Mathematicians of the late seventeenth century focused on two problems that derived from Greek geometry, particularly from attempts to determine the ratio of the circumference of a circle to its diameter, the value now called pi. The first, which was related to the question of measuring the circumference of a circle, was rectification: how to find a straight line (recta) equal in length to the arc of a curve. The second problem, which was tied to the question of ascertaining the area of a circle, concerned quadrature: how to find a square (quadratum) equal in area to a given two-dimensional space. Of course, the exact statement of these problems changed over the centuries, and thus the seventeenth century inherited a curious conglomerate of specific questions within the two broad categories.

However, the standards by which solutions to questions of rectification and quadrature were judged successful remained remarkably constant in the centuries separating Greek and seventeenth-century mathematicians. With the formalization of analytic procedures in more recent centuries, questions involving area and length are now usually solved by trivial integrations that yield a numerical answer. But in earlier times the solutions had to be geometrically constructable, and even in the seventeenth century algebraic solutions had to be reducible to geometry by means of standard constructions like those outlined by Descartes in his Géométrie and codified by van Schooten in his Latin translation and commentary, Geometria.

Because Archimedes had already found the area under the parabola by geometric methods, the feasibility of performing at least some quadratures was never doubted.