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

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            <s xml:id="echoid-s4876" xml:space="preserve">
              <pb o="504" file="0226" n="237" rhead="CHRIST. HUGENII"/>
            ni diviſi per z ad alteram partem æquationis transferantur,
              <lb/>
            ductisque omnibus in z, diviſio deinde fiat per terminos in
              <lb/>
            quibus initio non erat z, exiſtere tunc ipſam quantitatem z
              <lb/>
            ab una æquationis parte; </s>
            <s xml:id="echoid-s4877" xml:space="preserve">uti hîc fiet z = - {3ey
              <emph style="super">3</emph>
            + aeyx/3exx - aey}.
              <lb/>
            </s>
            <s xml:id="echoid-s4878" xml:space="preserve">Atque hinc intelligo ad conſequendam quantitatem z, po-
              <lb/>
            nendos tantum eos terminos æquationis ſecundæ, qui deſcri-
              <lb/>
            pti ſunt ex terminis æquationis primæ in quibus y, ſublato
              <lb/>
            tantum denominatore z, mutatiſque ſignis + & </s>
            <s xml:id="echoid-s4879" xml:space="preserve">-. </s>
            <s xml:id="echoid-s4880" xml:space="preserve">Dein-
              <lb/>
            de dividendo iſtos terminos per eos qui deſcripti ſunt ex ter-
              <lb/>
            minis æquationis primæ in quibus x. </s>
            <s xml:id="echoid-s4881" xml:space="preserve">Porro ex omnibus, tam
              <lb/>
            diviſis quàm dividentibus, patet rejici poſſe e, adeo ut in hoc
              <lb/>
            exemplo fiat z = - {y
              <emph style="super">3</emph>
            3 + ayx/3xx - ay}. </s>
            <s xml:id="echoid-s4882" xml:space="preserve">Itaque rejicitur {e/z} ex
              <lb/>
            terminis qui deſcripti ſunt ab iis qui habent y. </s>
            <s xml:id="echoid-s4883" xml:space="preserve">Sic autem
              <lb/>
            deſcriptos eos ſuperius diximus ut ducerentur in idem
              <lb/>
            {e/z}, præponereturque numerus dimenſionum y. </s>
            <s xml:id="echoid-s4884" xml:space="preserve">Itaque ni-
              <lb/>
            hil requiri apparet ad terminos hoſce (quatenus ad definien-
              <lb/>
            dam quantitatem z hic adhibentur) ex terminis æquationis
              <lb/>
            primæ, in quibus y, deſcribendos, quam ut præponamus
              <lb/>
            tantum iis numerum dimenſionum quas in ipſis habet y, ſigna-
              <lb/>
            que + & </s>
            <s xml:id="echoid-s4885" xml:space="preserve">- invertamus. </s>
            <s xml:id="echoid-s4886" xml:space="preserve">Sic nempe ab y
              <emph style="super">3</emph>
            - axy, deſcribetur
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            - 3y
              <emph style="super">3</emph>
            + axy. </s>
            <s xml:id="echoid-s4887" xml:space="preserve">A terminis verò qui deſcripti ſunt à terminis æ-
              <lb/>
            quationis primæ in quibus x, cum tantum e hîc rejiciendum
              <lb/>
            patuerit, cumque hos ita prius deſcriptos dixerimus ut unum
              <lb/>
            x mutaretur in e, præponereturque numerus dimenſionum
              <lb/>
            ipſius x; </s>
            <s xml:id="echoid-s4888" xml:space="preserve">apparet eos, quatenus h@c ad conſtituendum diviſo-
              <lb/>
            rum adhibentur, ſic tantum deſcribi opus eſſe ex terminis pro-
              <lb/>
            poſitæ æquationis in quibus x, ut præponatur iis numerus di-
              <lb/>
            menſionum ipſius x, ac deinde unum x auferatur. </s>
            <s xml:id="echoid-s4889" xml:space="preserve">Sic nem-
              <lb/>
            pe ab x
              <emph style="super">3</emph>
            - axy deſcribetur 3x
              <emph style="super">3</emph>
            - axy; </s>
            <s xml:id="echoid-s4890" xml:space="preserve">& </s>
            <s xml:id="echoid-s4891" xml:space="preserve">dempto ubique x
              <lb/>
            uno, fiet 3xx - ay. </s>
            <s xml:id="echoid-s4892" xml:space="preserve">Atque ex his ratio regulæ ab initio poſitæ
              <lb/>
            manifeſta eſt. </s>
            <s xml:id="echoid-s4893" xml:space="preserve">Nam quod ſigna + & </s>
            <s xml:id="echoid-s4894" xml:space="preserve">- in terminis qui deſcri-
              <lb/>
            buntur ab iis in quibusy, hîc immutanda diximus, in </s>
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