Among his later poems may be mentioned La Divine Tragedie (1916) and La Quadrature de l'Amour (1920).
The intercept on the axis of y is 2a/7r; therefore, if it were possible to accurately construct the curve, the quadrature of the circle would be effected.
On the other hand, it is worth noticing that the words " quadrature " and " cubature " are originally due to geometrical rather than numerical considerations; the former implying the construction of a square whose area shall be equal to that of a given surface, and the latter the construction of a cube whose volume shall be equal to that of a given solid.
He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the quadrature of the parabola y=xm, where m is a positive integer, the area of the curves when m is negative or fractional.
In the same work Wallis obtained an expression for the length of the element of a curve, which reduced the problem of rectification to that of quadrature.