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

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              <pb o="493" file="0215" n="226" rhead="GEOMET. VARIA."/>
            nihil opus eſſe deſcribi, cum utrobique mox delendi forent,
              <lb/>
            atque adeo illos tantum ſcribendos in quibus unum e vel plu-
              <lb/>
            ra inſunt, ut in exemplo noſtro - 2ce + 4ex + 2ee; </s>
            <s xml:id="echoid-s4659" xml:space="preserve">eoſ-
              <lb/>
            que æquandos nihilo. </s>
            <s xml:id="echoid-s4660" xml:space="preserve">Sed etiam illos quibus plura quam u-
              <lb/>
            num e inerunt, ſcribi ſruſtra apparet, cum diviſione facta
              <lb/>
            per e delendos poſtea conſtet, ut paulò ante diximus. </s>
            <s xml:id="echoid-s4661" xml:space="preserve">Ita-
              <lb/>
            que nulli præterea ab initio deſcribendi inter terminos poſte-
              <lb/>
            riores quam quibus inerit e ſimplex.</s>
            <s xml:id="echoid-s4662" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4663" xml:space="preserve">Hi autem termini ex terminis prioribus facilè deducuntur,
              <lb/>
            cum conſtet nihil aliud eſſe quam ſecundos terminos poteſta-
              <lb/>
            tum ab x + e, quia cæteri omnes plura quam unum e vel nullum
              <lb/>
            habent. </s>
            <s xml:id="echoid-s4664" xml:space="preserve">Adeo ut ubicunque in prioribus terminis habe-
              <lb/>
            tur x, ſcribendum ſit in poſterioribus e; </s>
            <s xml:id="echoid-s4665" xml:space="preserve">& </s>
            <s xml:id="echoid-s4666" xml:space="preserve">ubi habe-
              <lb/>
            tur xx in prioribus, ponendum 2ex in poſterioribus; </s>
            <s xml:id="echoid-s4667" xml:space="preserve">& </s>
            <s xml:id="echoid-s4668" xml:space="preserve">ubi
              <lb/>
            x
              <emph style="super">3</emph>
            in prioribus, in poſterioribus 3exx, atque ita deinceps.
              <lb/>
            </s>
            <s xml:id="echoid-s4669" xml:space="preserve">Dicti autem termini ſecundi cujuſque poteſtatis x + e exipſa
              <lb/>
            poteſtate x facilè deſcribuntur mutando unum x in e, & </s>
            <s xml:id="echoid-s4670" xml:space="preserve">
              <lb/>
            præponendo numerum dimenſionum ipſius x, ita enim ab
              <lb/>
            xx fit 2ex, & </s>
            <s xml:id="echoid-s4671" xml:space="preserve">ab x
              <emph style="super">3</emph>
            , 3exx; </s>
            <s xml:id="echoid-s4672" xml:space="preserve">atque in cæteris pari modo. </s>
            <s xml:id="echoid-s4673" xml:space="preserve">
              <lb/>
            Itaque ex terminis prioribus in quibus x, quos ſolos conſi-
              <lb/>
            derandos eſſe patuit, facilè etiam termini poſteriores, ii
              <lb/>
            quos nihilo adæquandos diximus, deſcribuntur; </s>
            <s xml:id="echoid-s4674" xml:space="preserve">multipli-
              <lb/>
            cando tantum ſingulos in numerum dimenſionum quas in ipſis
              <lb/>
            habet x. </s>
            <s xml:id="echoid-s4675" xml:space="preserve">Nam mutare unum x in e ne quidem opus eſt, cum
              <lb/>
            eodem redeat, ſive omnes poſtea per e ſive per x dividan-
              <lb/>
            tur, & </s>
            <s xml:id="echoid-s4676" xml:space="preserve">ex his quidem aperta eſt ratio compendii ad primam
              <lb/>
            partem regulæ pertinentis: </s>
            <s xml:id="echoid-s4677" xml:space="preserve">nunc ad alteram veniamus quæ
              <lb/>
            eſt hujuſmodi.</s>
            <s xml:id="echoid-s4678" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4679" xml:space="preserve">Si termini quos maximum aut minimum deſignare volu-
              <lb/>
            mus fractiones habeant in quarum denominatore occurrat
              <lb/>
            quantitas incognita, delendæ primùm ſunt quantitates co-
              <lb/>
            gnitæ ſi quæ adſint; </s>
            <s xml:id="echoid-s4680" xml:space="preserve">deinde ſi reliquæ quantitates non ha-
              <lb/>
            beant eundem denominatorem, eò reducendæ ſunt. </s>
            <s xml:id="echoid-s4681" xml:space="preserve">Tunc
              <lb/>
            termini ſinguli numeratorem fractionis conſtituentes, du-
              <lb/>
            cendi in terminos ſingulos denominatoris, productaque
              <lb/>
            ſingula multipla ſumenda ſecundum numerum quo </s>
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