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

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        <div xml:id="echoid-div123" type="section" level="1" n="53">
          <pb o="397" file="0111" n="118" rhead="ILLUST. QUORUND. PROB. CONSTRUCT."/>
        </div>
        <div xml:id="echoid-div126" type="section" level="1" n="54">
          <head xml:id="echoid-head83" xml:space="preserve">
            <emph style="sc">Probl</emph>
          . V.</head>
          <p style="it">
            <s xml:id="echoid-s2343" xml:space="preserve">DAto quadrato, & </s>
            <s xml:id="echoid-s2344" xml:space="preserve">duobus contiguis lateribus
              <lb/>
            productis, aptare ſub angulo interiori rectam
              <lb/>
            magnitudine datam quæ per angulum oppoſitum
              <lb/>
            tranſeat. </s>
            <s xml:id="echoid-s2345" xml:space="preserve">Oportet autem non minorem eſſe datam
              <lb/>
            quam ſit quadrati diameter dupla.</s>
            <s xml:id="echoid-s2346" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2347" xml:space="preserve">Datum ſit quadratum A B, productaque latera A F, A E.</s>
            <s xml:id="echoid-s2348" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">TAB. XLI.
            <lb/>
          Fig. 8.</note>
          <p>
            <s xml:id="echoid-s2349" xml:space="preserve">Data verò linea K, non minor duplâ A B diametro. </s>
            <s xml:id="echoid-s2350" xml:space="preserve">Et
              <lb/>
            oporteat per angulum B ponere rectam D C ipſi K æqua-
              <lb/>
            lem.</s>
            <s xml:id="echoid-s2351" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2352" xml:space="preserve">Si K æqualis fuerit duplæ A B, conſtructio manifeſta eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s2353" xml:space="preserve">tunc enim per B ducenda eſt quæ ſit ipſi A B ad angulos re-
              <lb/>
            ctos, eaque propoſitum efficiet. </s>
            <s xml:id="echoid-s2354" xml:space="preserve">Cum verò major erit K quam
              <lb/>
            dupla A B, conſtructio iiſdem verbis præcipitur atque in Pro-
              <lb/>
            blemate præcedenti: </s>
            <s xml:id="echoid-s2355" xml:space="preserve">& </s>
            <s xml:id="echoid-s2356" xml:space="preserve">demonſtratio quoque eſt eadem.</s>
            <s xml:id="echoid-s2357" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2358" xml:space="preserve">Quod autem circumferentia B C G ſecabit productam A F
              <lb/>
            hinc manifeſtum eſt. </s>
            <s xml:id="echoid-s2359" xml:space="preserve">Etenim quia K major eſt duplâ diame-
              <lb/>
            tro A B, erit K quadratum majus octo quadratis E B. </s>
            <s xml:id="echoid-s2360" xml:space="preserve">Itaque
              <lb/>
            quadratum E G majus quam quadrata novem ex E B; </s>
            <s xml:id="echoid-s2361" xml:space="preserve">ac pro-
              <lb/>
            inde E G major quam tripla E B. </s>
            <s xml:id="echoid-s2362" xml:space="preserve">Dimidia igitur B G, hoc
              <lb/>
            eſt, radius deſcripti ſemicirculi major quam E B vel B F;
              <lb/>
            </s>
            <s xml:id="echoid-s2363" xml:space="preserve">unde neceſſe eſt rectam A C ſecari à circumferentia B C G.</s>
            <s xml:id="echoid-s2364" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div127" type="section" level="1" n="55">
          <head xml:id="echoid-head84" xml:space="preserve">
            <emph style="sc">Probl.</emph>
          VI.</head>
          <p style="it">
            <s xml:id="echoid-s2365" xml:space="preserve">RHombo dato, & </s>
            <s xml:id="echoid-s2366" xml:space="preserve">uno latere producto, aptare
              <lb/>
            ſub angulo exteriori lineam magnitudine da-
              <lb/>
            tam quæ ad oppoſitum angulum pertineat.</s>
            <s xml:id="echoid-s2367" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2368" xml:space="preserve">Sit datus rhombus A B, cujus productum latus F A. </s>
            <s xml:id="echoid-s2369" xml:space="preserve">Data
              <lb/>
              <note position="right" xlink:label="note-0111-02" xlink:href="note-0111-02a" xml:space="preserve">TAB. XLII.
                <lb/>
              Fig. 1.</note>
            autem linea K. </s>
            <s xml:id="echoid-s2370" xml:space="preserve">Et oporteat ducere rectam B D C, ita ut
              <lb/>
            pars intercepta D C ſit ipſi K æqualis.</s>
            <s xml:id="echoid-s2371" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2372" xml:space="preserve">Ducatur diameter A B, & </s>
            <s xml:id="echoid-s2373" xml:space="preserve">latus B E producatur; </s>
            <s xml:id="echoid-s2374" xml:space="preserve">& </s>
            <s xml:id="echoid-s2375" xml:space="preserve">qua-
              <lb/>
            dratis ex K & </s>
            <s xml:id="echoid-s2376" xml:space="preserve">A B ſit æquale quadratum A G. </s>
            <s xml:id="echoid-s2377" xml:space="preserve">Et ſuper B </s>
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