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

Page concordance

< >
Scan Original
231 498
232 499
233 500
234 501
235 502
236 503
237 504
238 505
239 506
240
241
242
243 507
244 508
245 509
246 510
247 511
248 512
249 513
250 514
251 515
252 516
253 517
254 518
255 519
256 520
257
258
259
260
< >
page |< < (501) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div253" type="section" level="1" n="124">
          <p>
            <s xml:id="echoid-s4819" xml:space="preserve">
              <pb o="501" file="0223" n="234" rhead="GEOMET. VARIA."/>
            atque A F, F B, hoc eſt x & </s>
            <s xml:id="echoid-s4820" xml:space="preserve">y. </s>
            <s xml:id="echoid-s4821" xml:space="preserve">Nempe ſi in æquatione
              <lb/>
            propoſita pro x ſubſtituatur ubique x + e, & </s>
            <s xml:id="echoid-s4822" xml:space="preserve">pro y, ubique
              <lb/>
            y + {ey/z}, debebit æquatio hinc formata terminos omnes ha-
              <lb/>
            bere æquales nihilo; </s>
            <s xml:id="echoid-s4823" xml:space="preserve">hoc eſt
              <lb/>
            x
              <emph style="super">3</emph>
            + [3exx] + 3eex + e
              <emph style="super">3</emph>
            , + y
              <emph style="super">3</emph>
            + [{3ey
              <emph style="super">3</emph>
            /z}] + {3eey
              <emph style="super">3</emph>
            /zz} + {e
              <emph style="super">3</emph>
            y
              <emph style="super">3</emph>
            /z
              <emph style="super">3</emph>
            } = 0.
              <lb/>
            </s>
            <s xml:id="echoid-s4824" xml:space="preserve">- axy - [aey] - [{aeyx/z}] - {aeey/z}</s>
          </p>
          <p>
            <s xml:id="echoid-s4825" xml:space="preserve">In hac autem æquatione conſtat neceſſario terminos prio-
              <lb/>
            ris æquationis, ex qua formata eſt, contineri debere, nem-
              <lb/>
            pe x
              <emph style="super">3</emph>
            + y
              <emph style="super">3</emph>
            - axy: </s>
            <s xml:id="echoid-s4826" xml:space="preserve">qui cum ſint æquales nihilo ex proprie-
              <lb/>
            tate curvæ, idcirco his in æquatione deletis, neceſſe eſt etiam
              <lb/>
            reliquos nihilo æquari, in quibus ſingulis manifeſtum quoque
              <lb/>
            eſt vel unum e vel plura reperiri, ideoque omnes per e divi-
              <lb/>
            di poſſe. </s>
            <s xml:id="echoid-s4827" xml:space="preserve">Qui autem poſt hanc diviſionem non amplius ha-
              <lb/>
            bebunt e, eos, neglectis reliquis, ſcio nihilo æquari debe-
              <lb/>
            re, quantitatemque lineæ z ſive F E oſtenſuros; </s>
            <s xml:id="echoid-s4828" xml:space="preserve">ſi nempe
              <lb/>
            B E jam tanquam tangens conſideretur, ideoque F G, ſeu
              <lb/>
            e, infinitè parva. </s>
            <s xml:id="echoid-s4829" xml:space="preserve">Nam termini in quibus adhuc e ſupereſt,
              <lb/>
            etiam quantitates infinite parvas ſive omnino evaneſcentes
              <lb/>
            continebunt. </s>
            <s xml:id="echoid-s4830" xml:space="preserve">Et his quidem hactenus Fermatianæ regulæ
              <lb/>
            origo ac ratio declaratur: </s>
            <s xml:id="echoid-s4831" xml:space="preserve">nunc porro oſtendemus quomodo
              <lb/>
            eadem ad tantam brevitatem perducta ſit. </s>
            <s xml:id="echoid-s4832" xml:space="preserve">Video itaque ex
              <lb/>
            æquatione totâ noviſſimâ, tantum eos terminos ſeribi neceſ-
              <lb/>
            ſe eſſe quibus ineſt e ſimplex, velut hic 3exx + {3ey
              <emph style="super">3</emph>
            /z} - aey -
              <lb/>
            {aeyx/z} = 0. </s>
            <s xml:id="echoid-s4833" xml:space="preserve">Qui termini quomodo facili negotio ex datis æqua-
              <lb/>
            tionis terminis x
              <emph style="super">3</emph>
            + y
              <emph style="super">3</emph>
            - axy = 0, deſcribi poſſint, dein-
              <lb/>
            ceps explicandum. </s>
            <s xml:id="echoid-s4834" xml:space="preserve">Et primò quidem apparet 3exx +
              <lb/>
            {3ey
              <emph style="super">3</emph>
            /z} nihil aliud eſſe quam ſecundos terminos cuborum </s>
          </p>
        </div>
      </text>
    </echo>
Impressum