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

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          <figure number="97">
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            <emph style="bf">IV.</emph>
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            <emph style="bf">CHRISTIANI HUGENII</emph>
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            <emph style="bf">EPISTOLA</emph>
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          DE
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          CURVIS QUIBUSDAM PECULIARIBUS.</head>
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            <s xml:id="echoid-s4921" xml:space="preserve">MItto tibi conſtructionem Problematis, quod ſine
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            dubio Geometris placebit, ſi id cum ipſis com-
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            municare velis, cum pulcherrimum ſit, & </s>
            <s xml:id="echoid-s4922" xml:space="preserve">ſingula-
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            ria quædam contineat: </s>
            <s xml:id="echoid-s4923" xml:space="preserve">accepi hoc a Marchione
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            de l’Hoſpital, quem ex ſpecimine hoc & </s>
            <s xml:id="echoid-s4924" xml:space="preserve">variis aliis, in-
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            ter ſummos noſtri ævi Geometras referendum puto. </s>
            <s xml:id="echoid-s4925" xml:space="preserve">Hac
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            etiam occaſione ad te mitto quaſdam ex poſterioribus, ſuper
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            rebus fere ſimilibus, contemplationibus noſtris.</s>
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            <s xml:id="echoid-s4927" xml:space="preserve">Problema March. </s>
            <s xml:id="echoid-s4928" xml:space="preserve">eſt; </s>
            <s xml:id="echoid-s4929" xml:space="preserve">Invenire lineam rectam æqualem
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            datæ portioni lineæ logarithmicæ. </s>
            <s xml:id="echoid-s4930" xml:space="preserve">Ut hujus inveniat ſolu-
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            tionem, ſagaciter utitur Calculo differentiali celeberrimi Lei-
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            bnitii, & </s>
            <s xml:id="echoid-s4931" xml:space="preserve">reducit problema ad quadraturam curvæ, cujus æ-
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            quatio eſt, a
              <emph style="super">6</emph>
            = aaxxyy + y
              <emph style="super">4</emph>
            xx; </s>
            <s xml:id="echoid-s4932" xml:space="preserve">poſitis x & </s>
            <s xml:id="echoid-s4933" xml:space="preserve">y indeter
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            minatis, quæ angulum rectum efficiunt; </s>
            <s xml:id="echoid-s4934" xml:space="preserve">Hanc quadra-
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            turam oſtendit dependere à quadraturâ Hyperboles; </s>
            <s xml:id="echoid-s4935" xml:space="preserve">quæ da-
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            tur, ut notum eſt, poſitâ logarithmicâ deſcriptâ; </s>
            <s xml:id="echoid-s4936" xml:space="preserve">conſtru-
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            ctio autem huc redit. </s>
            <s xml:id="echoid-s4937" xml:space="preserve">Sit logarithmica indefinita A C D, a-
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              <note position="right" xlink:label="note-0231-01" xlink:href="note-0231-01a" xml:space="preserve">TAB. XLVI.
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              fig. 1.</note>
            ſymptos L O, ſubtangens conſtans data a, & </s>
            <s xml:id="echoid-s4938" xml:space="preserve">portio curvæ
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            ſit C D, cui æqualem rectam invenire oportet.</s>
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            <s xml:id="echoid-s4940" xml:space="preserve">Duc D L, C O perpendiculares ad aſymptoton, CE perpen-
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            dicularem ad D L, & </s>
            <s xml:id="echoid-s4941" xml:space="preserve">fac L T in aſymptoto æqualem ſubtan-
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            genti a, & </s>
            <s xml:id="echoid-s4942" xml:space="preserve">ductis rectis T D, T E, fiat T V = T D & </s>
            <s xml:id="echoid-s4943" xml:space="preserve">T </s>
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