Introductio in analysin infinitorum

PER SUBSTITUTIONEM. 45 CAP. III. $z = ( \frac{ax^n + \mathfrak{G}x^{n-1} + \gamma x^{n-2} + \delta x^{n-3} + \&c.}{ax^m + bx^{m-1} + cx^{m-2} + dx^{m-3} + \&c.} )^{\frac{1}{m-n}}$ & $y = x ( \frac{ax^n + \mathfrak{G}x^{n-1} + \gamma x^{n-2} + \delta x^{n-3} + \&c.}{ax^m + bx^{m-1} + cx^{m-2} + dx^{m-3} + \&c.} )^{\frac{1}{m-n}}$ Hæc scilicet resolutio locum habet, si in æquatione naturam Functionis $y$ per $z$ exprimente, duplex tantum ubique occurrit dimensionum ab $y$ & $z$ sumptarum numerus; uti in casu tractato in singulis terminis numerus dimensionum vel est $m$ vel $n$. 58. Si in aequatione inter $y$ & $z$ triplicis generis dimensiones occurrant, quarum summa tantum superet mediam, quantum hæc media infimam, ope resolutionis equationis quadratæ variabiles $y$ & $ [TRUNCATED]