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(2014) Alfred Tarski, Basel, Birkhäuser.
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.
Publication details
DOI: 10.1007/978-1-4939-1474-6_4
Full citation:
McFarland, A. , McFarland, J. , Smith, J.T. (2014)., Area, volume, measure, in A. Mcfarland, J. Mcfarland & J. T. Smith (eds.), Alfred Tarski, Basel, Birkhäuser, pp. 45-76.
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