Methodus inveniendi lineas curvas

ELASTICIS. 277 53. Sit $2aa=bb$, & cum fit $fin. \frac{ss}{bb} = \frac{s^3}{b^2} - \frac{s^7}{1.2.3 b^6} + \frac{s^{11}}{1.2.3.4.5 b^{10}} - \frac{s^{15}}{1.2.3.4.5.6.7 b^{14}} + \&c.$ $cof. \frac{ss}{bb} = 1 - \frac{s^5}{1.2 b^4} + \frac{s^9}{1.2.3.4 b^8} - \frac{s^{13}}{1.2.3.4.5.6 b^{12}} + \&c.$ coordinatae $x$ & $y$ curvae quaesitae commode per series infinitas exprimi poterunt: erit enim $x = s - \frac{s^5}{1.3 b^4} - \frac{s^9}{1.2.3.7 b^8} + \frac{s^{13}}{1.2.3.4.5.11 b^{12}} - \frac{s^{17}}{1.2.3.4.5.6.7.15 b^{16}} + \&c.$ [TRUNCATED]