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

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        <div xml:id="echoid-div228" type="section" level="1" n="114">
          <pb o="472" file="0192" n="202" rhead="HUGENII EXCEPSIO"/>
          <figure number="79">
            <image file="0192-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0192-01"/>
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        <div xml:id="echoid-div231" type="section" level="1" n="115">
          <head xml:id="echoid-head157" xml:space="preserve">IV.
            <lb/>
          EXCERPTA EX LITERIS
            <lb/>
          D
            <emph style="super">ni</emph>
          . HUGENII
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          DE RESPONSO, QUOD
            <lb/>
          D
            <emph style="super">nus</emph>
          . GREGORIUS
            <lb/>
          DEDIT AD EXAMEN LIBRI, CUI TITULUS EST,
            <lb/>
          VERA CIRCULI ET HYPERBOLÆ QUADRATURA.</head>
          <p>
            <s xml:id="echoid-s4188" xml:space="preserve">In circuli quadraturam inquirentes Geometræ, va-
              <lb/>
            ria & </s>
            <s xml:id="echoid-s4189" xml:space="preserve">quidem pulcherrima detexere, ideo ne u-
              <lb/>
            tili exercitio deſtituantur adverſus Gregorium de-
              <lb/>
            fendere conſtitui, quadraturam hanc detegi poſ-
              <lb/>
            ſe; </s>
            <s xml:id="echoid-s4190" xml:space="preserve">neque huc uſque reſponſionem hanc diſtuliſſem, niſi oc-
              <lb/>
            caſione controverſiæ noſtræ examen ſuſcepiſſem exactiſſimum
              <lb/>
            de proxima Circuli & </s>
            <s xml:id="echoid-s4191" xml:space="preserve">Hyperboles Quadratura: </s>
            <s xml:id="echoid-s4192" xml:space="preserve">in quo me
              <lb/>
            interpellarunt ſæpe alia impedimenta.</s>
            <s xml:id="echoid-s4193" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4194" xml:space="preserve">Dico nunc primo; </s>
            <s xml:id="echoid-s4195" xml:space="preserve">Quod ſpectat impoſſibilitatem analy-
              <lb/>
            ticam quadraturæ illarum figurarum, tantum abeſſe etiam poſt
              <lb/>
            ſupplementum demonſtrationum, quod D
              <emph style="super">nus</emph>
            Gregorius dedit,
              <lb/>
            impoſſibilitatem hanc bene probatam eſſe, ut adhuc dum in-
              <lb/>
            certum maneat, num Circulus & </s>
            <s xml:id="echoid-s4196" xml:space="preserve">quadratum diametri ejus ſint
              <lb/>
            incommenſurabilia, id eſt an non horum ratio per numeros
              <lb/>
            poſſit exprimi; </s>
            <s xml:id="echoid-s4197" xml:space="preserve">quod etiam applicari poteſt portioni deter-
              <lb/>
            minatæ Hyperboles & </s>
            <s xml:id="echoid-s4198" xml:space="preserve">figuræ huic inſcriptæ. </s>
            <s xml:id="echoid-s4199" xml:space="preserve">Quod ut demon-
              <lb/>
            ſtremus ſufficit obſervaſſe; </s>
            <s xml:id="echoid-s4200" xml:space="preserve">quod XI ejus Propoſitio & </s>
            <s xml:id="echoid-s4201" xml:space="preserve">ſup-
              <lb/>
            plementum nil probent quando in ejus ſerie convergen-
              <lb/>
            te determinantur quantitates a & </s>
            <s xml:id="echoid-s4202" xml:space="preserve">b per numeros ra-
              <lb/>
            tionales vel ſurdos; </s>
            <s xml:id="echoid-s4203" xml:space="preserve">quoniam tunc terminatio et-
              <lb/>
            iam poterit eſſe numerus quidam ſimilis; </s>
            <s xml:id="echoid-s4204" xml:space="preserve">& </s>
            <s xml:id="echoid-s4205" xml:space="preserve">con-
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            trarium per illam propoſitionem demonſtrari non </s>
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