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

Page concordance

< >
Scan Original
181 451
182 452
183 453
184 454
185 455
186 456
187 457
188 458
189 459
190 460
191 461
192 462
193 463
194 464
195 465
196 466
197 467
198 468
199 469
200 470
201 471
202 472
203 473
204 474
205 475
206 476
207 477
208 478
209 479
210 480
< >
page |< < (479) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div235" type="section" level="1" n="116">
          <p>
            <s xml:id="echoid-s4379" xml:space="preserve">
              <pb o="479" file="0199" n="209" rhead="SUPER HUGENII EXCEPT."/>
            dem modo, quo Z. </s>
            <s xml:id="echoid-s4380" xml:space="preserve">componitur à quantitatibus
              <lb/>
              <note position="right" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">
                <lb/>
              Vax {2ax/a + Vax}
                <lb/>
              m
                <lb/>
              n
                <lb/>
              </note>
            B, 2 B; </s>
            <s xml:id="echoid-s4381" xml:space="preserve">Item eodem modo componatur n ex
              <lb/>
            quantitatibus Vax, {2ax/a + Vax}: </s>
            <s xml:id="echoid-s4382" xml:space="preserve">quantitates m, n, non
              <lb/>
            ſunt indefinite æquales ex prop. </s>
            <s xml:id="echoid-s4383" xml:space="preserve">11 Si igitur in-
              <lb/>
            ter m & </s>
            <s xml:id="echoid-s4384" xml:space="preserve">n fingatur æquatio; </s>
            <s xml:id="echoid-s4385" xml:space="preserve">a manente quantitate indefinita,
              <lb/>
            æquatio inter m & </s>
            <s xml:id="echoid-s4386" xml:space="preserve">n tot habebit radices ſeu quantitates, in
              <lb/>
            quas reſolvitur x, quot quantitatum, inter ſe diverſas ra-
              <lb/>
            tiones habentium, binarii ſunt in rerum natura, quæ vices
              <lb/>
            quantitatum a, x, ſubire poſſunt, h. </s>
            <s xml:id="echoid-s4387" xml:space="preserve">e. </s>
            <s xml:id="echoid-s4388" xml:space="preserve">quæ eandem quan-
              <lb/>
            titatem Analyticè ex ſe ipſis componit eodem modo, quo
              <lb/>
            eandem quantitas componitur ex ipſarum media Geometri-
              <lb/>
            ca Vax, & </s>
            <s xml:id="echoid-s4389" xml:space="preserve">ex media Harmonica inter dictam mediam
              <lb/>
            Geometricam & </s>
            <s xml:id="echoid-s4390" xml:space="preserve">x, nempe {2ax/a + Vax,} ita ut compoſitio ſit eo-
              <lb/>
            dem modo quo Z componitur ex B & </s>
            <s xml:id="echoid-s4391" xml:space="preserve">2B. </s>
            <s xml:id="echoid-s4392" xml:space="preserve">atque ex Conſe-
              <lb/>
            ctario Prop. </s>
            <s xml:id="echoid-s4393" xml:space="preserve">10. </s>
            <s xml:id="echoid-s4394" xml:space="preserve">omnes quantitatum binarii, rationes quoque
              <lb/>
            diverſas inter ſe habentium, B 2 B, C D, E F, G H, &</s>
            <s xml:id="echoid-s4395" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4396" xml:space="preserve">in infinitum, poſſunt ſupplere vices quantitatum a, x, quo-
              <lb/>
            niam Z eodem modo componitur ex B 2 B, quo ex C D, E F,
              <lb/>
            vel G H, &</s>
            <s xml:id="echoid-s4397" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4398" xml:space="preserve">& </s>
            <s xml:id="echoid-s4399" xml:space="preserve">proinde æquatio inter m & </s>
            <s xml:id="echoid-s4400" xml:space="preserve">n radices habet
              <lb/>
            numero infinitas. </s>
            <s xml:id="echoid-s4401" xml:space="preserve">Sed omnis æquatio habet ad ſummum tot
              <lb/>
            radices, quot habet dimenſiones; </s>
            <s xml:id="echoid-s4402" xml:space="preserve">& </s>
            <s xml:id="echoid-s4403" xml:space="preserve">proinde æquatio inter
              <lb/>
            m & </s>
            <s xml:id="echoid-s4404" xml:space="preserve">n dimenſiones habet numero infinitas, quod eſt abſur-
              <lb/>
            dum; </s>
            <s xml:id="echoid-s4405" xml:space="preserve">ideoque Z ſeu Circuli Sector non poteſt analyticè
              <lb/>
            componi ex Polygonis definitis B, 2B. </s>
            <s xml:id="echoid-s4406" xml:space="preserve">quod demonſtran-
              <lb/>
            dum erat. </s>
            <s xml:id="echoid-s4407" xml:space="preserve">Hinc manifeſtum eſt, Terminationem cujuſlibet
              <lb/>
            ſeriei convergentis, ſi non poſſit componi ex terminis con-
              <lb/>
            vergentibus indefinitè, nec poſſe componi definitè; </s>
            <s xml:id="echoid-s4408" xml:space="preserve">adeo-
              <lb/>
            que evaneſcit ſimul cum noſtra diſtinctione Objectio Huge-
              <lb/>
            nii prima.</s>
            <s xml:id="echoid-s4409" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4410" xml:space="preserve">Idem in Objectione ſua ſecunda non videtur advertiſſe,
              <lb/>
            me non ſolum in Prop. </s>
            <s xml:id="echoid-s4411" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4412" xml:space="preserve">ſed etiam in toto meo Tracta-
              <lb/>
            tulo intelligere per Extractionem radicum, Reſolutionem
              <lb/>
            omnium poteſtatum ſive purarum ſive affectarum; </s>
            <s xml:id="echoid-s4413" xml:space="preserve">omnium
              <lb/>
            quippe eadem eſt ratio, neque ulla imaginabilis eſt in de-
              <lb/>
            monſtratione diverſitas, ſive Sector ſupponatur Radix </s>
          </p>
        </div>
      </text>
    </echo>
Impressum