Introductio in analysin infinitorum

LIB. I. 272 DE PARTITIONE Quot modis datus numerus per additionem formari potest ex omnibus numeris integris inter se inæqualibus; totidem modis idem numerus formari poterit per additionem ex numeris tantum imparibus, sive æqualibus sive inæqualibus. 327. Cum igitur, ut ante vidimus, fit $P=1-x-x^2+x^5+x^7-x^{12}-x^{15}+x^{22}+x^{26}-x^{35}-x^{40}+\text{&c.}$, erit, scribendo $xx$ loco $x$, $PQ=1-x^2-x^4+x^{10}+x^{14}-x^{24}-x^{30}+x^{44}+x^{52}-\text{&c.}$, Quocirca erit hanc per illam dividendo $Q = \frac{1-x^2-x^4+x^{10}+x^{14}-x^{24}-x^{30}+\text{&c.}}{1-x-x^2+x^5+x^7-x^{12}-x^{15}+x^{22}+x^{26}-\text{&c.}}$ Erit ergo Series $Q$ pariter recurrens, atque ex Serie $\frac{1}{P}$ oritur, [TRUNCATED]