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

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            <s xml:id="echoid-s5108" xml:space="preserve">
              <pb o="514" file="0238" n="250" rhead="CHRISTIANI HUGENII"/>
            Tangentis proprietatem; </s>
            <s xml:id="echoid-s5109" xml:space="preserve">Problema, quod mihi apparuit
              <lb/>
            difficillimum. </s>
            <s xml:id="echoid-s5110" xml:space="preserve">Solutio Marchionis exſtat in 34. </s>
            <s xml:id="echoid-s5111" xml:space="preserve">Diario Pari-
              <lb/>
            ſienſi anni ultimi, quare hanc hic non trado.</s>
            <s xml:id="echoid-s5112" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5113" xml:space="preserve">Alterum eſt ejus reſponſum de aliâ curvâ valde cognitâ, & </s>
            <s xml:id="echoid-s5114" xml:space="preserve">
              <lb/>
            quam Carteſius aliter adhuc conſideravit, ut & </s>
            <s xml:id="echoid-s5115" xml:space="preserve">Huddenius
              <lb/>
            eo tempore, quo negotia Reip. </s>
            <s xml:id="echoid-s5116" xml:space="preserve">non impediebant, quo-
              <lb/>
            minus vacaret ſtudiis. </s>
            <s xml:id="echoid-s5117" xml:space="preserve">Curva in fig. </s>
            <s xml:id="echoid-s5118" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5119" xml:space="preserve">exhibetur, fo-
              <lb/>
              <note position="left" xlink:label="note-0238-01" xlink:href="note-0238-01a" xml:space="preserve">TAB. XLVI.
                <lb/>
              fig. 4.</note>
            lium A B C H circumſcribit & </s>
            <s xml:id="echoid-s5120" xml:space="preserve">utrimque ſeſe extendit juxta
              <lb/>
            Aſymptoton E F G. </s>
            <s xml:id="echoid-s5121" xml:space="preserve">Æquatio ejus eſt x
              <emph style="super">3</emph>
            + y
              <emph style="super">3</emph>
            = xyn ſi A D
              <lb/>
            ponatur x in recta, quæ cum diametro C A format angulum
              <lb/>
            45 graduum; </s>
            <s xml:id="echoid-s5122" xml:space="preserve">perpendicularis DB, vel D H, vel D K, y; </s>
            <s xml:id="echoid-s5123" xml:space="preserve">& </s>
            <s xml:id="echoid-s5124" xml:space="preserve">
              <lb/>
            n recta data. </s>
            <s xml:id="echoid-s5125" xml:space="preserve">Cum ipſi indicaſſem, me inveniſſe qua-
              <lb/>
            draturam hujus curvæ, & </s>
            <s xml:id="echoid-s5126" xml:space="preserve">quod contentum folii A B C H
              <lb/>
            eſſet = {1/6} nn id eſt {1/3} quadrati diametri A C; </s>
            <s xml:id="echoid-s5127" xml:space="preserve">quod ſpa-
              <lb/>
            tium infinitum inter Aſymptoton & </s>
            <s xml:id="echoid-s5128" xml:space="preserve">ambo curvæ brachia
              <lb/>
            etiam ejuſdem magnitudinis eſſent; </s>
            <s xml:id="echoid-s5129" xml:space="preserve">& </s>
            <s xml:id="echoid-s5130" xml:space="preserve">quod quadratura ge-
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            neralis ſegmentorum exprimeretur per unicum terminum;
              <lb/>
            </s>
            <s xml:id="echoid-s5131" xml:space="preserve">ille invenit veram illam quadraturam generalem. </s>
            <s xml:id="echoid-s5132" xml:space="preserve">Scilicet quod
              <lb/>
            contentum ſegmentorum A H vel A K exprimatur per {nxx/6y}
              <lb/>
            & </s>
            <s xml:id="echoid-s5133" xml:space="preserve">ſegmenti A B per {nyy/6x}; </s>
            <s xml:id="echoid-s5134" xml:space="preserve">ſed ulterius mihi affirmat ſe eo
              <lb/>
            perveniſſe per tres diverſas vias; </s>
            <s xml:id="echoid-s5135" xml:space="preserve">quod miror, cum per-
              <lb/>
            ſuaſum habeam me non parum profeciſſe unicam dete-
              <lb/>
            gendo.</s>
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