in the Classical Mechanics (2nd. Ed.) book of Herbert Goldstein, p. 75 it says: "Equations 3-18 and 3-20 are the two remaining integrations, and formally the problem has been reduced to quadratures..."
It is not clear to me what a quadrature is, is it simply the integration process through some numerical analysis method such as trapezoidal rule? Or is it the process of reducing the order of the initial partial differential equation by using constants of motion?