Introductio in analysin infinitorum

PER SERIES INFINITAS. 55 $\frac{xx+x}{xx-x-1} = \frac{-x(1+x)}{1+x-xx}$. Jam $\frac{1+x}{1+x-xx} = 1+xx-x^3+2x^4-3x^5+5x^6-\&c.$; unde erit $y = -x+0x^2+x^3+x^4-2x^5+3x^6-5x^7+\&c.$ &c. Vel ponatur $z = \frac{1-x}{1+x}$, erit $y = \frac{2-2x}{1-4x-xx}$; unde fit $y = 2-10x-42xx-178x^3-754x^4-\&c.$ cujusmodi Series recurrentes pro $y$ innumerabiles inveniri possunt. 71. Functiones irrationales ex hoc theoremate universali in Series infinitas transformari solent, quod fit $(P+Q)^{\frac{m}{n}}$ $= P^{\frac{m}{n}} + \frac{m}{n} P^{\frac{m-n}{n}} Q + \frac{m(m-n)}{n \cdot 2n} P^{\frac{m-2n}{n}} Q^2 + \frac{m(m-n)(m-2n [TRUNCATED]