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

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          <p>
            <s xml:id="echoid-s1843" xml:space="preserve">
              <pb o="382" file="0094" n="100" rhead="CHRISTIANI HUGENII"/>
            ret portionem A B C ad inſcriptum triangulum minorem ha-
              <lb/>
            bere rationem quam triplam ſeſquitertiam D F ad duplam
              <lb/>
            E B, hoc eſt, diametrum B F, unà cum tripla E D. </s>
            <s xml:id="echoid-s1844" xml:space="preserve">Quod
              <lb/>
            erat demonſtrandum.</s>
            <s xml:id="echoid-s1845" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div99" type="section" level="1" n="45">
          <head xml:id="echoid-head68" xml:space="preserve">
            <emph style="sc">Theor</emph>
          . XVI.
            <emph style="sc">Propos</emph>
          . XIX.</head>
          <p style="it">
            <s xml:id="echoid-s1846" xml:space="preserve">ARcus quilibet ſemicirumferentiâ minor, ma-
              <lb/>
            jor eſt ſuâ ſubtenſâ ſimul & </s>
            <s xml:id="echoid-s1847" xml:space="preserve">triente differen-
              <lb/>
            tiæ quâ ſubtenſa ſinum excedit. </s>
            <s xml:id="echoid-s1848" xml:space="preserve">Idem verò minor
              <lb/>
            quam ſubtenſa ſimul cum ea quæ ad dictum trien-
              <lb/>
            tem ſeſe habeat, ut quadrupla ſubtenſa juncta ſi-
              <lb/>
            nui ad ſubtenſam duplam cum ſinu triplo.</s>
            <s xml:id="echoid-s1849" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1850" xml:space="preserve">Eſto circulus cujus D centrum, diameter F B. </s>
            <s xml:id="echoid-s1851" xml:space="preserve">Et ſit ar-
              <lb/>
              <note position="left" xlink:label="note-0094-01" xlink:href="note-0094-01a" xml:space="preserve">TAB. XL.
                <lb/>
              Fig. 5.</note>
            cus B A ſemicircumferentiâ minor, cui ſubtenſa ducatur
              <lb/>
            B A, ſinus autem A M: </s>
            <s xml:id="echoid-s1852" xml:space="preserve">quæ nimirum diametro F B ſit ad
              <lb/>
            angulos rectos. </s>
            <s xml:id="echoid-s1853" xml:space="preserve">Porro ipſi A M ſit æqualis recta G H, & </s>
            <s xml:id="echoid-s1854" xml:space="preserve">
              <lb/>
            G I æqualis ſubtenſæ A B. </s>
            <s xml:id="echoid-s1855" xml:space="preserve">Exceſſus igitur eſt H I; </s>
            <s xml:id="echoid-s1856" xml:space="preserve">cujus
              <lb/>
            triens I K ipſi G I adjiciatur. </s>
            <s xml:id="echoid-s1857" xml:space="preserve">Oſtendendum eſt primo, ar-
              <lb/>
            cum A B totâ G K majorem eſſe. </s>
            <s xml:id="echoid-s1858" xml:space="preserve">Hoc autem ex Theore-
              <lb/>
            mate 7. </s>
            <s xml:id="echoid-s1859" xml:space="preserve">eſt manifeſtum. </s>
            <s xml:id="echoid-s1860" xml:space="preserve">At cum ipſi G I additur IO quæ
              <lb/>
            ad I K trientem ipſius H I rationem habeat, quam quadru-
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            pla G I una cum G H ad duplam G I cum tripla G H.
              <lb/>
            </s>
            <s xml:id="echoid-s1861" xml:space="preserve">Dico totam G O arcu A B majorem eſſe. </s>
            <s xml:id="echoid-s1862" xml:space="preserve">Conſtituantur enim
              <lb/>
            ſuper lineis G H, H I, IO, triangula quorum communis
              <lb/>
            vertex ſit L, altitudo autem æqualis radio D B. </s>
            <s xml:id="echoid-s1863" xml:space="preserve">Et junga-
              <lb/>
            tur D A, ducaturque diameter circuli C E quæ rectam
              <lb/>
            A B bifariam dividat in N, arcum vero A B in E. </s>
            <s xml:id="echoid-s1864" xml:space="preserve">Et jun-
              <lb/>
            gantur A E, E B.</s>
            <s xml:id="echoid-s1865" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1866" xml:space="preserve">Quoniam igitur O I eſt ad I K ut quadrupla G I unà
              <lb/>
            cum G H ad duplam G I cum tripla G H; </s>
            <s xml:id="echoid-s1867" xml:space="preserve">ſumptis conſequen-
              <lb/>
            tium triplis erit O I ad I H (hæc enim tripla eſt I K,) ut
              <lb/>
            quadrupla G I unà cum G H ad ſexcuplam G I cum non-
              <lb/>
            cupla G H. </s>
            <s xml:id="echoid-s1868" xml:space="preserve">Et componendo, O H ad H I, ut </s>
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