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

Table of Notes

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            <s xml:id="echoid-s4943" xml:space="preserve">
              <pb o="508" file="0232" n="244" rhead="CHRIST. HUGENII"/>
            = T E: </s>
            <s xml:id="echoid-s4944" xml:space="preserve">tunc junge VD, ductâque ipſi parallelâ I K, e pun-
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            cto K, ubi occurrit ipſi D L, duc parallelam aſymptoto
              <lb/>
            K A, ſecantem D V in F, C O in X, & </s>
            <s xml:id="echoid-s4945" xml:space="preserve">Logarithmicam in
              <lb/>
            A. </s>
            <s xml:id="echoid-s4946" xml:space="preserve">Tum rectæ A X & </s>
            <s xml:id="echoid-s4947" xml:space="preserve">F K ſimul ſumtæ erunt æquales cur-
              <lb/>
            væ C D.</s>
            <s xml:id="echoid-s4948" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4949" xml:space="preserve">Solutio hujus Problematis, prout ego invenio, poteſt et-
              <lb/>
            iam reduci ad quadraturam curvæ, cujus Æquatio eſt
              <lb/>
            a
              <emph style="super">4</emph>
            = xxyy - aayy, quæ, ut & </s>
            <s xml:id="echoid-s4950" xml:space="preserve">altera, dependet à quadratu-
              <lb/>
            ra Hyperboles, uti poſſem ſatis facile demonſtrare; </s>
            <s xml:id="echoid-s4951" xml:space="preserve">ſed
              <lb/>
            conſtructio à modo deſcripta non differt.</s>
            <s xml:id="echoid-s4952" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4953" xml:space="preserve">Neſcio, an multæ lineæ curvæ hanc habeant proprietatem
              <lb/>
            ut ipſarum longitudines per ipſas curvas menſurari queant;
              <lb/>
            </s>
            <s xml:id="echoid-s4954" xml:space="preserve">interim ecce unam, quam haud ita pridem inveni, dignam, ut
              <lb/>
            videbis, quæ & </s>
            <s xml:id="echoid-s4955" xml:space="preserve">ob alia etiam notetur; </s>
            <s xml:id="echoid-s4956" xml:space="preserve">Eſt curva A X K O
              <lb/>
              <note position="left" xlink:label="note-0232-01" xlink:href="note-0232-01a" xml:space="preserve">TAB. XLVI.
                <lb/>
              fig. 2.</note>
            extenſa in infinitum ſecundum rectam D N, quæ eſt ejus a-
              <lb/>
            ſymptos, ad quam A D, tangens ad verticem A, inſiſtit
              <lb/>
            perpendicularis; </s>
            <s xml:id="echoid-s4957" xml:space="preserve">curvæ princeps & </s>
            <s xml:id="echoid-s4958" xml:space="preserve">ſimpliciſſima pro-
              <lb/>
            prietas eſt, ut omnis tangens inter punctum contactus & </s>
            <s xml:id="echoid-s4959" xml:space="preserve">
              <lb/>
            aſymptoton, ut K N, ſit æqualis lineæ A D; </s>
            <s xml:id="echoid-s4960" xml:space="preserve">curva pariter ex-
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            tenditur ad alteram partem hujus perpendicularis A D. </s>
            <s xml:id="echoid-s4961" xml:space="preserve">Ut
              <lb/>
            invenias rectam lineam æqualem portioni hujus curvæ datæ a
              <lb/>
            vertice A, ut A K (ſic enim invenies alias portiones quaſcun-
              <lb/>
            que) duc K P perpendicularem ad A D, & </s>
            <s xml:id="echoid-s4962" xml:space="preserve">deſcripto arcu
              <lb/>
            circuli P Q, qui habeat centrum D & </s>
            <s xml:id="echoid-s4963" xml:space="preserve">radium D P, quæ-
              <lb/>
            re in A B parallelâ Aſymptoto punctum B, quod ſit centrum
              <lb/>
            circumferentiæ circuli, quæ tranſit per A & </s>
            <s xml:id="echoid-s4964" xml:space="preserve">tangit arcum PQ,
              <lb/>
            quod facile eſt; </s>
            <s xml:id="echoid-s4965" xml:space="preserve">porro ductâ rectâ B D, ſume in illâ DY = DA,
              <lb/>
            & </s>
            <s xml:id="echoid-s4966" xml:space="preserve">e puncto Y duc parallelam Aſymptoto uſque ad curvam in
              <lb/>
            X, tunc Y X erit æqualis curvæ A K; </s>
            <s xml:id="echoid-s4967" xml:space="preserve">Et natura hujus lineæ
              <lb/>
            talis eſt, ut ſi ſumas tot proportionales quot volueris, in re-
              <lb/>
            cta A D, incipiendo a D, ut DS, DI, DP & </s>
            <s xml:id="echoid-s4968" xml:space="preserve">ducas applica-
              <lb/>
            tas SR, IO, PK: </s>
            <s xml:id="echoid-s4969" xml:space="preserve">partes interceptæ curvæ, ut R O, O K,
              <lb/>
            omnes ſint æquales.</s>
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          </p>
          <p>
            <s xml:id="echoid-s4971" xml:space="preserve">Ad quadraturam Hyperboles quoque inſervit curva hæc; </s>
            <s xml:id="echoid-s4972" xml:space="preserve">nam
              <lb/>
            eadem recta Y X facit cum A D rectangulum æquale ſpatio
              <lb/>
            Hyperbolico A D E V, terminato lineis A D, E V </s>
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