Before computing volumes with the integral, let us see an intuitive principle that characterises them geometrically, without yet using integral calculus: Cavalieri’s principle (Bonaventura Cavalieri, a pupil of Galileo, 1635). It is the same principle that justifies the equidecomposability of plane figures, and by summing “infinitely many infinitesimal cross-sections” it anticipates integral calculus by a century.