Introductio in analysin infinitorum

38 DE TRANSFORMATIONE FUNCTIONUM LIB. I. ergo $c+dz=(a+bz)xx$, hincque $z=\frac{c-axx}{bxx-d}$. Quare porro fiet $a+bz=\frac{bc-ad}{bxx-d}$; & ob $y=\sqrt{((a+bz)(c+dz))}$ $=(a+bz)x$ habebitur $y=\frac{(bc-ad)x}{bxx-d}$. Functio ergo irrationalis $y=\sqrt{((a+bz)(c+dz))}$ ad rationalitatem per- ducitur ope substitutionis $z=\frac{c-axx}{bxx-d}$, quippe quae dabit $y=\frac{(bc-ad)x}{bxx-d}$. Sic, si fuerit $y=\sqrt{(aa-zz)}=\sqrt{((a+z)(a-z))}$; ob $b=+1$; $c=a$, $d=-1$, ponatur $z=\frac{a-axx}{1+xx}$, eritque $y=\frac{2ax}{1+xx}$. Quoties ergo quantitas post signum $\sqrt{}$ habuerit duos Factores simplices reales, hoc modo reductio ad rationalitatem absolvetur; sin autem Factores bini simplices fuerint imaginarii, sequenti modo uti praestabit. 51. Sit $y=\ [TRUNCATED]