[146] Logik (1873, 1889), Eng. trans. ii. 17.
[147] Op. cit. ii. 289.
[148] Introd. to Logic., trans. Abbott, p. 10.
[149] Ueber Annahmen (1902, &c.).
[150] Logik (1880, and in later editions).
[151] Yet see Studies in Logic, by John Dewey and others (1903).
LOGOCYCLIC CURVE, STROPHOID or FOLIATE, a cubic curve generated by increasing or diminishing the radius vector of a variable point Q on a straight line AB by the distance QC of the point from the foot of the perpendicular drawn from the origin to the fixed line. The polar equation is r cos θ = a(1 ± sinθ), the upper sign referring to the case when the vector is increased, the lower when it is diminished. Both branches are included in the Cartesian equation (x2 + y2)(2a − x) = a2x, where a is the distance of the line from the origin. If we take for axes the fixed line and the perpendicular through the initial point, the equation takes the form y √(a − x) = x √(a + x). The curve resembles the folium of Descartes, and has a node between x = 0, x = a, and two branches asymptotic to the line x = 2a.