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

Page concordance

< >
Scan Original
241
242 155
243 156
244
245
246
247 157
248 158
249 159
250 160
251
252
253
254 161
255 162
256 163
257 164
258
259
260
261 165
262 166
263
264
265
266 167
267 168
268 169
269 170
270
< >
page |< < (116) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div198" type="section" level="1" n="71">
          <pb o="116" file="0172" n="188" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s2679" xml:space="preserve">Præter haſce autem paraboloides lineas, alias item inve-
              <lb/>
              <note position="left" xlink:label="note-0172-01" xlink:href="note-0172-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
                <lb/>
                <emph style="sc">RUM CUR-</emph>
                <lb/>
                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO</emph>
              -
                <lb/>
                <emph style="sc">NE</emph>
              .</note>
            nimus, à quibus, non abſimili conſtructione, deducuntur
              <lb/>
            curvæ rectis comparabiles. </s>
            <s xml:id="echoid-s2680" xml:space="preserve">Aſſimilantur autem hyperbolis,
              <lb/>
            eo quod aſymptotos ſuas habent, ſed tantum angulum re-
              <lb/>
            ctum conſtituentes. </s>
            <s xml:id="echoid-s2681" xml:space="preserve">Et harum primam quidem ſtatuimus hy-
              <lb/>
            perbolam ipſam, quæ eſt è coni ſectione.</s>
            <s xml:id="echoid-s2682" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2683" xml:space="preserve">Reliquarum vero naturam ut explicemus; </s>
            <s xml:id="echoid-s2684" xml:space="preserve">ſunto P S, S K,
              <lb/>
              <note position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">TAB. XVII.
                <lb/>
              Fig. 3.</note>
            aſymptoti curvæ A B, rectum angulum comprehendentes,
              <lb/>
            & </s>
            <s xml:id="echoid-s2685" xml:space="preserve">à curvæ puncto quolibet B ducatur B K parallela P S,
              <lb/>
            ſitque S K = x; </s>
            <s xml:id="echoid-s2686" xml:space="preserve">K B = y. </s>
            <s xml:id="echoid-s2687" xml:space="preserve">Si igitur hyperbola ſit A B,
              <lb/>
            ſcimus rectangulum linearum S K, K B, hoc eſt, rectan-
              <lb/>
            gulum x y ſemper eidem quadrato æquale eſſe, quod voce-
              <lb/>
            tur a a.</s>
            <s xml:id="echoid-s2688" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2689" xml:space="preserve">Proxima vero hyperboloidum erit, in quaſolidum ex qua-
              <lb/>
            drato lineæ S K, in altitudinem K B ductum, hoc eſt, ſo-
              <lb/>
            lidum x x y, cubo certo æquabitur, qui vocetur a
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s2690" xml:space="preserve">Atque
              <lb/>
            ita innumeræ aliæ hujus generis hyperboloides exiſtunt, qua-
              <lb/>
            rum proprietatem ſequens tabella fingulis æquationibus ex-
              <lb/>
            hibet, ſimulque rationem conſtruendi curvam D C, cujus
              <lb/>
            evolutione quæque generetur.</s>
            <s xml:id="echoid-s2691" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          # x y = a
            <emph style="super">2</emph>
          # # {1/2} B M + {1/2} B Z
            <lb/>
          # x
            <emph style="super">2</emph>
          y = a
            <emph style="super">3</emph>
          # # {2/3} B M + {1/3} B Z
            <lb/>
          Si # x y
            <emph style="super">2</emph>
          = a
            <emph style="super">3</emph>
          # Erit # {1/3} B M + {2/3} B Z # = B D
            <lb/>
          # x
            <emph style="super">3</emph>
          y = a
            <emph style="super">4</emph>
          # # {3/4} B M + {1/4} B Z
            <lb/>
          # x y
            <emph style="super">3</emph>
          = a
            <emph style="super">4</emph>
          # # {1/4} B M + {3/4} B Z
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2692" xml:space="preserve">Recta D B M Z curvam A B, ut antea quoque, ſecat
              <lb/>
            ad angulos rectos, occurritque aſymptotis S K, S P, in M
              <lb/>
            & </s>
            <s xml:id="echoid-s2693" xml:space="preserve">Z. </s>
            <s xml:id="echoid-s2694" xml:space="preserve">Si igitur exempli gratia hyperbola fuerit A B, cujus
              <lb/>
            æquatio eſt x y = a
              <emph style="super">2</emph>
            , ſumetur B D = {1/2} B M + {1/2} B Z,
              <lb/>
            quemadmodum tabella præcipit. </s>
            <s xml:id="echoid-s2695" xml:space="preserve">Eritque punctum Din cur-
              <lb/>
            va D C quæſita, cujus alia quotlibet puncta ſic inveniri po-
              <lb/>
            terunt, & </s>
            <s xml:id="echoid-s2696" xml:space="preserve">portio ejus quælibet rectæ lineæ adæquari. </s>
            <s xml:id="echoid-s2697" xml:space="preserve">Et
              <lb/>
            hæc quidem eadem illa eſt curva, cujus relationem ad axem
              <lb/>
            hyperbolæ ſuperius æquatione expreſſimus. </s>
            <s xml:id="echoid-s2698" xml:space="preserve">Conſtructio au-
              <lb/>
            tem tabellæ hujus plane eadem eſt quæ ſuperioris.</s>
            <s xml:id="echoid-s2699" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2700" xml:space="preserve">Cæterum, quoniam tum ad harum curvarum, tum ad </s>
          </p>
        </div>
      </text>
    </echo>
Impressum