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

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            <s xml:id="echoid-s4710" xml:space="preserve">
              <pb o="496" file="0218" n="229" rhead="CHRIST. HUGENII"/>
            meratoris partis alterius e carentes, omitti poſſe, cum quan-
              <lb/>
            titates inde ortæ eædem utrinque eſſent futuræ ideoque de-
              <lb/>
            lendæ. </s>
            <s xml:id="echoid-s4711" xml:space="preserve">Quare in terminis poſterioribus ii tantum ab ini-
              <lb/>
            tio ſcribendi erant in quibus unum e, omiſſis omnibus reli-
              <lb/>
            quis, ut æquatio hîc futura ſit iſta
              <lb/>
            {bx
              <emph style="super">3</emph>
            - ccxx - 2bccx/bcc + x
              <emph style="super">3</emph>
            } = {3bexx - 2ccex - 2bcce/3exx}</s>
          </p>
          <p>
            <s xml:id="echoid-s4712" xml:space="preserve">Hîc jam multiplicationes alternæ per denominatores in-
              <lb/>
            ſtituendæ eſſent ad tollendas fractiones. </s>
            <s xml:id="echoid-s4713" xml:space="preserve">Verum examinan-
              <lb/>
            do diligentius quænam futura ſint harum multiplicationum
              <lb/>
            producta, aliud adhuc compendium inveniemus, & </s>
            <s xml:id="echoid-s4714" xml:space="preserve">nec
              <lb/>
            ſcribendos quidem omnino eſſe terminos poſteriores: </s>
            <s xml:id="echoid-s4715" xml:space="preserve">quia
              <lb/>
            enim deſcribuntur ex prioribus mutato x in e, præpoſito-
              <lb/>
            que numero dimenſionum ipſius x, non difficile eſt col-
              <lb/>
            ligere ex ſolis terminis prioribus quænam futura ſint iſta
              <lb/>
            omnia producta.</s>
            <s xml:id="echoid-s4716" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4717" xml:space="preserve">Ita quoniam propter - ccxx in prioribus, habetur -
              <lb/>
            2ccex in poſterioribus; </s>
            <s xml:id="echoid-s4718" xml:space="preserve">& </s>
            <s xml:id="echoid-s4719" xml:space="preserve">propter x
              <emph style="super">3</emph>
            in denominatore prio-
              <lb/>
            rum, in poſteriorum denominatore eſt 3exx; </s>
            <s xml:id="echoid-s4720" xml:space="preserve">facile per-
              <lb/>
            ſpicitur utraque producta ex - ccxx in 3exx & </s>
            <s xml:id="echoid-s4721" xml:space="preserve">ex -
              <lb/>
            2ccex in x
              <emph style="super">3</emph>
            , quæ ſunt - 3ccex
              <emph style="super">4</emph>
            & </s>
            <s xml:id="echoid-s4722" xml:space="preserve">- 2ccex
              <emph style="super">4</emph>
            , eaſdem
              <lb/>
            literas habitura, ſed diverſos numeros præpoſitos 3 & </s>
            <s xml:id="echoid-s4723" xml:space="preserve">2,
              <lb/>
            idque inde fieri quòd in termino ccxx unam dimenſio-
              <lb/>
            nem minus habeat x quam in termino x
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s4724" xml:space="preserve">Itaque & </s>
            <s xml:id="echoid-s4725" xml:space="preserve">au-
              <lb/>
            ferendo poſtea ex utraque parte æquationis, - 2ccex
              <emph style="super">4</emph>
            , ap-
              <lb/>
            paret ſuperfuturum - ccex
              <emph style="super">4</emph>
            à parte terminorum priorum.
              <lb/>
            </s>
            <s xml:id="echoid-s4726" xml:space="preserve">Quare ab initio hoc ſciri poteſt, multiplicando tantum in
              <lb/>
            terminis prioribus - ccxx numeratoris in x
              <emph style="super">3</emph>
            denomina-
              <lb/>
            toris, unumque x in e mutando, ac productum ſimplex ſcri-
              <lb/>
            bendo; </s>
            <s xml:id="echoid-s4727" xml:space="preserve">quia differentia dimenſionum x in iſtis duobus ter-
              <lb/>
            minis eſt unitas.</s>
            <s xml:id="echoid-s4728" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4729" xml:space="preserve">Eadem ratione producta ex - 2bccx in 3exx, & </s>
            <s xml:id="echoid-s4730" xml:space="preserve">ex -
              <lb/>
            2bcce in x
              <emph style="super">3</emph>
            , quæ eaſdem literas habent, ſunt enim -
              <lb/>
            6bccex
              <emph style="super">3</emph>
            & </s>
            <s xml:id="echoid-s4731" xml:space="preserve">- 2bccex
              <emph style="super">3</emph>
            , habebunt numeros præpoſitos </s>
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