Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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            <s xml:id="echoid-s4993" xml:space="preserve">
              <pb o="510" file="0234" n="246" rhead="CHRISTIANI HUGENII"/>
            ſcriptiones ſectionum Conicarum, quæ fiunt per inſtrumen-
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            ta, haberemus inde & </s>
            <s xml:id="echoid-s4994" xml:space="preserve">quadraturam Hyperboles & </s>
            <s xml:id="echoid-s4995" xml:space="preserve">perfe-
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            ctam conſtructionem omnium Problematum, quæ ad hanc
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            quadraturam reducuntur; </s>
            <s xml:id="echoid-s4996" xml:space="preserve">ut inter alia ſunt, determinatio
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            punctorum Catenariæ, & </s>
            <s xml:id="echoid-s4997" xml:space="preserve">logarithmi. </s>
            <s xml:id="echoid-s4998" xml:space="preserve">Si enim B Y ſit =
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            A C, quæ ſumitur in axe Catenariæ, id eſt D B = DC ap-
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            plicata ejus C G erit = Y X; </s>
            <s xml:id="echoid-s4999" xml:space="preserve">& </s>
            <s xml:id="echoid-s5000" xml:space="preserve">eadem quoque Y X eſt lo-
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            garithmus rationis quam habet A D ad P D; </s>
            <s xml:id="echoid-s5001" xml:space="preserve">id eſt, æqualis
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            eſt diſtantiæ duarum linearum A D, P D, vel aliarum duarum qua-
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            rumcunque, quæ eandem habent rationem, ordinatarum per-
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            pendicularium ad Aſymptoton lineæ logarithmicæ, quæ habet
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            D A pro Subtangente univerſali; </s>
            <s xml:id="echoid-s5002" xml:space="preserve">unde poſſunt inveniri logarith-
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            mi tabularum, prout demonſtravi in additione ad diſſertationem
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            de cauſa gravitatis. </s>
            <s xml:id="echoid-s5003" xml:space="preserve">Leibnitius, qui primus initium fecit redu-
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            ctionis curvæ Catenariæ ad leges Geometriæ, ipſam illam
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            lineam ope veræ Catenæ tenuiſſimæ formatam, dixit inſer-
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            vire poſſe inventioni logarithmorum, vel quadraturæ Hy-
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            perboles; </s>
            <s xml:id="echoid-s5004" xml:space="preserve">licet ad id cognita requiratur (ut quidem ipſe no-
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            verat) longitudo rectæ, quam vocat curvæ Parametrum,
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            cujus inventionem non demonſtrat. </s>
            <s xml:id="echoid-s5005" xml:space="preserve">Ita ut noſtra qua-
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            dratrix in his uſibus præferenda videatur, quia poſt de-
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            ſcriptionem Parameter ejus, quæ eſt univerſalis ejus Tan-
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            gens, datur.</s>
            <s xml:id="echoid-s5006" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s5007" xml:space="preserve">Sed quoniam hæc materia me perduxit ad conſideratio-
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            nem Catenariæ quæ elegantiſſimis hujus temporis Geome-
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            trarum inquiſitionibus occaſionem præbuit, libet hic addere
              <lb/>
            quam inveni peculiarem ſatis methodum qua hæc delincatur cur-
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            va, quod eſt omnium difficillimum inter ea quæ de hac ſibi inqui-
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            renda propoſuere Mathematici. </s>
            <s xml:id="echoid-s5008" xml:space="preserve">Inter illa, quæ inſerenda dedi in
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            actis Lipſienſibus cum pulcris & </s>
            <s xml:id="echoid-s5009" xml:space="preserve">eruditis Leibnitii & </s>
            <s xml:id="echoid-s5010" xml:space="preserve">Ber-
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            noullii inventis, dixi, me reduxiſſe conſtructionem vel
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            inventionem punctorum hujus lineæ ad quadra@uram curvæ,
              <lb/>
            cujus æquatio eſt a
              <emph style="super">4</emph>
            = aaxx + yyxx ; </s>
            <s xml:id="echoid-s5011" xml:space="preserve">& </s>
            <s xml:id="echoid-s5012" xml:space="preserve">me
              <note symbol="*" position="left" xlink:label="note-0234-01" xlink:href="note-0234-01a" xml:space="preserve">Vide ſupra
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              pag. 29@.</note>
            ſe, hanc quadraturam dependere à cognitione ſummæ ſe-
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            cantium arcuum circuli, quæ æqualiter creſcerent per mi-
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            nima; </s>
            <s xml:id="echoid-s5013" xml:space="preserve">quæ ſumma jam dudum reducta fuerat ad </s>
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