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

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            <s xml:id="echoid-s4138" xml:space="preserve">
              <pb o="470" file="0190" n="200" rhead="JAC. GREG. RESP."/>
            lem eſſe impoſſibilem. </s>
            <s xml:id="echoid-s4139" xml:space="preserve">Sed omnium maxime admiror, Cla-
              <lb/>
            riſſimum Virum non animadvertiſſe in 8. </s>
            <s xml:id="echoid-s4140" xml:space="preserve">definitione, Quan-
              <lb/>
            titates C, D, E, compoſitionem ingredientes, ſemper eſſe
              <lb/>
            eaſdem, nempe definitas & </s>
            <s xml:id="echoid-s4141" xml:space="preserve">invariabiles, ipſos autem termi-
              <lb/>
            nos A, B, eſſe indefinitos & </s>
            <s xml:id="echoid-s4142" xml:space="preserve">variabiles, nimirum in F,
              <lb/>
            G, & </s>
            <s xml:id="echoid-s4143" xml:space="preserve">infinitos alios: </s>
            <s xml:id="echoid-s4144" xml:space="preserve">at quis eſt qui non videt Hugenii
              <lb/>
            {b2 m/a2 + ba} non minus eſſe indefinitam, quam ſunt ipſi termini?
              <lb/>
            </s>
            <s xml:id="echoid-s4145" xml:space="preserve">Deinde in Proœmio noſtræ Geometriæ Partis univerſalis,
              <lb/>
            ſic dico. </s>
            <s xml:id="echoid-s4146" xml:space="preserve">Alii objiciunt contra prop. </s>
            <s xml:id="echoid-s4147" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4148" xml:space="preserve">ita: </s>
            <s xml:id="echoid-s4149" xml:space="preserve">ſi addatur
              <lb/>
            a
              <emph style="super">3</emph>
            termino a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b & </s>
            <s xml:id="echoid-s4150" xml:space="preserve">temino ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, enervetur vis u-
              <lb/>
            triuſque demonſtrationis. </s>
            <s xml:id="echoid-s4151" xml:space="preserve">Reſpondeo, a
              <emph style="super">3</emph>
            eſſe quantitatem
              <lb/>
            indefinitam, & </s>
            <s xml:id="echoid-s4152" xml:space="preserve">alias quantitates indefinitas præter ipſos
              <lb/>
            terminos convergentes compoſitionem non poſſe ingredi, quod
              <lb/>
            analyſtam latere non poteſt: </s>
            <s xml:id="echoid-s4153" xml:space="preserve">Eodem modo reſpondeo Huge-
              <lb/>
            nio {bbm/a2 + ab} eſſe quantitatem indefinitam, & </s>
            <s xml:id="echoid-s4154" xml:space="preserve">ideo compoſitio-
              <lb/>
            nem non poſſe ingredi: </s>
            <s xml:id="echoid-s4155" xml:space="preserve">Si autem mihi objiciat, in ſeptima
              <lb/>
            me credidiſſe, {mae - mbe/ad - bd} fuiſſe quantitatem indefinitam; </s>
            <s xml:id="echoid-s4156" xml:space="preserve">Re-
              <lb/>
            ſpondeo, etiamſi diviſio per a-b à me ſatis inconſideratè ne-
              <lb/>
            glecta ſit, apertè tamen conſtat, me hoc cognoviſſe, ex di-
              <lb/>
            verſitate methodorum, quibus utor in ſeptima & </s>
            <s xml:id="echoid-s4157" xml:space="preserve">decima,
              <lb/>
            quippe iſta particulari, in qua quantitatem illam quæro, & </s>
            <s xml:id="echoid-s4158" xml:space="preserve">
              <lb/>
            hac generali, in qua illam ſuppono; </s>
            <s xml:id="echoid-s4159" xml:space="preserve">nulla enim alia ratio
              <lb/>
            hujus diverſitatis excogitari poteſt; </s>
            <s xml:id="echoid-s4160" xml:space="preserve">quod etiam ex ipſis ſepti-
              <lb/>
            ma & </s>
            <s xml:id="echoid-s4161" xml:space="preserve">decima eſt manifeſtum, cum appellem ſemper termi-
              <lb/>
            nos convergentes quantitates indefinitas, hoc ipſo ſatis ſi-
              <lb/>
            gnificans, nullas alias quantitates indefinitas calculo in-
              <lb/>
            eſſe.</s>
            <s xml:id="echoid-s4162" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4163" xml:space="preserve">Semper credidi in rebus ſcientificis verba ita candidè eſſe
              <lb/>
            explicanda (ſi modo poſſibile ſit) ut diſcurſus nullum inclu-
              <lb/>
            dat abſurdum; </s>
            <s xml:id="echoid-s4164" xml:space="preserve">at Hugenius fatis percipit, diſcurſum nihil
              <lb/>
            continere abſurdi, modò nulla quantitas indefinita præter i-
              <lb/>
            pſos terminos compoſitionem ingrediatur; </s>
            <s xml:id="echoid-s4165" xml:space="preserve">judicat tamen abſ-
              <lb/>
            que omni ratione, me contrarium exiſtimaſſe; </s>
            <s xml:id="echoid-s4166" xml:space="preserve">libenter enim
              <lb/>
            optarem Hugenium aſſignaſſe locum, ubi aſſero, illam </s>
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