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

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              <pb o="380" file="0092" n="98" rhead="CHRISTIANI HUGENII"/>
            M L rectangulo contento lineis B L, S P: </s>
            <s xml:id="echoid-s1780" xml:space="preserve">rectangulum au-
              <lb/>
            tem B L P majus eo quod ſub B L, S P continetur: </s>
            <s xml:id="echoid-s1781" xml:space="preserve">erit
              <lb/>
            quadratum N L majus quadrato M L, & </s>
            <s xml:id="echoid-s1782" xml:space="preserve">N L linea major
              <lb/>
            quam M L. </s>
            <s xml:id="echoid-s1783" xml:space="preserve">Idem autem continget ubicunque inter B & </s>
            <s xml:id="echoid-s1784" xml:space="preserve">S
              <lb/>
            aliqua ordinatim applicabitur. </s>
            <s xml:id="echoid-s1785" xml:space="preserve">Igitur partem circumferentiæ
              <lb/>
            B F totam extra parabolam ferri neceſſe eſt, eâdemque ra-
              <lb/>
            tione partem B G. </s>
            <s xml:id="echoid-s1786" xml:space="preserve">Rurſus quia rectangulum B D P æquale
              <lb/>
            eſt quadrato D A; </s>
            <s xml:id="echoid-s1787" xml:space="preserve">rectangulum verò ſub B D, S P conten-
              <lb/>
            tum quadrato D H; </s>
            <s xml:id="echoid-s1788" xml:space="preserve">erit H D major quam A D potentiâ,
              <lb/>
            ideoque & </s>
            <s xml:id="echoid-s1789" xml:space="preserve">longitudine. </s>
            <s xml:id="echoid-s1790" xml:space="preserve">Idemque eveniet ubicunque inter
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            S, D, ordinatim aliqua applicabitur. </s>
            <s xml:id="echoid-s1791" xml:space="preserve">Quare partes circum-
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            ferentiæ F A, itemque G C intra parabolam cadent. </s>
            <s xml:id="echoid-s1792" xml:space="preserve">Fiunt
              <lb/>
            igitur ſpatia quædam F N B M, & </s>
            <s xml:id="echoid-s1793" xml:space="preserve">B Q G, itemque alia
              <lb/>
            H F A, G C K. </s>
            <s xml:id="echoid-s1794" xml:space="preserve">Quorum hæc cum tota ſint infra lineam
              <lb/>
            F G, etiam centrum commune gravitatis eorum infra eandem
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            erit. </s>
            <s xml:id="echoid-s1795" xml:space="preserve">At parabolicæ portionis H B K centrum grav eſt in
              <lb/>
            ipſa F G, nimirum S punctum . </s>
            <s xml:id="echoid-s1796" xml:space="preserve">Ergo partis
              <note symbol="*" position="left" xlink:label="note-0092-01" xlink:href="note-0092-01a" xml:space="preserve">8. lib. 2.
                <lb/>
              Archim. de
                <lb/>
              Æquipond.</note>
            A F M B Q G C centrum grav. </s>
            <s xml:id="echoid-s1797" xml:space="preserve">erit ſupra rectam F G.
              <lb/>
            </s>
            <s xml:id="echoid-s1798" xml:space="preserve">Sed ſupra hanc ſitum quoque apparet centrum grav. </s>
            <s xml:id="echoid-s1799" xml:space="preserve">ſpatio-
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            rum F M B N, B Q G, quum tota ſint ſupra ipſam
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            F G. </s>
            <s xml:id="echoid-s1800" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1801" xml:space="preserve">ſpatii ex hiſce duobus & </s>
            <s xml:id="echoid-s1802" xml:space="preserve">A F M B Q G C
              <lb/>
            compoſiti, hoc eſt, portionis circuli A B C centrum grav. </s>
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              <lb/>
            ſupra lineam F G reperietur: </s>
            <s xml:id="echoid-s1804" xml:space="preserve">quumque ſit in B D diametro,
              <lb/>
            minus aberit à vertice B quam punctum S. </s>
            <s xml:id="echoid-s1805" xml:space="preserve">Quod erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s1806" xml:space="preserve"/>
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        <div xml:id="echoid-div95" type="section" level="1" n="44">
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            <emph style="sc">Theor</emph>
          . XV.
            <emph style="sc">Propos</emph>
          . XVIII.</head>
          <p style="it">
            <s xml:id="echoid-s1807" xml:space="preserve">CIrculi portio ſemicirculo minor ad inſcriptum
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            triangulum maximum majorem rationem habet
              <lb/>
            quam ſeſquitertiam, minorem vero quam diameter
              <lb/>
            portionis reliquæ tripla ſeſquitertia ad circuli diame-
              <lb/>
            trum cum tripla ea, quæ à centro circuli pertingit
              <lb/>
            ad portionis baſin.</s>
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