Methodus inveniendi lineas curvas

AD CURVAS INVENIENDAS ABSOLUTA. 33 EXEMPLUM VII. 38. Invenire curvam, in qua fit $\int (xx+yy)^n dx \sqrt{(1+pp)}$ maximum vel minimum. Cum hic fit $Z = (xx+yy)^n \sqrt{(1+pp)}$, erit $dZ = 2n(xx+yy)^{n-1}(xdx+ydy)\sqrt{(1+pp)} + \frac{(xx+yy)^n pdp}{\sqrt{(1+pp)}}$, ergo $N = 2n(xx+yy)^{n-1}y\sqrt{(1+pp)}$ & $P = \frac{(xx+yy)^n p}{\sqrt{(1+pp)}}$; ex quo pro curva quaesita ista habebitur aequatio $2n(xx+yy)^{n-1}ydx\sqrt{(1+pp)} = d\frac{(xx+yy)^n p}{\sqrt{(1+pp)}} = \frac{2n(xx+yy)^{n-1}p(xdx+ydy)}{\sqrt{(1+pp)}} + \frac{dp(xx+yy)^n}{(1+pp)^{\frac{3}{2}}}$, quae per $(xx+yy)^{n-1}$ divisa, ac per $\sqrt{(1+pp)}$ multiplicata, abit in $\frac{2nydx}{x} = \frac{2 [TRUNCATED]