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

Table of Notes

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            <s xml:id="echoid-s2634" xml:space="preserve">
              <pb o="114" file="0168" n="183" rhead="CHRISTIANI HUGENII"/>
            tem M K ad M K + 3 K S, ita M B ad M B + 3 B Z:
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            <s xml:id="echoid-s2635" xml:space="preserve">
              <note position="left" xlink:label="note-0168-01" xlink:href="note-0168-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
                <lb/>
                <emph style="sc">RUMCUR-</emph>
                <lb/>
                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO-</emph>
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                <emph style="sc">NE.</emph>
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            erit proinde M B ad M D ut M B ad M B + 3 B Z. </s>
            <s xml:id="echoid-s2636" xml:space="preserve">Un-
              <lb/>
            de liquet M D æqualem ſumendam ipſi M B + 3 B Z. </s>
            <s xml:id="echoid-s2637" xml:space="preserve">At-
              <lb/>
            que ita quotlibet puncta curvæ C D E invenire licebit. </s>
            <s xml:id="echoid-s2638" xml:space="preserve">Cu-
              <lb/>
            jus curvæ portio quælibet ut D S, rectæ D B, quæ para-
              <lb/>
            boloidi S A B ad angulos rectos occurrit, æqualis erit.
              <lb/>
            </s>
            <s xml:id="echoid-s2639" xml:space="preserve">Conſtat autem geometricam eſſe, & </s>
            <s xml:id="echoid-s2640" xml:space="preserve">ſi velimus, poſſumus
              <lb/>
            æquatione aliqua relationem exprimere punctorum omnium
              <lb/>
            ipſius ad puncta axis S K.</s>
            <s xml:id="echoid-s2641" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2642" xml:space="preserve">Simili modo autem, ſi inquiramus in paraboloide illa ſive
              <lb/>
              <note position="left" xlink:label="note-0168-02" xlink:href="note-0168-02a" xml:space="preserve">TAB. XVII.
                <lb/>
              Fig. 1.</note>
            parabola cubica, in qua cubi ordinatim applicatarum ad
              <lb/>
            axem, ſunt inter ſe ſicut portiones axis abſciſſæ, inveniemus
              <lb/>
            curvam cujus evolutione deſcribitur, quæque proinde rectæ
              <lb/>
            lineæ æquari poterit, nihilo difficiliori conſtructione per pun-
              <lb/>
            cta determinari. </s>
            <s xml:id="echoid-s2643" xml:space="preserve">Nam ſi fuerit illa S A B; </s>
            <s xml:id="echoid-s2644" xml:space="preserve">axis S M; </s>
            <s xml:id="echoid-s2645" xml:space="preserve">(di-
              <lb/>
            citur autem improprie axis in hac curva, cum forma ejus ſit
              <lb/>
            ejusmodi, ut ductâ S Z, quæ ſecet S M ad angulos rectos,
              <lb/>
            ea portiones ſimiles curvæ habeat ad partes oppoſitas;) </s>
            <s xml:id="echoid-s2646" xml:space="preserve">aga-
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            rur per punctum quodlibet B, in paraboloide ſumptum, re-
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            cta B D, quæ curvam ad angulos rectos ſecet, axique ejus
              <lb/>
            occurrat in M, rectæ vero S Z in Z. </s>
            <s xml:id="echoid-s2647" xml:space="preserve">Deinde ſumatur B D
              <lb/>
            æqualis dimidiæ B M, unà cum ſesquialtera B Z. </s>
            <s xml:id="echoid-s2648" xml:space="preserve">Eritque
              <lb/>
            D unum è punctis curvæ quæſitæ R D vel R I, cujus evo-
              <lb/>
            lutione, juncta tamen recta quadam R A, deſcribetur para-
              <lb/>
            boloides S A B. </s>
            <s xml:id="echoid-s2649" xml:space="preserve">Sunt autem hic, quod notatu dignum eſt,
              <lb/>
            quodque in aliis etiam nonnullis harum paraboloidum con-
              <lb/>
            tingit, duæ evolutiones in partes contrarias, quarum utra-
              <lb/>
            que à puncto certo A initium capit; </s>
            <s xml:id="echoid-s2650" xml:space="preserve">ita ut evolutione ipſius
              <lb/>
            A R D, in infinitum porro continuatæ, deſcribatur para-
              <lb/>
            boloidis pars infinita A B F; </s>
            <s xml:id="echoid-s2651" xml:space="preserve">evolutione autem totius A R I,
              <lb/>
            ſimiliter in infinitum extenſæ, tantum particula A S. </s>
            <s xml:id="echoid-s2652" xml:space="preserve">Pun-
              <lb/>
            ctum autem A definitur, ſumptâ S P quæ ſit ad latus re-
              <lb/>
            ctum paraboloidis, ſicut unitas ad radicem quadrato-qua-
              <lb/>
            draticam numeri 91125, (is cubus eſt ex 45) applicatâque
              <lb/>
            ordinatim P A. </s>
            <s xml:id="echoid-s2653" xml:space="preserve">Unde porro punctum R, confinium dua-
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            rum curvarum R D, R I, invenitur ſicut cætera omnia </s>
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