Area, volume, measure

Andrew McFarland

Joanna McFarland

James T. Smith

pp. 45-76

in: Andrew McFarland, Joanna McFarland, James T. Smith (eds), Alfred Tarski, Basel, Birkhäuser, 2014

Abstract

The synthetic approach to the theory of area and volume initiated by Euclid is described in the first section of this chapter. The area a of a polygonal region P is computed by decomposing P into a finite number of polygonal components with disjoint interiors, which can be reassembled to form a rectangle R with unit base: a is then the altitude of R. The volume of a polyhedral region can be reckoned in a similar way, but for that it is necessary to use some form of Eudoxus's method of exhaustion.