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

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            eodem modo, quo analyticè componitur eadem quantitas ex
              <lb/>
            terminis ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, 2b
              <emph style="super">2</emph>
            a; </s>
            <s xml:id="echoid-s3175" xml:space="preserve">addendo, ſubtrahendo, multi-
              <lb/>
            plicando & </s>
            <s xml:id="echoid-s3176" xml:space="preserve">dividendo terminos a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b, ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            & </s>
            <s xml:id="echoid-s3177" xml:space="preserve">radices
              <lb/>
            ex factis extrahendo, eadem fieret quantitas ac ſi eodem mo-
              <lb/>
            do adderentur, ſubducerentur, multiplicarentur & </s>
            <s xml:id="echoid-s3178" xml:space="preserve">divide-
              <lb/>
            rentur termini ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, 2b
              <emph style="sub">2</emph>
            a, & </s>
            <s xml:id="echoid-s3179" xml:space="preserve">radices eædem ex factis
              <lb/>
            extraherentur, ſed poſterius fieri non poteſt, ergo nec prius;
              <lb/>
            </s>
            <s xml:id="echoid-s3180" xml:space="preserve">minorem ſic probo, ſi eadem fieret quantitas ex additione,
              <lb/>
            ſubductione, multiplicatione, diviſione & </s>
            <s xml:id="echoid-s3181" xml:space="preserve">radicum extractio-
              <lb/>
            ne terminorum a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b, ab
              <emph style="super">2</emph>
            + b
              <emph style="super">3</emph>
            , quæ fieret ex eadem ad-
              <lb/>
            ditione, ſubductione, multiplicatione, diviſione & </s>
            <s xml:id="echoid-s3182" xml:space="preserve">radicum
              <lb/>
            extractione terminorum ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, 2b
              <emph style="super">2</emph>
            a; </s>
            <s xml:id="echoid-s3183" xml:space="preserve">tunc addendo æ-
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            quales quantitates terminis a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b, ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a, vel ab illis
              <lb/>
            ſive ipſorum factis æquales quantitates ſubducendo, vel il-
              <lb/>
            los ſive ipſorum factos æqualibus quantitatibus multiplican-
              <lb/>
            do vel dividendo, vel denique illos ſive ipſorum factos eo-
              <lb/>
            dem modo in ſe multiplicando, vel ex iisdem easdem radi-
              <lb/>
            ces extrahendo, hasce analyticas operationes aliquo modo
              <lb/>
            mutando, reiterando vel utrumque vel neutrum faciendo,
              <lb/>
            fieri poſſent duo ultima producta, nempe unum à termino
              <lb/>
            ab
              <emph style="super">2</emph>
            + b
              <emph style="sub">3</emph>
            & </s>
            <s xml:id="echoid-s3184" xml:space="preserve">alterum à termino 2b
              <emph style="super">2</emph>
            a; </s>
            <s xml:id="echoid-s3185" xml:space="preserve">ita ut ultimum produ-
              <lb/>
            ctum ex termino a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b cum ultimo producto ex termino
              <lb/>
            ab
              <emph style="super">2</emph>
            + b
              <emph style="sub">3</emph>
            additum, ſubductum, multiplicatum, diviſum, & </s>
            <s xml:id="echoid-s3186" xml:space="preserve">
              <lb/>
            ex facto radice aliqua extracta (haſce analyticas operationes
              <lb/>
            aliquo modo mutando, reiterando vel utrumque vel neu-
              <lb/>
            trum faciendo) eandem efficiat quantitatem quam efficit ul-
              <lb/>
            timum productum ex termino ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a cum ultimo produ-
              <lb/>
            cto ex termino 2b
              <emph style="super">2</emph>
            a eodem omnino modo additum, ſubdu-
              <lb/>
            ctum, multiplicatum, diviſum, & </s>
            <s xml:id="echoid-s3187" xml:space="preserve">ex facto eadem etiam ra-
              <lb/>
            dice extracta, haſce analyticas operationes eodem omnino
              <lb/>
            modo mutando, reiterando vel utrumque vel neutrum fa-
              <lb/>
            ciendo; </s>
            <s xml:id="echoid-s3188" xml:space="preserve">ſed poſterius eſt abſurdum ergò & </s>
            <s xml:id="echoid-s3189" xml:space="preserve">prius: </s>
            <s xml:id="echoid-s3190" xml:space="preserve">ſequela
              <lb/>
            majoris patet ex octava definitione hujus, minorem ſic pro-
              <lb/>
            bo, in termino a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b reperitur poteſtas ipſius a nempe
              <lb/>
            a
              <emph style="super">3</emph>
            , quæ eſt altior ulla poteſtate ejusdem a in termino
              <lb/>
            ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a; </s>
            <s xml:id="echoid-s3191" xml:space="preserve">& </s>
            <s xml:id="echoid-s3192" xml:space="preserve">proinde terminos a
              <emph style="super">3</emph>
            + a
              <emph style="super">2</emph>
            b, ba
              <emph style="sub">2</emph>
            + b
              <emph style="super">2</emph>
            a, </s>
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