In this examination of the Babylonian cuneiform "algebra" texts,
based on a detailed investigation of the terminology and discursive
organization of the texts, Jens Hoyrup proposes that the
traditional interpretation must be rejected. The texts turn out to
speak not of pure numbers, but of the dimensions and areas of
rectangles and other measurable geometrical magnitudes, often
serving as representatives of other magnitudes (prices, workdays,
etc...), much as pure numbers represent concrete magnitudes in
modern applied algebra. Moreover, the geometrical procedures are
seen to be reasoned to the same extent as the solutions of modern
equation algebra, though not built on any explicit deductive
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