Introductio in analysin infinitorum

RECURRENTIBUS. 191 CAP. XIII. $p+q = \alpha$ & $pq = \mathfrak{b}$ : atque Seriei terminus generalis erit $(Ap^n + Bq^n)z^n$. Hinc facto $n=0$, erit $\mathcal{A} = A+B$; & facto $n=1$ erit $\mathcal{A} = Ap+Bq$; unde fit $\mathcal{A}q-B = A(q-p)$ & $A = \frac{\mathcal{A}q-B}{q-p}$; & $B = \frac{Ap-\mathcal{A}}{p-q}$. Inventis autem valoribus A & B, erit $P = Ap^n+Bq^n$ & $Q=Ap^{n+1}+Bq^{n+1}$. Tum vero erit $AB = \frac{\mathcal{B}\mathcal{B} - \alpha \mathcal{A}\mathcal{B} + \mathfrak{b}\mathcal{A}\mathcal{A}}{4\mathfrak{b}-\alpha\alpha}$. 227. Hinc deduci potest modus quemvis terminum ex unico praecedente formandi, cum ad hoc per legem progressionis duo requirantur. Cum enim fit $P = Ap^n+Bq^n$ & $Q = Ap \cdot p^n + Bq \cdot q^n$ erit $Pq-Q = A( [TRUNCATED]