Cavalieri was an Italian mathematician and student of Galileo. Mathematicians Galileo Johannes Kepler (x-y), and Cavalieri the areas, volumes of gemetric figures by "the method of indivisibles", treating the figure as composed of an infinite number of "atoms" of area or volume whose "sum" gave the area or volume of the figure. In 1635, in his book, Geometria indivisibilibis, Cavalieri stated what became known as "Cavalieri's Principle" for handling the "indivisibles" reliably to obtain correct answers: If two solids have the same height, and if their cross sections taken parallel to and at equal distances from their bases are always equal, then the solids have the same volume. This was a stepping stone towards the calculus, but is not usually taught to students.

See Mathematics, The Science of Patterns, Keith Devlin.