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

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            <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>
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