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

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          <p>
            <s xml:id="echoid-s3214" xml:space="preserve">
              <pb o="432" file="0150" n="159" rhead="VERA CIRCULI"/>
            jungo: </s>
            <s xml:id="echoid-s3215" xml:space="preserve">quantitas non poteſt componi analyticè ex terminis
              <lb/>
            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>
            , eodem modo quo componitur eadem
              <lb/>
            quantitas ex 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-s3216" xml:space="preserve">quoniam adden-
              <lb/>
            do, ſubſtrahendo, multiplicando, dividendo duo binomia
              <lb/>
            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-s3217" xml:space="preserve">radices ex ultimo facto extrahendo,
              <lb/>
            plura fiunt nomina in ultimo producto, quam ſi eodem mo-
              <lb/>
            do adderentur, ſubducerentur, multiplicarentur, divideren-
              <lb/>
            tur, binomium ba
              <emph style="super">2</emph>
            + b
              <emph style="super">2</emph>
            a & </s>
            <s xml:id="echoid-s3218" xml:space="preserve">ſimplex quantitas 2b
              <emph style="super">2</emph>
            a, & </s>
            <s xml:id="echoid-s3219" xml:space="preserve">eæ-
              <lb/>
            dem quoque radices ex facto extraherentur; </s>
            <s xml:id="echoid-s3220" xml:space="preserve">& </s>
            <s xml:id="echoid-s3221" xml:space="preserve">ſi plura ſint
              <lb/>
            nomina in uno producto quam in altero, impoſſibile eſt ut
              <lb/>
            ſint indefinitè æqualia, quod eſt propoſitum, reliqua enim
              <lb/>
            ex priore demonſtratione haberi poſſunt.</s>
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        <div xml:id="echoid-div169" type="section" level="1" n="79">
          <head xml:id="echoid-head115" xml:space="preserve">SCHOLIUM.</head>
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            <s xml:id="echoid-s3223" xml:space="preserve">Obſcurum fortaſſis videbitur hoc theorema ob multas in-
              <lb/>
            uſitatas in geometria voces quas hic adhibere oportet,
              <lb/>
            & </s>
            <s xml:id="echoid-s3224" xml:space="preserve">ob multa ſuppoſita lemmata, quæ demonſtrare pigebat,
              <lb/>
            quoniam cuivis analyſtæ vel prima lectione ſunt obvia, ex
              <lb/>
            natura enim operationum analyticarum omnino dependent.</s>
            <s xml:id="echoid-s3225" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3226" xml:space="preserve">Locus hic requirit ut aliquid dicam de proportione inter
              <lb/>
            triangulum A B P & </s>
            <s xml:id="echoid-s3227" xml:space="preserve">ſectorem A B I P; </s>
            <s xml:id="echoid-s3228" xml:space="preserve">quod ut fiat, adver-
              <lb/>
            tendum eſt veriſſimum philoſophorum axioma, nempe omnem
              <lb/>
            noſtram cognitionem à ſenſu ortum habere: </s>
            <s xml:id="echoid-s3229" xml:space="preserve">inter proportio-
              <lb/>
            nes enim, ſola commenſurabilis ſenſu attingitur & </s>
            <s xml:id="echoid-s3230" xml:space="preserve">perfectè
              <lb/>
            ab humana mente intelligitur; </s>
            <s xml:id="echoid-s3231" xml:space="preserve">incommenſurabilis enim à ma-
              <lb/>
            thematicis ſolummodo adhuc contemplatur, quatenus com-
              <lb/>
            menſurabilis cujusdam rationis eſt ſubduplicata, ſubtriplica-
              <lb/>
            ta, &</s>
            <s xml:id="echoid-s3232" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3233" xml:space="preserve">vel ex talium additione, ſubductione, &</s>
            <s xml:id="echoid-s3234" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3235" xml:space="preserve">genita:
              <lb/>
            </s>
            <s xml:id="echoid-s3236" xml:space="preserve">hoc eſt, quantitas quæ quantitati propoſitæ eſt incommen-
              <lb/>
            ſurabilis ex eo ſolummodo ab humana mente contemplatur,
              <lb/>
            quod ex aliquot quantitatum cognitarum & </s>
            <s xml:id="echoid-s3237" xml:space="preserve">propoſitæ quan-
              <lb/>
            titati commenſurabilium additione, ſubductione, multiplica-
              <lb/>
            tione, diviſione & </s>
            <s xml:id="echoid-s3238" xml:space="preserve">radicum extractione componi poſſit: </s>
            <s xml:id="echoid-s3239" xml:space="preserve">at
              <lb/>
            ex hactenus demonſtratis manifeſtum eſt ſectorem A B I P
              <lb/>
            non poſſe componi ex additione, ſubductione, </s>
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