"Kepler's attempts at integration... led Cavalieri to develop his method of indivisibles... which may also have been suggested to him by Aristotle's tract De lineis insecabilibus [On indivisible lines]... It may also have been suggested by one of the fragments of Xenocrates (c. 350 B.C.)... who wrote upon indivisible lines. ... Cavalieri... seems to have looked upon a solid as made up practically of superposed surfaces, a surface as made up of lines, and a line as made up of points, these component parts being the ultimate possible elements in the decomposition of the magnitude. He then proceeded to find lengths, areas, and volumes of the summation of these "indivisibles," that is, by the summation of an infinite number of s. Such a conception of magnitude cannot be satisfactory to any scientific mind, but it formed a kind of intuitive step in the development of the method of integration and undoubtedly stimulated men like Leibniz to exert their powers to place the theory upon a scientific foundation. ... Cavalieri was able to solve various elementary problems in the mensuration of lengths, areas, and volumes, and also to give a fairly satisfactory proof of the theorem of Pappus with respect to the volume generated by the revolution of a plane figure about an axis."