </s>
            <s xml:id="echoid-s3768" xml:space="preserve">horum exempla aliquot.</s>
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