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

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          <pb o="318" file="0018" n="18" rhead="THEOR. DE QUADRAT."/>
          <p>
            <s xml:id="echoid-s111" xml:space="preserve">Quoniam igitur F H, L K ſunt diametro B D parallelæ,
              <lb/>
            ſuntque D F, D L æquales, oportet lineam H K, quæ duas
              <lb/>
            F H, L K conjungit, à diametro B D bifariam ſecari; </s>
            <s xml:id="echoid-s112" xml:space="preserve">qua-
              <lb/>
            re eadem H K parallela erit baſi A C , & </s>
            <s xml:id="echoid-s113" xml:space="preserve">E H K G
              <note symbol="1" position="left" xlink:label="note-0018-01" xlink:href="note-0018-01a" xml:space="preserve">5. lib. 2.
                <lb/>
              con.</note>
            linea. </s>
            <s xml:id="echoid-s114" xml:space="preserve">Itaque E C parallelogrammum eſt; </s>
            <s xml:id="echoid-s115" xml:space="preserve">cujus oppoſita la-
              <lb/>
            tera quum bifariam dividat diameter B D, erit in ea paral-
              <lb/>
            lelogrammi centrum gravitatis . </s>
            <s xml:id="echoid-s116" xml:space="preserve">Eâdem ratione
              <note symbol="2" position="left" xlink:label="note-0018-02" xlink:href="note-0018-02a" xml:space="preserve">9. lib. 1.
                <lb/>
              Arch. de
                <lb/>
              Æquipond.</note>
            gramma erunt H M, N O, P Q, & </s>
            <s xml:id="echoid-s117" xml:space="preserve">ſingulorum centra gra-
              <lb/>
            vitatis in linea B D. </s>
            <s xml:id="echoid-s118" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s119" xml:space="preserve">figuræ ex omnibus dictis pa-
              <lb/>
            rallelogrammis compoſitæ centrum gravitatis in eadem B D
              <lb/>
            reperiri neceſſe eſt. </s>
            <s xml:id="echoid-s120" xml:space="preserve">Iſta autem figura eadem eſt quæ portio-
              <lb/>
            ni ordinatè fuerat circumſcripta. </s>
            <s xml:id="echoid-s121" xml:space="preserve">Ergo figuræ portioni ordi-
              <lb/>
            natè circumſcriptæ centrum gravitatis conſtat eſſe in B D por-
              <lb/>
            tionis diametro. </s>
            <s xml:id="echoid-s122" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s123" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div17" type="section" level="1" n="12">
          <head xml:id="echoid-head24" xml:space="preserve">
            <emph style="sc">Theorema</emph>
          IV.</head>
          <p style="it">
            <s xml:id="echoid-s124" xml:space="preserve">POrtionis hyperboles, ellipſis & </s>
            <s xml:id="echoid-s125" xml:space="preserve">circuli, centrum
              <lb/>
            gravitatis eſt in portionis diametro.</s>
            <s xml:id="echoid-s126" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s127" xml:space="preserve">Eſto portio hyperboles, vel ellipſis vel circuli dimidiâ pri-
              <lb/>
              <note position="left" xlink:label="note-0018-03" xlink:href="note-0018-03a" xml:space="preserve">TAB. XXXIV.
                <lb/>
              Fig. 4.</note>
            mum figurâ non major, A B C; </s>
            <s xml:id="echoid-s128" xml:space="preserve">diameter ejus B D. </s>
            <s xml:id="echoid-s129" xml:space="preserve">O-
              <lb/>
            ſtendendum eſt, in B D reperiri portionis A B C gravitatis
              <lb/>
            centrum.</s>
            <s xml:id="echoid-s130" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s131" xml:space="preserve">Si enim fieri poteſt, ſit extra diametrum in E, & </s>
            <s xml:id="echoid-s132" xml:space="preserve">ducatur
              <lb/>
            E H diametro B D parallela. </s>
            <s xml:id="echoid-s133" xml:space="preserve">Dividendo itaque D C conti-
              <lb/>
            nuè bifariam, relinquetur tandem linea minor quam D H;
              <lb/>
            </s>
            <s xml:id="echoid-s134" xml:space="preserve">ſit ea D F, & </s>
            <s xml:id="echoid-s135" xml:space="preserve">circumſcribatur portioni figura ordinatè ex
              <lb/>
            parallelogrammis quorum baſes æquales ſint lineæ D F, & </s>
            <s xml:id="echoid-s136" xml:space="preserve">
              <lb/>
            jungantur B A, B C. </s>
            <s xml:id="echoid-s137" xml:space="preserve">Figuræ itaque portioni circumſcri-
              <lb/>
            ptæ centrum gravitatis eſt in B D portionis diametro. </s>
            <s xml:id="echoid-s138" xml:space="preserve">Sit hoc
              <lb/>
            K, & </s>
            <s xml:id="echoid-s139" xml:space="preserve">jungatur E K, producaturque, & </s>
            <s xml:id="echoid-s140" xml:space="preserve">occurrat ei A L
              <lb/>
            parallela B D. </s>
            <s xml:id="echoid-s141" xml:space="preserve">Quia autem portio major eſt triangulo A B C,
              <lb/>
            & </s>
            <s xml:id="echoid-s142" xml:space="preserve">exceſſus quo figura circumſcripta portionem ſuperat, mi-
              <lb/>
            nor parallelogrammo B F, uti ſupra demonſtratum fuit ;</s>
            <s xml:id="echoid-s143" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0018-04" xlink:href="note-0018-04a" xml:space="preserve">Theor. 1.</note>
            erit major ratio portionis A B C ad dictum exceſſum, quàm
              <lb/>
            trianguli A B C ad B F parallelogrammum, id eſt </s>
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