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

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            <s xml:id="echoid-s4894" xml:space="preserve">
              <pb o="505" file="0227" n="238" rhead="CEOMET. VARIA"/>
            verò nulla omnino immutanda, id eodem redire liquet cùm
              <lb/>
            quantitatem negatam, ſive minorem nihilo, tanquam affir-
              <lb/>
            matam conſiderandam ibi dixerimus. </s>
            <s xml:id="echoid-s4895" xml:space="preserve">Ut autem ratio obſer-
              <lb/>
            vationis ibidem adjectæ, in utram partem linea F E accipien-
              <lb/>
            da ſit, intelligatur, repetemus figuram in principio poſitam,
              <lb/>
              <note position="right" xlink:label="note-0227-01" xlink:href="note-0227-01a" xml:space="preserve">TAB. XLV.
                <lb/>
              fig. 5.</note>
            ubi vidimus A G eſſe x + e, E G vero z + e; </s>
            <s xml:id="echoid-s4896" xml:space="preserve">unde fiebat GD
              <lb/>
            + y + {ey/z}. </s>
            <s xml:id="echoid-s4897" xml:space="preserve">Si autem tangens ab altera parte lineæ B F cadere
              <lb/>
            intelligatur, velut be, atque hæc primùm curvam ſecare fin-
              <lb/>
            gatur, ut ibi factum eſt in d, ducaturque dg parallela bf; </s>
            <s xml:id="echoid-s4898" xml:space="preserve">fiet
              <lb/>
            ponendo rurſus fg = e, fe = z, ut A g quidem fiat x + e,
              <lb/>
            ſed eg erit z - e, unde gd = y - {ey/z}. </s>
            <s xml:id="echoid-s4899" xml:space="preserve">Atque hinc porrò fa-
              <lb/>
            cile eſt perſpicere æquationem ſecundam, quæ ex propoſita
              <lb/>
            æquatione, x
              <emph style="super">3</emph>
            + y
              <emph style="super">3</emph>
            - axy = o deſcribitur, hoc caſu fore
              <lb/>
            3exx - {3ey3/z} - aey + {aeyx/z} = o, termini ut nempe qui per
              <lb/>
            z dividuntur, habeant ſigna contraria iis quæ habebant
              <lb/>
            in æquatione deſcripta caſu priori, quæ erat 3exx +
              <lb/>
            {3ey
              <emph style="super">3</emph>
            /z} - aey - {aeyx/z}. </s>
            <s xml:id="echoid-s4900" xml:space="preserve">Ex hac verò priori ſequitur, quan-
              <lb/>
            do quantitas 3exx - aey, ſive quando 3xx - ay (quæ diviſo-
              <lb/>
            rem conſtituit ſecundum regulam) fuerit minor nihilo, ſive ne-
              <lb/>
            gata, tunc quantitatem reliquam {3ey
              <emph style="super">3</emph>
            /z} - {aeyx/z}; </s>
            <s xml:id="echoid-s4901" xml:space="preserve">ſive etiam
              <lb/>
            3y
              <emph style="super">3</emph>
            - ayx (quæ quantitatem dividendam ſecundùm regulam
              <lb/>
            conſtituit) eſſe affirmatam, aut cum illa eſt affirmata, hanc eſ-
              <lb/>
            ſenegatam; </s>
            <s xml:id="echoid-s4902" xml:space="preserve">quia omnes ſimul æquationis termini æquantur ni-
              <lb/>
            hilo. </s>
            <s xml:id="echoid-s4903" xml:space="preserve">At contra ex illa æquatione 3exx - {3ey
              <emph style="super">3</emph>
            /z} - aey +
              <lb/>
            {aeyx/z} = o, ſequitur, quando quantitas 3exx - aey, ſive
              <lb/>
            3xx - ay, fuerit negata, tunc reliquam - {3ey
              <emph style="super">3</emph>
            /z} + </s>
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