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

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          <p>
            <s xml:id="echoid-s2243" xml:space="preserve">
              <pb o="395" file="0109" n="116" rhead="ILLUST. QUORUND. PROB. CONSTRUCT."/>
            eſt, diametro A C vel L K; </s>
            <s xml:id="echoid-s2244" xml:space="preserve">& </s>
            <s xml:id="echoid-s2245" xml:space="preserve">ablatâ communi L O, re-
              <lb/>
            linquentur æquales L G, O K. </s>
            <s xml:id="echoid-s2246" xml:space="preserve">Eſt autem rectangulum
              <lb/>
            K G L æquale rectangulo A G B. </s>
            <s xml:id="echoid-s2247" xml:space="preserve">Ergo ut K G ad G A
              <lb/>
            ita B G ad G L. </s>
            <s xml:id="echoid-s2248" xml:space="preserve">Sed ut K G ad G A ita eſt O G ad G B
              <lb/>
            & </s>
            <s xml:id="echoid-s2249" xml:space="preserve">ita reliqua O K, hoc eſt, L G ad B A. </s>
            <s xml:id="echoid-s2250" xml:space="preserve">Ergo ut O G,
              <lb/>
            hoc eſt, A C ad G B ita B G ad G L & </s>
            <s xml:id="echoid-s2251" xml:space="preserve">G L ad A B.
              <lb/>
            </s>
            <s xml:id="echoid-s2252" xml:space="preserve">Quod erat demonſtr. </s>
            <s xml:id="echoid-s2253" xml:space="preserve">Hujus autem conſtructionis inventio
              <lb/>
            eandem cum præcedenti originem habet.</s>
            <s xml:id="echoid-s2254" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div120" type="section" level="1" n="52">
          <head xml:id="echoid-head81" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s2255" xml:space="preserve">SInt datæ A B & </s>
            <s xml:id="echoid-s2256" xml:space="preserve">Q quibus duas medias proportionales in-
              <lb/>
              <note position="right" xlink:label="note-0109-01" xlink:href="note-0109-01a" xml:space="preserve">TAB. XLI.
                <lb/>
              Fig. 6.</note>
            venire opus ſit; </s>
            <s xml:id="echoid-s2257" xml:space="preserve">A B autem quam Q major.</s>
            <s xml:id="echoid-s2258" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2259" xml:space="preserve">Dimidiæ Q ſumatur æqualis A F, & </s>
            <s xml:id="echoid-s2260" xml:space="preserve">productâ A B u-
              <lb/>
            trimque, ſit ipſi æqualis B R. </s>
            <s xml:id="echoid-s2261" xml:space="preserve">Erigatur autem ad A B perpen-
              <lb/>
            dicularis F C, & </s>
            <s xml:id="echoid-s2262" xml:space="preserve">ipſi R A æqualis ponatur R C: </s>
            <s xml:id="echoid-s2263" xml:space="preserve">& </s>
            <s xml:id="echoid-s2264" xml:space="preserve">junga-
              <lb/>
            tur B C, & </s>
            <s xml:id="echoid-s2265" xml:space="preserve">huic parallela ducatur A E. </s>
            <s xml:id="echoid-s2266" xml:space="preserve">Denique applica-
              <lb/>
            tâ regulâ ad punctum C, moveatur ea quouſque poſitionem
              <lb/>
            habeat C D, faciens C E æqualem A D. </s>
            <s xml:id="echoid-s2267" xml:space="preserve">Dico inter A B & </s>
            <s xml:id="echoid-s2268" xml:space="preserve">
              <lb/>
            Q duas medias eſſe C E, E D.</s>
            <s xml:id="echoid-s2269" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2270" xml:space="preserve">Jungatur enim C A. </s>
            <s xml:id="echoid-s2271" xml:space="preserve">Igitur quia æquales ſunt R A, R C
              <lb/>
            & </s>
            <s xml:id="echoid-s2272" xml:space="preserve">angulus C F A rectus, erit R A ad A C ut A C ad du-
              <lb/>
            plam A F, hoc eſt, Q: </s>
            <s xml:id="echoid-s2273" xml:space="preserve">ac proinde quadratum A C æqua-
              <lb/>
            le rectangulo ſub R A & </s>
            <s xml:id="echoid-s2274" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s2275" xml:space="preserve">Quadratum autem A C cum
              <lb/>
            quadrato A D & </s>
            <s xml:id="echoid-s2276" xml:space="preserve">duplo rectangulo D A F, hoc eſt, ſub
              <lb/>
            D A & </s>
            <s xml:id="echoid-s2277" xml:space="preserve">Q contento, æquatur quadrato D C. </s>
            <s xml:id="echoid-s2278" xml:space="preserve">Igitur
              <note symbol="*" position="right" xlink:label="note-0109-02" xlink:href="note-0109-02a" xml:space="preserve">12. 2. E-
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              lem.</note>
            dratum D C æquabitur quadrato D A unà cum rectangulis
              <lb/>
            ſub D A, Q, & </s>
            <s xml:id="echoid-s2279" xml:space="preserve">ſub R A, Q, hoc eſt, unà cum rectan-
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            gulo ſub D R & </s>
            <s xml:id="echoid-s2280" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s2281" xml:space="preserve">Quadratum autem D B æquale rectan-
              <lb/>
            gulo R D A & </s>
            <s xml:id="echoid-s2282" xml:space="preserve">quadrato A B . </s>
            <s xml:id="echoid-s2283" xml:space="preserve">Igitur ut
              <note symbol="*" position="right" xlink:label="note-0109-03" xlink:href="note-0109-03a" xml:space="preserve">6.2. Elem.</note>
            D B ad quadratum D C, hoc eſt, ut quadr. </s>
            <s xml:id="echoid-s2284" xml:space="preserve">A B ad quadr.
              <lb/>
            </s>
            <s xml:id="echoid-s2285" xml:space="preserve">A D, (eſt enim ut D B ad D C ſic A B ad E C ſive A D)
              <lb/>
            ita erit rectangulum R D A cum quadrato A B ad rectan-
              <lb/>
            gulum ſub R D, Q, cum quadrato A D. </s>
            <s xml:id="echoid-s2286" xml:space="preserve">Quamobrem & </s>
            <s xml:id="echoid-s2287" xml:space="preserve">
              <lb/>
            rectangulum R D A ad rectangulum ſub R D, Q, ſicut quadr. </s>
            <s xml:id="echoid-s2288" xml:space="preserve">
              <lb/>
            A B ad quadr. </s>
            <s xml:id="echoid-s2289" xml:space="preserve">A D . </s>
            <s xml:id="echoid-s2290" xml:space="preserve">Eſt autem ut quadratum A B
              <note symbol="*" position="right" xlink:label="note-0109-04" xlink:href="note-0109-04a" xml:space="preserve">19. 5. E-
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              lem.</note>
            quadr. </s>
            <s xml:id="echoid-s2291" xml:space="preserve">A D, ita A B ad E D longitudine: </s>
            <s xml:id="echoid-s2292" xml:space="preserve">nam ut B A ad A </s>
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