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

Table of Notes

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              <pb o="478" file="0198" n="208" rhead="JAC. GREG. CONSID."/>
            indefinita reſolvetur in aliquam particularem, reſolutio fie-
              <lb/>
            ret vel ab Analyſi ſpecioſa vel numeroſa. </s>
            <s xml:id="echoid-s4347" xml:space="preserve">Sed neutrum dici
              <lb/>
            poteſt. </s>
            <s xml:id="echoid-s4348" xml:space="preserve">E. </s>
            <s xml:id="echoid-s4349" xml:space="preserve">Major patet ex ſufficienti enumeratione. </s>
            <s xml:id="echoid-s4350" xml:space="preserve">Minor
              <lb/>
            ſic probatur: </s>
            <s xml:id="echoid-s4351" xml:space="preserve">Non ab Analyſi ſpecioſa, quoniam hæc Me-
              <lb/>
            thodus indefinita ad eam eſt irreducibilis, ut patet ex Prop.
              <lb/>
            </s>
            <s xml:id="echoid-s4352" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4353" xml:space="preserve">Non à Numeroſa, quæ hic eſt interminabilis, proinde-
              <lb/>
            que invariabilis.</s>
            <s xml:id="echoid-s4354" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4355" xml:space="preserve">In hanc ultimam diſtinctionem reſolvitur 1. </s>
            <s xml:id="echoid-s4356" xml:space="preserve">objectio Hu-
              <lb/>
            genii. </s>
            <s xml:id="echoid-s4357" xml:space="preserve">Velim enim Nobiliſſ. </s>
            <s xml:id="echoid-s4358" xml:space="preserve">Virum conſiderare, omnem
              <lb/>
            plenam Problematis ſolutionem eſſe indefinitam. </s>
            <s xml:id="echoid-s4359" xml:space="preserve">Nam Me-
              <lb/>
            thodi particulares, cum ſint infinitæ, exhiberi omnes ne-
              <lb/>
            queunt; </s>
            <s xml:id="echoid-s4360" xml:space="preserve">neque dirigi poſſunt à tenore Problematis quippe
              <lb/>
            illis omnibus communi: </s>
            <s xml:id="echoid-s4361" xml:space="preserve">Ideoque requiritur Methodus Ge-
              <lb/>
            neralis ſeu Indefinita, Particularium directrix. </s>
            <s xml:id="echoid-s4362" xml:space="preserve">Agnoſco u-
              <lb/>
            tique Methodos Particulares caſu ſæpe inveniri abſque ope
              <lb/>
            Generalis; </s>
            <s xml:id="echoid-s4363" xml:space="preserve">attamen fatendum eſt Geometris, nullam eſſe,
              <lb/>
            nec poſſe fieri Mothodum Particularem, in quam reſolubi-
              <lb/>
            lis non ſit Methodus indefinita. </s>
            <s xml:id="echoid-s4364" xml:space="preserve">Si igitur Methodus Indefi-
              <lb/>
            nita omni reſolutioni ſit impervia (ut in Prop. </s>
            <s xml:id="echoid-s4365" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4366" xml:space="preserve">eſt de-
              <lb/>
            monſtratum) eodem modo omnes Particulares reſolutionem
              <lb/>
            @tiam reſpuent; </s>
            <s xml:id="echoid-s4367" xml:space="preserve">proindeque tam Definita, quam Indefinita
              <lb/>
            nullam compoſitionem agnoſcit. </s>
            <s xml:id="echoid-s4368" xml:space="preserve">Talis enim Compoſitio,
              <lb/>
            qualis Reſolutio.</s>
            <s xml:id="echoid-s4369" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4370" xml:space="preserve">Etiamſi prædicta, meo quidem judicio, adundè ſufficiant,
              <lb/>
            ne tamen ullus relinquatur cavillationi locus, 11
              <emph style="super">mam</emph>
            noſtram
              <lb/>
            Prop. </s>
            <s xml:id="echoid-s4371" xml:space="preserve">etiam in Definitis hic demonſtrabimus. </s>
            <s xml:id="echoid-s4372" xml:space="preserve">Sit ergò B
              <lb/>
            Polygonum intra Circuli ſectorem, 2 B Polygonum circum-
              <lb/>
            ſcriptum & </s>
            <s xml:id="echoid-s4373" xml:space="preserve">priori ſimile; </s>
            <s xml:id="echoid-s4374" xml:space="preserve">ſufficit enim Polygonorum propor-
              <lb/>
            tionem definire, ut Theorema definitè demonſtretur. </s>
            <s xml:id="echoid-s4375" xml:space="preserve">Con-
              <lb/>
            tinuetur ſeries convergens ut ſit ejus teminatio
              <lb/>
              <note position="right" xlink:label="note-0198-01" xlink:href="note-0198-01a" xml:space="preserve">
                <lb/>
              B # 2 B
                <lb/>
              C # D
                <lb/>
              E # F
                <lb/>
              G # H
                <lb/>
              ## Z
                <lb/>
              a # x
                <lb/>
              </note>
            feu Circuli Sector Z. </s>
            <s xml:id="echoid-s4376" xml:space="preserve">Dico, Z non poſſe com-
              <lb/>
            poni analyticè ex Polygonis definitis B, 2 B. </s>
            <s xml:id="echoid-s4377" xml:space="preserve">Si
              <lb/>
            fieri poteſt, componatur Z Analytice ex Poly-
              <lb/>
            gonis Definitis B, 2 B. </s>
            <s xml:id="echoid-s4378" xml:space="preserve">ſintque duæ quantitates
              <lb/>
            Indefinitæ a & </s>
            <s xml:id="echoid-s4379" xml:space="preserve">x, è quibus componatur m </s>
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