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

Page concordance

< >
Scan Original
151 94
152 95
153 96
154
155
156
157 97
158 98
159 99
160 100
161 101
162 102
163 103
164 104
165
166
167
168 105
169 106
170
171
172
173 107
174 108
175 109
176 110
177 111
178 112
179
180
< >
page |< < (114) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div198" type="section" level="1" n="71">
          <p>
            <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:
              <lb/>
            </s>
            <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>
                <lb/>
                <emph style="sc">NE.</emph>
              </note>
            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-
              <lb/>
            rur per punctum quodlibet B, in paraboloide ſumptum, re-
              <lb/>
            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-
              <lb/>
            rum curvarum R D, R I, invenitur ſicut cætera omnia </s>
          </p>
        </div>
      </text>
    </echo>
Impressum