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

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          <figure number="54">
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        <div xml:id="echoid-div106" type="section" level="1" n="47">
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            <emph style="sc">Christiani</emph>
            <emph style="sc">Hugenii</emph>
          C. F.</head>
          <head xml:id="echoid-head71" xml:space="preserve">ILLVSTRIVM QVORVNDAM</head>
          <head xml:id="echoid-head72" xml:space="preserve">PROBLEMATVM CONSTRVCTIONES.</head>
          <head xml:id="echoid-head73" xml:space="preserve">
            <emph style="sc">Probl</emph>
          . I.</head>
          <head xml:id="echoid-head74" style="it" xml:space="preserve">Datam ſphæram plano ſecare, ut portiones
            <lb/>
          inter ſe rationem habeant datam.</head>
          <p>
            <s xml:id="echoid-s1995" xml:space="preserve">HOc Archimedes problema reſolvit lib. </s>
            <s xml:id="echoid-s1996" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1997" xml:space="preserve">de
              <lb/>
            Sphæra & </s>
            <s xml:id="echoid-s1998" xml:space="preserve">Cylind. </s>
            <s xml:id="echoid-s1999" xml:space="preserve">Compoſitionem autem pro-
              <lb/>
            miſſam non videtur explicuiſſe, niſi ipſius eſt il-
              <lb/>
            la quam Eutocius in vetuſto quodam libro reper-
              <lb/>
            tam commentariis ſuis inferuit. </s>
            <s xml:id="echoid-s2000" xml:space="preserve">Ea vero parabo-
              <lb/>
            les & </s>
            <s xml:id="echoid-s2001" xml:space="preserve">hyperboles interſectione perficitur, uti & </s>
            <s xml:id="echoid-s2002" xml:space="preserve">illa cujus
              <lb/>
            Dionyſidorus autor eſt, quæ tamen à priori differt. </s>
            <s xml:id="echoid-s2003" xml:space="preserve">Præter
              <lb/>
            has tertiam quoque adfert Eutocius è Dioclis de Pyriis li-
              <lb/>
            bro, quæ hyperboles & </s>
            <s xml:id="echoid-s2004" xml:space="preserve">ellipſis deſcriptionem requirit. </s>
            <s xml:id="echoid-s2005" xml:space="preserve">No-
              <lb/>
            ſtra autem quam hic conſcribemus anguli triſectionem poſtu-
              <lb/>
            lat; </s>
            <s xml:id="echoid-s2006" xml:space="preserve">Et hæc conſtruendi ratio in ſolidis problematibus quo-
              <lb/>
            dammodo ſimpliciſſima videtur, atque ad uſum maxime ac-
              <lb/>
            commodata.</s>
            <s xml:id="echoid-s2007" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2008" xml:space="preserve">Eſto igitur data ſphæra cujus centrum M, diameter C A.
              <lb/>
            </s>
            <s xml:id="echoid-s2009" xml:space="preserve">
              <note position="left" xlink:label="note-0102-01" xlink:href="note-0102-01a" xml:space="preserve">TAB. XLI.
                <lb/>
              Fig. 1.</note>
            Et data ſit proportio lineæ S ad T majoris ad minorem.
              <lb/>
            </s>
            <s xml:id="echoid-s2010" xml:space="preserve">Intelligatur ſecari ſphæra plano ſecundum A C diametrum,
              <lb/>
            ſitque maximus in ea circulus C B A D. </s>
            <s xml:id="echoid-s2011" xml:space="preserve">Et producatur
              <lb/>
            utrimque diameter C A, & </s>
            <s xml:id="echoid-s2012" xml:space="preserve">ponatur ſemidiametro æqua-
              <lb/>
            lis utraque harum C H, A E. </s>
            <s xml:id="echoid-s2013" xml:space="preserve">Et dividatur tota H E in
              <lb/>
            Q, ut ſit E Q ad Q H ſicut S ad T. </s>
            <s xml:id="echoid-s2014" xml:space="preserve">Ipſi autem M Q æqua-
              <lb/>
            lis ponatur ad circumferentiam recta A R. </s>
            <s xml:id="echoid-s2015" xml:space="preserve">Et ei quæ ter-
              <lb/>
            tiam partem ſubtendit arcus A R, æqualis ſumatur M N.</s>
            <s xml:id="echoid-s2016" xml:space="preserve"/>
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