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

Table of Notes

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            verſos, propterea quod in - 2bccx una tantum eſt dimen-
              <lb/>
            ſio x; </s>
            <s xml:id="echoid-s4732" xml:space="preserve">at in x
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            tres, unde ablato ex utraque parte æqua-
              <lb/>
            tionis - 2bccex
              <emph style="super">3</emph>
            , ſcio ſuperfuturum à parte terminorum
              <lb/>
            priorum - 4bccex
              <emph style="super">3</emph>
            : </s>
            <s xml:id="echoid-s4733" xml:space="preserve">quod rurſus ab initio cognoſci po-
              <lb/>
            tuit, quia eadem quantitas oritur, multiplicando - 2bccx
              <lb/>
            numeratoris terminorum priorum, in x
              <emph style="super">3</emph>
            denominatoris,
              <lb/>
            mutandoque unum x in e, & </s>
            <s xml:id="echoid-s4734" xml:space="preserve">productum multiplicando per
              <lb/>
            2, quæ eſt differentia dimenſionum x in terminis - 2bccx
              <lb/>
            & </s>
            <s xml:id="echoid-s4735" xml:space="preserve">x
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s4736" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4737" xml:space="preserve">At quoniam in bx
              <emph style="super">3</emph>
            & </s>
            <s xml:id="echoid-s4738" xml:space="preserve">in x
              <emph style="super">3</emph>
            eadem eſt dimenſio x,
              <lb/>
            ſequetur producta ex bx
              <emph style="super">3</emph>
            in 3exx, & </s>
            <s xml:id="echoid-s4739" xml:space="preserve">ex 3bexx in x
              <emph style="super">3</emph>
            ,
              <lb/>
            tum literas eaſdem, tum eoſdem numeros præpoſitos ha-
              <lb/>
            bitura, ideoque ſeſe mutuo ſublatura, ut proinde multi-
              <lb/>
            plicatio illa omitti poſſit.</s>
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            <s xml:id="echoid-s4741" xml:space="preserve">Atque hujuſmodi animadverſionibus inventum eſt quod in
              <lb/>
            regula præcipitur, terminos ſingulos numeratoris in ſingu-
              <lb/>
            los denominatoris terminos eſſe ducendos, productaque quæ-
              <lb/>
            libet multipla ſumenda ſecundum differentiam dimenſionum
              <lb/>
            quantitatis incognitæ in terminis binis qui in ſe mutuò ducun-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s4742" xml:space="preserve">Nam quod non præcipitur unum x in e mutandum, id
              <lb/>
            hanc rationem habet, quod non referat utrum poſtea per e an
              <lb/>
            per x omnes termini dividantur.</s>
            <s xml:id="echoid-s4743" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4744" xml:space="preserve">Quod vero ſi ſigna affectionis vera productis ſingulis præ-
              <lb/>
            ponenda dicuntur, quoties dimenſiones x plures ſunt in nu-
              <lb/>
            meratore quam in denominatore, id quoque ex jam dictis in-
              <lb/>
            telligetur; </s>
            <s xml:id="echoid-s4745" xml:space="preserve">uti conſequenter etiam hoc quod contraria ſigna
              <lb/>
            ſunt adponenda, quoties dimenſionum numerus contra ſe
              <lb/>
            habet. </s>
            <s xml:id="echoid-s4746" xml:space="preserve">Velut hîc, productum ex bx
              <emph style="super">3</emph>
            in bcc ſcribendum
              <lb/>
            eſt cum ſigno - præpoſito numero 3, ut fiat - 3bbccx
              <emph style="super">3</emph>
            ,
              <lb/>
            quia nempe propter bx
              <emph style="super">3</emph>
            ſcimus in poſterioribus terminis
              <lb/>
            fore 3bexx; </s>
            <s xml:id="echoid-s4747" xml:space="preserve">quod ductum in bcc faciet + 3bbccexx, ſed
              <lb/>
            tranſlatum in partem priorem æquationis, fiet - 3bbccexx;
              <lb/>
            </s>
            <s xml:id="echoid-s4748" xml:space="preserve">ſive, non mutato x in e, - 3bbccx
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s4749" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4750" xml:space="preserve">Quod denique in regula habetur, quoties in prioribus ter-
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            minis priusquam ad eundem denominatorem reducantur,
              <lb/>
            quantitates cognitæ occurrunt eas primum omnium </s>
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