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

Page concordance

< >
Scan Original
151 424
152 425
153 426
154 427
155 428
156 429
157 430
158 431
159 432
160 433
161 434
162 435
163 436
164 437
165 438
166 439
167 440
168 441
169 442
170 443
171 444
172 445
173 446
174 447
175 448
176 449
177 450
178
179
180
< >
page |< < (505) 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-s4894" xml:space="preserve">
              <pb o="505" file="0227" n="238" rhead="CEOMET. VARIA"/>
            verò nulla omnino immutanda, id eodem redire liquet cùm
              <lb/>
            quantitatem negatam, ſive minorem nihilo, tanquam affir-
              <lb/>
            matam conſiderandam ibi dixerimus. </s>
            <s xml:id="echoid-s4895" xml:space="preserve">Ut autem ratio obſer-
              <lb/>
            vationis ibidem adjectæ, in utram partem linea F E accipien-
              <lb/>
            da ſit, intelligatur, repetemus figuram in principio poſitam,
              <lb/>
              <note position="right" xlink:label="note-0227-01" xlink:href="note-0227-01a" xml:space="preserve">TAB. XLV.
                <lb/>
              fig. 5.</note>
            ubi vidimus A G eſſe x + e, E G vero z + e; </s>
            <s xml:id="echoid-s4896" xml:space="preserve">unde fiebat GD
              <lb/>
            + y + {ey/z}. </s>
            <s xml:id="echoid-s4897" xml:space="preserve">Si autem tangens ab altera parte lineæ B F cadere
              <lb/>
            intelligatur, velut be, atque hæc primùm curvam ſecare fin-
              <lb/>
            gatur, ut ibi factum eſt in d, ducaturque dg parallela bf; </s>
            <s xml:id="echoid-s4898" xml:space="preserve">fiet
              <lb/>
            ponendo rurſus fg = e, fe = z, ut A g quidem fiat x + e,
              <lb/>
            ſed eg erit z - e, unde gd = y - {ey/z}. </s>
            <s xml:id="echoid-s4899" xml:space="preserve">Atque hinc porrò fa-
              <lb/>
            cile eſt perſpicere æquationem ſecundam, quæ ex propoſita
              <lb/>
            æquatione, x
              <emph style="super">3</emph>
            + y
              <emph style="super">3</emph>
            - axy = o deſcribitur, hoc caſu fore
              <lb/>
            3exx - {3ey3/z} - aey + {aeyx/z} = o, termini ut nempe qui per
              <lb/>
            z dividuntur, habeant ſigna contraria iis quæ habebant
              <lb/>
            in æquatione deſcripta caſu priori, quæ erat 3exx +
              <lb/>
            {3ey
              <emph style="super">3</emph>
            /z} - aey - {aeyx/z}. </s>
            <s xml:id="echoid-s4900" xml:space="preserve">Ex hac verò priori ſequitur, quan-
              <lb/>
            do quantitas 3exx - aey, ſive quando 3xx - ay (quæ diviſo-
              <lb/>
            rem conſtituit ſecundum regulam) fuerit minor nihilo, ſive ne-
              <lb/>
            gata, tunc quantitatem reliquam {3ey
              <emph style="super">3</emph>
            /z} - {aeyx/z}; </s>
            <s xml:id="echoid-s4901" xml:space="preserve">ſive etiam
              <lb/>
            3y
              <emph style="super">3</emph>
            - ayx (quæ quantitatem dividendam ſecundùm regulam
              <lb/>
            conſtituit) eſſe affirmatam, aut cum illa eſt affirmata, hanc eſ-
              <lb/>
            ſenegatam; </s>
            <s xml:id="echoid-s4902" xml:space="preserve">quia omnes ſimul æquationis termini æquantur ni-
              <lb/>
            hilo. </s>
            <s xml:id="echoid-s4903" xml:space="preserve">At contra ex illa æquatione 3exx - {3ey
              <emph style="super">3</emph>
            /z} - aey +
              <lb/>
            {aeyx/z} = o, ſequitur, quando quantitas 3exx - aey, ſive
              <lb/>
            3xx - ay, fuerit negata, tunc reliquam - {3ey
              <emph style="super">3</emph>
            /z} + </s>
          </p>
        </div>
      </text>
    </echo>
Impressum