Introductio in analysin infinitorum

PER SUSTITUTIONEM. 39 resolvi poterit, qui casus ad §. præced. reducitur. Sæpenume- CAP. III. ro autem commodius ad hanc formam reducitur, $y = \surd(aa+(b+cz)(d+ez))$; pro qua ad rationalitatem perducenda ponatur $y=a+(b+cz)x$, eritque $d+ez = 2ax+bxx+cxxz$; unde fit $z = \frac{d-2ax-bxx}{cxx-e}$, & $y = \frac{ae+(cd-be)x-acxx}{cxx-e}$. Interdum commodius fieri potest reductio ad hanc formam, $y = \surd(aazz+(b+cz)(d+ez))$. Tum ponatur $y = az+(b+cz)x$; erit $d+ez = 2axz+bxx+cxxz$ & $z = \frac{bxx-d}{e-2ax-cxx}$, atque $y = \frac{-ad+(be-cd)x-abxx}{e-2ax-cxx}$. EXEMPLUM. Si habeatur ista ipsius $z$ Functio irrationalis $y = \surd(-1+3z-2zz)$; quæ cum reduci queat ad hanc formam $y = \surd(1-2 [TRUNCATED]