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

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        <div xml:id="echoid-div251" type="section" level="1" n="123">
          <p>
            <s xml:id="echoid-s4762" xml:space="preserve">
              <pb o="499" file="0221" n="232" rhead="GEOMET. VARIA."/>
            per hæc quæ nunc trademus fiet, quæ jam olim, multò an-
              <lb/>
            te iſtas literas vulgatas conſcripſimus.</s>
            <s xml:id="echoid-s4763" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4764" xml:space="preserve">Præcipuum verò operæ pretium tunc fuit compendioſa hu-
              <lb/>
            juſce regulæ contractio, quam, quoad potui, proſecutus,
              <lb/>
            tandem in ipſas illas inſignes Huddenii, Sluſiique regulas
              <lb/>
            deſinere inveni, quas mihi Viri hi Clariſſimi uterque ferè eo-
              <lb/>
            dem tempore exhibuerant: </s>
            <s xml:id="echoid-s4765" xml:space="preserve">an vero hac eadem viâ an aliâ in
              <lb/>
            illas inciderint nondum mihi compertum.</s>
            <s xml:id="echoid-s4766" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4767" xml:space="preserve">Sit data linea curva ut B C, quæ cognitam relationem ha-
              <lb/>
              <note position="right" xlink:label="note-0221-01" xlink:href="note-0221-01a" xml:space="preserve">TAB. XLV.
                <lb/>
              fig. 2.</note>
            beat ad rectam aliquam poſitione datam A F; </s>
            <s xml:id="echoid-s4768" xml:space="preserve">ac proinde ap-
              <lb/>
            plicatâ è puncto quolibet curvæ, ut B, rectâ B F, in dato
              <lb/>
            angulo B F A, datoque in recta A F puncto A, certa æqua-
              <lb/>
            tione relatio quæ eſt inter A F & </s>
            <s xml:id="echoid-s4769" xml:space="preserve">F B expreſſa habeatur. </s>
            <s xml:id="echoid-s4770" xml:space="preserve">Ex-
              <lb/>
            empli gratiâ, appellando A F, x; </s>
            <s xml:id="echoid-s4771" xml:space="preserve">F B, y, ſit æquatio x
              <emph style="super">3</emph>
              <lb/>
            = xya - y
              <emph style="super">3</emph>
            , ubi a lineam quandam datam ſignificare cen-
              <lb/>
            ſenda eſt.</s>
            <s xml:id="echoid-s4772" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4773" xml:space="preserve">Quod ſi jam ad punctum B tangens ducenda ſit B E, quæ
              <lb/>
            occurrat rectæ A F in E, voceturque F E, z, ejus longitu-
              <lb/>
            do per hanc regulam Fermatianæ regulæ compendiariam, in-
              <lb/>
            venietur, ex ſola æquatione data.</s>
            <s xml:id="echoid-s4774" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4775" xml:space="preserve">Tranſlatis terminis omnibus æquationis datæ ad unam æqua-
              <lb/>
            tionis partem, qui proinde æquales fiunt nihilo, multiplicen-
              <lb/>
            tur primò termini ſinguli, in quibus reperitur y, per nume-
              <lb/>
            rum dimenſionum quas in ipſis habet y, atque ea erit quan-
              <lb/>
            titas dividenda. </s>
            <s xml:id="echoid-s4776" xml:space="preserve">Deinde ſimiliter termini ſinguli in quibus x,
              <lb/>
            multiplicentur per numerum dimenſionum quas in ipſis habet
              <lb/>
            x, & </s>
            <s xml:id="echoid-s4777" xml:space="preserve">è ſingulis unum x tollatur; </s>
            <s xml:id="echoid-s4778" xml:space="preserve">atque hæc quantitas pro diviſo-
              <lb/>
            re erit ſubſcribenda quantitati dividendæ jam inventæ. </s>
            <s xml:id="echoid-s4779" xml:space="preserve">Quo fa-
              <lb/>
            cto habebitur quantitas æqualis z ſive F E. </s>
            <s xml:id="echoid-s4780" xml:space="preserve">Signa autem + & </s>
            <s xml:id="echoid-s4781" xml:space="preserve">-
              <lb/>
            eadem ubique retinenda ſunt; </s>
            <s xml:id="echoid-s4782" xml:space="preserve">atque etiam ſi forte quantitas di-
              <lb/>
            viſoris, vel dividenda, vel utraque minor nihilo ſive negata ſit,
              <lb/>
            tamen tanquam adfirmatæ ſunt conſiderandæ: </s>
            <s xml:id="echoid-s4783" xml:space="preserve">hoc tantum
              <lb/>
            obſervando, ut cum altera adfirmata eſt, altera negata, tunc
              <lb/>
            F E ſumatur verſus punctum A, cum verò utraque vel affir-
              <lb/>
            mata eſt vel negata, ut tunc ſumatur F E in partem contra-
              <lb/>
            riam.</s>
            <s xml:id="echoid-s4784" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div253" type="section" level="1" n="124">
          <head xml:id="echoid-head171" style="it" xml:space="preserve">Tom. II. Rrr</head>
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