 In the 17th century, infinitary considerations in geometry opened the way to new geometrical techniques in quadratures and cubatures—i.e. the determination of areas of plane figures and of volumes of solid figures, respectively. We owe to Cavalieri and Torricelli a geometrical theory of indivisibles that was later put in an arithmetico-algebraic setting by Wallis (1656). Cavalieri’s original idea (1635) was that the relation between the areas of two plane figures could be obtained by a systematic comparison of what he called the indivisibles of the figures. An indivisible of a figure is a geometrical entity of lower dimension than the figure itself. An indivisible of a line is a point; an indivisible of a plane figure is a line segment; an indivisible of a solid is a plane figure. Consider a square with top side AB and bottom side CD. An indivisible of the square is any arbitrary segment with the same length as AB that can be obtained by letting AB move parallel to itself until it reaches CD. See the