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

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          <p>
            <s xml:id="echoid-s2321" xml:space="preserve">
              <pb o="104" file="0152" n="164" rhead="CHRISTIANI HUGENII"/>
            portionalis linea H. </s>
            <s xml:id="echoid-s2322" xml:space="preserve">Erit hæc radius circuli qui ſuperficiei
              <lb/>
              <note position="left" xlink:label="note-0152-01" xlink:href="note-0152-01a" 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">EVOLURIO-</emph>
                <lb/>
                <emph style="sc">NE</emph>
              .</note>
            ſphæroidis propoſiti æqualis ſit.</s>
            <s xml:id="echoid-s2323" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div187" type="section" level="1" n="68">
          <head xml:id="echoid-head92" style="it" xml:space="preserve">Conoidis hyperbolici ſuperficiei curvæ circulum
            <lb/>
          æqualem invenire.</head>
          <p>
            <s xml:id="echoid-s2324" xml:space="preserve">ESto conoides hyperbolicum cujus axis A B, ſectio per
              <lb/>
              <note position="left" xlink:label="note-0152-02" xlink:href="note-0152-02a" xml:space="preserve">TAB. XIV.
                <lb/>
              Fig. 4.</note>
            axem hyperbola C A D, cujus latus tranſverſum E A,
              <lb/>
            centrum F, latus rectum A G.</s>
            <s xml:id="echoid-s2325" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2326" xml:space="preserve">Sumatur in axe recta A H, æqualis dimidio lateri recto
              <lb/>
            A G. </s>
            <s xml:id="echoid-s2327" xml:space="preserve">& </s>
            <s xml:id="echoid-s2328" xml:space="preserve">ut H F ad A F longitudine ita, ſit A F ad F K
              <lb/>
            potentiâ. </s>
            <s xml:id="echoid-s2329" xml:space="preserve">Et intelligatur vertice K alia hyperbola deſcripta
              <lb/>
            K L M, eodem axe & </s>
            <s xml:id="echoid-s2330" xml:space="preserve">centro F cum priore, quæque late-
              <lb/>
            ra rectum & </s>
            <s xml:id="echoid-s2331" xml:space="preserve">transverſum illi reciproce proportionalia habeat.
              <lb/>
            </s>
            <s xml:id="echoid-s2332" xml:space="preserve">Occurrat autem ipſi producta B C in M, ſitque A L paralle-
              <lb/>
            la B C. </s>
            <s xml:id="echoid-s2333" xml:space="preserve">Erit jam ſicut ſpatium A L M B, tribus rectis lineis
              <lb/>
            & </s>
            <s xml:id="echoid-s2334" xml:space="preserve">curva hyperbolica comprehenſum, ad dimidium quadra-
              <lb/>
            tum ex B C, ita ſuperficies conoidis curva ad circulum ba-
              <lb/>
            ſeos ſuæ, cujus diameter C D. </s>
            <s xml:id="echoid-s2335" xml:space="preserve">Unde conſtructio reliqua
              <lb/>
            facile abſolvetur, poſitâ hyperbolæ quadraturâ.</s>
            <s xml:id="echoid-s2336" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2337" xml:space="preserve">Quum igitur conoidis parabolici ſuperficies ad circulum
              <lb/>
            redigatur, æque ac ſuperficies ſphæræ, ex notis geometriæ
              <lb/>
            regulis; </s>
            <s xml:id="echoid-s2338" xml:space="preserve">in ſuperficie ſphæroidis oblongi, ut idem fiat, po-
              <lb/>
            nendum eſt arcus circumferentiæ longitudinem æquari poſſe
              <lb/>
            lineæ rectæ. </s>
            <s xml:id="echoid-s2339" xml:space="preserve">Ad ſphæroidis vero lati, itemque ad conoidis
              <lb/>
            hyperbolici ſuperficiem eadem ratione complanandam, hy-
              <lb/>
            perbolæ quadratura requiritur. </s>
            <s xml:id="echoid-s2340" xml:space="preserve">Nam parabolicæ lineæ lon-
              <lb/>
            gitudo, quam in ſphæroide hoc adhibuimus, pendet à qua-
              <lb/>
            dratura hyperbolæ, ut mox oſtendemus.</s>
            <s xml:id="echoid-s2341" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2342" xml:space="preserve">Verum, quod non indignum animadverſione videtur, in-
              <lb/>
            venimus absque ulla hyperbolicæ quadraturæ ſuppoſitione,
              <lb/>
            circulum æqualem conſtrui ſuperficiei utrique ſimul, ſphæ-
              <lb/>
            roidis lati & </s>
            <s xml:id="echoid-s2343" xml:space="preserve">conoidis hyperbolici.</s>
            <s xml:id="echoid-s2344" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2345" xml:space="preserve">Dato enim ſphæroide quovis lato, poſſe inveniri conoi-
              <lb/>
            des hyperbolicum, vel contra, dato conoide hyperbolico,
              <lb/>
            poſſe inveniri ſphæroides latum ejusmodi, ut utriusque </s>
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