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

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            <s xml:id="echoid-s291" xml:space="preserve">
              <pb o="324" file="0024" n="24" rhead="THEOR. DE QUADRAT."/>
            portione punctum L. </s>
            <s xml:id="echoid-s292" xml:space="preserve">Dico portionem ad inſcriptum trian-
              <lb/>
            gulum A B C eam habere rationem, quam duæ tertiæ to-
              <lb/>
            tius E D ad F L.</s>
            <s xml:id="echoid-s293" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s294" xml:space="preserve">Conſtituatur enim ad diametrum, ut in præcedentibus,
              <lb/>
            triangulus K F H; </s>
            <s xml:id="echoid-s295" xml:space="preserve">ſcilicet ut quadratum F G æquetur re-
              <lb/>
            ctangulo E D B, & </s>
            <s xml:id="echoid-s296" xml:space="preserve">ut baſis K H ſit baſi A C æqualis & </s>
            <s xml:id="echoid-s297" xml:space="preserve">
              <lb/>
            parallela: </s>
            <s xml:id="echoid-s298" xml:space="preserve">ejuſque trianguli ſit centrum gravitatis M, ſum-
              <lb/>
            ptâ nimirum F M æquali duabus tertiis lineæ F G .</s>
            <s xml:id="echoid-s299" xml:space="preserve"/>
          </p>
          <note symbol="1" position="left" xml:space="preserve">14. lib. 1.
            <lb/>
          Arch. de
            <lb/>
          Æquip.</note>
          <p>
            <s xml:id="echoid-s300" xml:space="preserve">Eſt itaque triangulus K F H ad A B C triangulum, ut
              <lb/>
            F G ad B D: </s>
            <s xml:id="echoid-s301" xml:space="preserve">verùm ut F G ad B D, ita eſt E D ad F G,
              <lb/>
            quia quadratum F G æquale eſt rectangulo E D B; </s>
            <s xml:id="echoid-s302" xml:space="preserve">& </s>
            <s xml:id="echoid-s303" xml:space="preserve">ut
              <lb/>
            E D ad F G, ita ſunt duæ tertiæ E D ad duas tertias F G,
              <lb/>
            id eſt F M; </s>
            <s xml:id="echoid-s304" xml:space="preserve">ergo triangulus K F H ad triangulum A B C,
              <lb/>
            ut duæ tertiæ E D ad F M. </s>
            <s xml:id="echoid-s305" xml:space="preserve">Eſt autem portio hyperboles
              <lb/>
            ad triangulum K F H, ut F M ad F L , quoniam
              <note symbol="2" position="left" xlink:label="note-0024-02" xlink:href="note-0024-02a" xml:space="preserve">7. lib. 1.
                <lb/>
              Archim. de
                <lb/>
              Æquipond.</note>
            librium portionis & </s>
            <s xml:id="echoid-s306" xml:space="preserve">trianguli K F H eſt in puncto F , &</s>
            <s xml:id="echoid-s307" xml:space="preserve"> centra gravitatis ſingulorum puncta L & </s>
            <s xml:id="echoid-s308" xml:space="preserve">M; </s>
            <s xml:id="echoid-s309" xml:space="preserve">ex æquali igi-
              <lb/>
              <note symbol="3" position="left" xlink:label="note-0024-03" xlink:href="note-0024-03a" xml:space="preserve">Thcor. 5. h.</note>
            tur in proportione perturbata, erit portio ad triangulum
              <lb/>
            A B C, ut duæ tertiæ lineæ E D ad F L : </s>
            <s xml:id="echoid-s310" xml:space="preserve">quod erat
              <note symbol="4" position="left" xlink:label="note-0024-04" xlink:href="note-0024-04a" xml:space="preserve">23. lib. 5.
                <lb/>
              Elem.</note>
            monſtrandum.</s>
            <s xml:id="echoid-s311" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div31" type="section" level="1" n="16">
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            <emph style="sc">Theorema</emph>
          VII.</head>
          <p style="it">
            <s xml:id="echoid-s312" xml:space="preserve">OMnis ellipſis vel circuli portio ad triangulum
              <lb/>
            inſcriptum, eandem cum ipſa baſin habentem
              <lb/>
            eandemque altitudinem, hanc habet rationem; </s>
            <s xml:id="echoid-s313" xml:space="preserve">quam
              <lb/>
            ſubſeſquialtera diametri portionis reliquæ, ad eam
              <lb/>
            quæ ex figuræ centro ducitur ad centrum gravitatis
              <lb/>
            in portione.</s>
            <s xml:id="echoid-s314" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s315" xml:space="preserve">Eſto ellipſis vel circuli portio primùm dimidiâ figurâ non
              <lb/>
              <note position="left" xlink:label="note-0024-05" xlink:href="note-0024-05a" xml:space="preserve">TAB. XXXV.
                <lb/>
              Fig. 4. 5.</note>
            major, & </s>
            <s xml:id="echoid-s316" xml:space="preserve">inſcriptus ei triangulus A B C, eandem cum
              <lb/>
            portione baſin habens, eandemque altitudinem; </s>
            <s xml:id="echoid-s317" xml:space="preserve">diameter au-
              <lb/>
            tem portionis ſit B D, quæ producatur, & </s>
            <s xml:id="echoid-s318" xml:space="preserve">manifeſtum eſt
              <lb/>
            quod tranſibit per centrum figuræ; </s>
            <s xml:id="echoid-s319" xml:space="preserve">ſit hoc F, & </s>
            <s xml:id="echoid-s320" xml:space="preserve">diameter
              <lb/>
            portionis reliquæ D E. </s>
            <s xml:id="echoid-s321" xml:space="preserve">Et ponatur centrum gravitatis in </s>
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