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

Page concordance

< >
Scan Original
101 383
102 384
103 385
104 386
105
106 386
107
108 387
109
110 389
111 390
112 391
113 392
114 393
115 394
116 395
117 396
118 397
119 398
120
121
122
123 399
124 400
125 401
126 402
127 403
128 404
129
130
< >
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