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

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            <s xml:id="echoid-s2292" xml:space="preserve">
              <pb o="396" file="0110" n="117" rhead="CHRISTIANI HUGENII"/>
            ſic C E, hoc eſt, ipſa A D ad E D. </s>
            <s xml:id="echoid-s2293" xml:space="preserve">Ergo rectangulum
              <lb/>
            R D A ad rectangulum ſub R D, Q, hoc eſt, A D ad Q
              <lb/>
            ſicut A B ad E D. </s>
            <s xml:id="echoid-s2294" xml:space="preserve">Et permutando & </s>
            <s xml:id="echoid-s2295" xml:space="preserve">invertendo, B A ad
              <lb/>
            A D ut E D ad Q. </s>
            <s xml:id="echoid-s2296" xml:space="preserve">Atqui ut B A ad A D, hoc eſt, C E
              <lb/>
            ita C E ad E D. </s>
            <s xml:id="echoid-s2297" xml:space="preserve">Ergo ut A B ad C E ita C E ad E D, & </s>
            <s xml:id="echoid-s2298" xml:space="preserve">
              <lb/>
            E D ad Q. </s>
            <s xml:id="echoid-s2299" xml:space="preserve">Itaque inter A B & </s>
            <s xml:id="echoid-s2300" xml:space="preserve">Q mediæ proportionales
              <lb/>
            ſunt C E, E D. </s>
            <s xml:id="echoid-s2301" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s2302" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div123" type="section" level="1" n="53">
          <head xml:id="echoid-head82" xml:space="preserve">
            <emph style="sc">Probl</emph>
          . IV.</head>
          <p style="it">
            <s xml:id="echoid-s2303" xml:space="preserve">QUadrato dato & </s>
            <s xml:id="echoid-s2304" xml:space="preserve">uno latere producto, aptare
              <lb/>
            ſub angulo exteriori rectam magnitudine da-
              <lb/>
            tam quæ ad angulum oppoſitum pertineat.</s>
            <s xml:id="echoid-s2305" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2306" xml:space="preserve">Eſto quadratum B A cujus productum ſit latus F A. </s>
            <s xml:id="echoid-s2307" xml:space="preserve">Data
              <lb/>
              <note position="left" xlink:label="note-0110-01" xlink:href="note-0110-01a" xml:space="preserve">TAB. XLI.
                <lb/>
              Fig. 7.</note>
            verò linea K. </s>
            <s xml:id="echoid-s2308" xml:space="preserve">Et oporteat ducere rectam B D C, ita ut
              <lb/>
            pars intercepta D C ſit datæ K æqualis.</s>
            <s xml:id="echoid-s2309" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2310" xml:space="preserve">Quadratis ex K & </s>
            <s xml:id="echoid-s2311" xml:space="preserve">E B ſit æquale quadratum E G; </s>
            <s xml:id="echoid-s2312" xml:space="preserve">& </s>
            <s xml:id="echoid-s2313" xml:space="preserve">
              <lb/>
            ſuper B G diametro deſcribatur ſemicirculus B C G ſecans
              <lb/>
            rectam F A productam in C, & </s>
            <s xml:id="echoid-s2314" xml:space="preserve">ducatur B D C. </s>
            <s xml:id="echoid-s2315" xml:space="preserve">Dico D C
              <lb/>
            æqualem eſſe ipſi K. </s>
            <s xml:id="echoid-s2316" xml:space="preserve">Jungantur enim C G, G D; </s>
            <s xml:id="echoid-s2317" xml:space="preserve">ſitque
              <lb/>
            C H ipſi B G ad angulos rectos.</s>
            <s xml:id="echoid-s2318" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2319" xml:space="preserve">Quia igitur ſimiles ſunt trianguli B E D, C H G, & </s>
            <s xml:id="echoid-s2320" xml:space="preserve">la-
              <lb/>
            tera B E, C H circa angulos rectos inter ſe æqualia, erit
              <lb/>
            & </s>
            <s xml:id="echoid-s2321" xml:space="preserve">latus D B æquale lateri G C, & </s>
            <s xml:id="echoid-s2322" xml:space="preserve">D E ipſi G H. </s>
            <s xml:id="echoid-s2323" xml:space="preserve">Sunt
              <lb/>
            autem quadrata D C, C G, hoc eſt, quadrata D C, C H,
              <lb/>
            & </s>
            <s xml:id="echoid-s2324" xml:space="preserve">H G æqualia quadrato D G , hoc eſt, quadratis G
              <note symbol="*" position="left" xlink:label="note-0110-02" xlink:href="note-0110-02a" xml:space="preserve">47.1. Elem.</note>
            E D. </s>
            <s xml:id="echoid-s2325" xml:space="preserve">Ergo dempto hinc quadrato E D, inde vero quadrato
              <lb/>
            H G; </s>
            <s xml:id="echoid-s2326" xml:space="preserve">erunt duo quadrata D C & </s>
            <s xml:id="echoid-s2327" xml:space="preserve">C H æqualia quadrato
              <lb/>
            E G, hoc eſt, quadratis ex K & </s>
            <s xml:id="echoid-s2328" xml:space="preserve">E B . </s>
            <s xml:id="echoid-s2329" xml:space="preserve">Quadratum
              <note symbol="*" position="left" xlink:label="note-0110-03" xlink:href="note-0110-03a" xml:space="preserve">Ex con-
                <lb/>
              ſtruct.</note>
            E B æquale eſt quadrato C H. </s>
            <s xml:id="echoid-s2330" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s2331" xml:space="preserve">reliquum quadra-
              <lb/>
            tum D C æquabitur K quadrato; </s>
            <s xml:id="echoid-s2332" xml:space="preserve">& </s>
            <s xml:id="echoid-s2333" xml:space="preserve">recta D C ipſi K. </s>
            <s xml:id="echoid-s2334" xml:space="preserve">Quod
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s2335" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2336" xml:space="preserve">Demonſtratio hæc ab ea diverſa eſt quæ apud Pappum A-
              <lb/>
            lex. </s>
            <s xml:id="echoid-s2337" xml:space="preserve">legitur lib 7. </s>
            <s xml:id="echoid-s2338" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s2339" xml:space="preserve">72. </s>
            <s xml:id="echoid-s2340" xml:space="preserve">Conſtructio verò non differt. </s>
            <s xml:id="echoid-s2341" xml:space="preserve">Cæ-
              <lb/>
            terum eandem ad caſum quoque ſequentem pertinere inveni-
              <lb/>
            mus.</s>
            <s xml:id="echoid-s2342" xml:space="preserve"/>
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