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

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        <div xml:id="echoid-div112" type="section" level="1" n="49">
          <pb o="393" file="0107" n="114" rhead="ILLUST. QUORUND. PROB. CONSTRUCT."/>
        </div>
        <div xml:id="echoid-div115" type="section" level="1" n="50">
          <head xml:id="echoid-head78" xml:space="preserve">
            <emph style="sc">Probl</emph>
          . III.</head>
          <head xml:id="echoid-head79" style="it" xml:space="preserve">Datis duabus rectis duas medias propor-
            <lb/>
          tionales invenire.</head>
          <p>
            <s xml:id="echoid-s2172" xml:space="preserve">VEterum Geometrarum ad hoc Problema conſtructiones
              <lb/>
            complures retulit Eutocius ad lib. </s>
            <s xml:id="echoid-s2173" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2174" xml:space="preserve">Archimedis de
              <lb/>
            Sphæra & </s>
            <s xml:id="echoid-s2175" xml:space="preserve">Cylindro, at non omnes inventione diverſas, uti
              <lb/>
            recte quoque ipſe animadvertit. </s>
            <s xml:id="echoid-s2176" xml:space="preserve">Heronis enim inventionem
              <lb/>
            ſecuti videntur Apollonius & </s>
            <s xml:id="echoid-s2177" xml:space="preserve">Philo Byzantius: </s>
            <s xml:id="echoid-s2178" xml:space="preserve">quanquam
              <lb/>
            Heronem Apollonio ætate poſteriorem nonnulli exiſtiment.
              <lb/>
            </s>
            <s xml:id="echoid-s2179" xml:space="preserve">Dioclis modum Pappus & </s>
            <s xml:id="echoid-s2180" xml:space="preserve">Sporus. </s>
            <s xml:id="echoid-s2181" xml:space="preserve">Nicomedea autem con-
              <lb/>
            ſtructio præ cæteris ſubtilis ibidem extat, quam Fr. </s>
            <s xml:id="echoid-s2182" xml:space="preserve">Viëta
              <lb/>
            paulò aliter concinnatam ſuo Geometriæ ſupplemento inſe-
              <lb/>
            ruit. </s>
            <s xml:id="echoid-s2183" xml:space="preserve">R. </s>
            <s xml:id="echoid-s2184" xml:space="preserve">Carteſii egregia eſt & </s>
            <s xml:id="echoid-s2185" xml:space="preserve">nova per paraboles & </s>
            <s xml:id="echoid-s2186" xml:space="preserve">cir-
              <lb/>
            cumferentiæ interſectionem, cujus demonſtratio legitur in
              <lb/>
            libris Harmonicôn M. </s>
            <s xml:id="echoid-s2187" xml:space="preserve">Merſenni. </s>
            <s xml:id="echoid-s2188" xml:space="preserve">Noſtræ autem ſequen-
              <lb/>
            tes.</s>
            <s xml:id="echoid-s2189" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2190" xml:space="preserve">Sit datarum linearum major A C, quæ bifariam ſecetur
              <lb/>
              <note position="right" xlink:label="note-0107-01" xlink:href="note-0107-01a" xml:space="preserve">TAB. XLI.
                <lb/>
              Fig. 4.</note>
            in E. </s>
            <s xml:id="echoid-s2191" xml:space="preserve">Minor autem ſit A B, quæ ſic conſtituatur ut trian-
              <lb/>
            gulus E A B habeat crura æqualia A E, E B. </s>
            <s xml:id="echoid-s2192" xml:space="preserve">Et perficia-
              <lb/>
            tur parallelogrammum C A B D. </s>
            <s xml:id="echoid-s2193" xml:space="preserve">Et producantur A C,
              <lb/>
            A B. </s>
            <s xml:id="echoid-s2194" xml:space="preserve">Porro applicetur regula ad punctum D, & </s>
            <s xml:id="echoid-s2195" xml:space="preserve">moveatur
              <lb/>
            quousque poſitionem habeat G F, abſcindens nimirum E F
              <lb/>
            æqualem rectæ E G; </s>
            <s xml:id="echoid-s2196" xml:space="preserve">(Hoc autem vel ſæpius tentando aſſe-
              <lb/>
            quemur, vel deſcriptâ hyperbole, uti poſtea oſtendetur)
              <lb/>
            Dico inter A C, A B medias duas inventas eſſe B G,
              <lb/>
            C F.</s>
            <s xml:id="echoid-s2197" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2198" xml:space="preserve">Sit enim E K ipſi A B ad angulos rectos. </s>
            <s xml:id="echoid-s2199" xml:space="preserve">Quia igitur
              <lb/>
            B E æqualis E A, dividetur A B in K bifariam: </s>
            <s xml:id="echoid-s2200" xml:space="preserve">adjecta au-
              <lb/>
            tem eſt linea B G. </s>
            <s xml:id="echoid-s2201" xml:space="preserve">Ergo rectangulum A G B cum quadrato
              <lb/>
            ex K B, æquabitur quadrato K G. </s>
            <s xml:id="echoid-s2202" xml:space="preserve">Et addito utrimque qua-
              <lb/>
            drato K E, erit rectangulum A G B unà cum quadratis
              <lb/>
            B K, K E, hoc eſt unà cum quadrato B E, æquale qua-
              <lb/>
            drato E G. </s>
            <s xml:id="echoid-s2203" xml:space="preserve">Similiter quia A C bifariam dividitur in E, & </s>
            <s xml:id="echoid-s2204" xml:space="preserve"/>
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