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

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        <div xml:id="echoid-div88" type="section" level="1" n="41">
          <pb o="377" file="0089" n="95" rhead="DE CIRCULI MAGNIT. INVENTA."/>
          <p>
            <s xml:id="echoid-s1693" xml:space="preserve">Hoc Theorema alterum eſt ex iis quibus Cyclometria
              <lb/>
            Willebrordi Snellii tota innititur, quæque demonſtraſſe ipſe
              <lb/>
            videri voluit, argumentatione uſus quæ meram quæſiti pe-
              <lb/>
            titionem continet. </s>
            <s xml:id="echoid-s1694" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1695" xml:space="preserve">alterum ſubjungemus, quod utile
              <lb/>
            eſt imprimis & </s>
            <s xml:id="echoid-s1696" xml:space="preserve">contemplatione digniſſimum.</s>
            <s xml:id="echoid-s1697" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div90" type="section" level="1" n="42">
          <head xml:id="echoid-head65" xml:space="preserve">
            <emph style="sc">Theor</emph>
          . XIII.
            <emph style="sc">Prop</emph>
          . XVI.</head>
          <p style="it">
            <s xml:id="echoid-s1698" xml:space="preserve">
              <emph style="bf">S</emph>
            I diametro circuli ſemidiameter in directum adji-
              <lb/>
            ciatur, & </s>
            <s xml:id="echoid-s1699" xml:space="preserve">ab adjectæ termino recta ducatur quæ
              <lb/>
            circulum ſecet, occurr atque tangenti circulum ad ter-
              <lb/>
            minum diametri oppoſitum: </s>
            <s xml:id="echoid-s1700" xml:space="preserve">Intercipiet eapartem tan-
              <lb/>
            gentis arcu adjacente abſciſſo minorem.</s>
            <s xml:id="echoid-s1701" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1702" xml:space="preserve">Eſto circulus, cujus diameter A B; </s>
            <s xml:id="echoid-s1703" xml:space="preserve">quæ producatur, & </s>
            <s xml:id="echoid-s1704" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">TAB. XL.
                <lb/>
              Fig. 1.</note>
            ſit A C ſemidiametro æqualis. </s>
            <s xml:id="echoid-s1705" xml:space="preserve">Et ducatur recta C L,
              <lb/>
            quæ circumferentiam ſecundò ſecet in E; </s>
            <s xml:id="echoid-s1706" xml:space="preserve">occurratque tan-
              <lb/>
            genti in L, ei nimirum quæ circulum contingit in termino
              <lb/>
            diametri B. </s>
            <s xml:id="echoid-s1707" xml:space="preserve">Dico interceptam B L arcu B E minorem eſſe.
              <lb/>
            </s>
            <s xml:id="echoid-s1708" xml:space="preserve">Jungantur enim A E, E B, poſitâque A H ipſi A E æqua-
              <lb/>
            li ducatur H E & </s>
            <s xml:id="echoid-s1709" xml:space="preserve">producatur, occurratque tangenti in K. </s>
            <s xml:id="echoid-s1710" xml:space="preserve">
              <lb/>
            Denique ſit E G diametro A B ad angulos rectos, E D ve-
              <lb/>
            ro tangenti B L. </s>
            <s xml:id="echoid-s1711" xml:space="preserve">Quoniam igitur iſoſceles eſt triangulus
              <lb/>
            H A E, erunt anguli inter ſe æquales H & </s>
            <s xml:id="echoid-s1712" xml:space="preserve">H E A. </s>
            <s xml:id="echoid-s1713" xml:space="preserve">Quia
              <lb/>
            autem angulus A E B rectus eſt, etiam recto æquales erunt
              <lb/>
            duo ſimul H E A, K E B. </s>
            <s xml:id="echoid-s1714" xml:space="preserve">Verùm duo quoque iſti H & </s>
            <s xml:id="echoid-s1715" xml:space="preserve">
              <lb/>
            H K B uni recto æquantur, quoniam in triangulo H K B
              <lb/>
            rectus eſt angulus B. </s>
            <s xml:id="echoid-s1716" xml:space="preserve">Ergo demptis utrimque æqualibus,
              <lb/>
            hinc nimirum angulo H, inde angulo H E A, relinquen-
              <lb/>
            tur inter ſe æquales anguli K E B, H K B. </s>
            <s xml:id="echoid-s1717" xml:space="preserve">Triangulus
              <lb/>
            igitur iſoſceles eſt K B E, ejuſque latera æqualia E B, B K. </s>
            <s xml:id="echoid-s1718" xml:space="preserve">
              <lb/>
            Eſt autem B D æqualis E G. </s>
            <s xml:id="echoid-s1719" xml:space="preserve">Ergo D K differentia eſt quâ
              <lb/>
            B E excedit E G. </s>
            <s xml:id="echoid-s1720" xml:space="preserve">Porro quoniam eſt A G ad A E, ut A E
              <lb/>
            ad A B, erunt duæ ſimul A G, A B majores duplâ A E .</s>
            <s xml:id="echoid-s1721" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0089-02" xlink:href="note-0089-02a" xml:space="preserve">25.5. Elem.</note>
            Ideoque A E, hoc eſt, A H minor quam dimidia </s>
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