Introductio in analysin infinitorum

112 DE INVESTIGATIONE LIB. I. formulæ $a^n + z^n$; quæ regula semper est tenenda quoties cof. $\phi$ fit vel $+1$ vel $-1$. EXEMPLUM. Evolvamus aliquot casus, quo isti Factores clarius ob oculos ponantur, atque hos casus in duas classes distribuamus, prout $n$ fuerit numerus vel par vel impar. Si $n=1$ Formulæ $a+z$ Factor est $a+z$ Si $n=2$ Formulæ $a^2+z^2$ Factor est $a^2+z^2$ Si $n=3$ Formulæ $a^3+z^3$ Factores sunt $a^2 - 2az.cof.\frac{1}{3}\pi + z^2$ $a+z$ Si $n=4$ Formulæ $a^4+z^4$ Factores funt $a^2 - 2az.cof.\frac{1}{4}\pi + z^2$ $a^2 - 2az.cof.\frac{3}{4}\pi + z^2$ Si $n=5$ Formulæ $a^5+z^5$ Factores funt $a^2 - 2az.cof [TRUNCATED]