Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Table of contents

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[211.] CATALOGUS QUORUNDAM LIBRORUM, Qui apud Janssonios Van der Aa, Bibliopolas Lugduni Batavorum, venales proſtant.
Page: 560
[212.] AVIS AU RELIEUR.
Page: 563
[213.] BERIGT AAN DEN BOEKBINDER.
Page: 563
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        <div xml:id="echoid-div240" type="section" level="1" n="119">
          <p>
            <s xml:id="echoid-s4550" xml:space="preserve">
              <pb o="487" file="0207" n="217" rhead="GEOMET. VARIA."/>
            o x; </s>
            <s xml:id="echoid-s4551" xml:space="preserve">eritque punctum N in hyperbola quæſita, quæ proin-
              <lb/>
            de rurſus data erit.</s>
            <s xml:id="echoid-s4552" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4553" xml:space="preserve">Sumpta enim in caſu primo A B = x ad arbitrium, eique
              <lb/>
              <note position="right" xlink:label="note-0207-01" xlink:href="note-0207-01a" xml:space="preserve">fig. 4.</note>
            applicata B C = y in angulo dato, quæ ad hyperbolam in-
              <lb/>
            ventam terminetur, oſtendendum ſit quod</s>
          </p>
          <p>
            <s xml:id="echoid-s4554" xml:space="preserve">y = l - {nx/z} + √mm - ox + {ppxx.</s>
            <s xml:id="echoid-s4555" xml:space="preserve">/gg} </s>
          </p>
        </div>
        <div xml:id="echoid-div243" type="section" level="1" n="120">
          <head xml:id="echoid-head165" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s4556" xml:space="preserve">Occurrat B C utrinque ſi opus ſit producta, aſymptotis
              <lb/>
            in O & </s>
            <s xml:id="echoid-s4557" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s4558" xml:space="preserve">Ex conſtructione eſt I X vel I Y = {{1/2}og/p},
              <lb/>
            I V = {{1/2}ogg/pp}, Ratio verò data I K ad K L, eadem nempe
              <lb/>
            quæ z ad n. </s>
            <s xml:id="echoid-s4559" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s4560" xml:space="preserve">angulus I K L datus eſt. </s>
            <s xml:id="echoid-s4561" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s4562" xml:space="preserve">ra-
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            tio I K ad I L, quæ ſit ea quæ z ad a. </s>
            <s xml:id="echoid-s4563" xml:space="preserve">Ergo quia ut I K
              <lb/>
            ad I L ita I V ad I M, erit I M = {{1/2}aogg/zpp}. </s>
            <s xml:id="echoid-s4564" xml:space="preserve">Ut autem I M ad
              <lb/>
            IX, hoc eſt ut {{1/2}aogg/zpp} ad {{1/2}go/p}, ſive ut ag ad pz, ita M L,
              <lb/>
            ſive M I minus I L, hoc eſt, {{1/2}aogg}zpp - {ax/z} ad L O vel L Q;
              <lb/>
            </s>
            <s xml:id="echoid-s4565" xml:space="preserve">quæ itaque erit {{1/2}og/p} - {px/g}. </s>
            <s xml:id="echoid-s4566" xml:space="preserve">Porro quia B K = l, & </s>
            <s xml:id="echoid-s4567" xml:space="preserve">L K = {nx/z},
              <lb/>
            erit B L = l - {nx/z}, quà ablatâ à B C=y, fit L C = y - l + {nx/z}. </s>
            <s xml:id="echoid-s4568" xml:space="preserve">
              <lb/>
            Propter hyperbolam verò erit rectangulum Q C O æquale
              <lb/>
            rectangulo Y S X. </s>
            <s xml:id="echoid-s4569" xml:space="preserve">Sed rectangulum Q C O æquale eſt
              <lb/>
            quadrato L O minus quadrato L C, hoc eſt quadrato ab
              <lb/>
            {{1/2}go/p} - {px/g} minus quadrato ab y - l + {nx/z}: </s>
            <s xml:id="echoid-s4570" xml:space="preserve">quorum </s>
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