This property is referred to as the "irrationality of dispersion."
Moreover the greater depths of the curves (or "curvature powers") in itself neutralize more or less the advantages obtained from the reduced irrationality of dispersion.
The general test of irrationality which he established is that, if a l a, a, be an interminate continued fraction, a l, a2,
The great abstract ideas (considered directly and not merely in tacit use) which have dominated the science were due to them - namely, ratio, irrationality, continuity, the point, the straight line, the plane.
In 1761 he proved the irrationality of 7r; a simpler proof was given somewhat later by Legendre.