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Abstrakt

The aim of the paper is to reconstruct the historical development of classical algebra from Al Chwárizmí to Lagrange and to analyse the fundamental epistemological shifts, which occurred in the understanding of basic algebraic concepts. The paper opens with a general characteristics of algebraic thought as conceptualisation of motor schemes. That puts algebra into a contrast with geometry, which is based on conceptualization of the schemes of visual perception. From contrasting these two ways of conceptualisation, the motor and the visual, the autohor tries to explain why the ancient Greeks did not develop algebraic thought. Further he uses his theory of evolution of linguistic form to interpret the changes of the language of algebra beginning with Al Chwárizmí's verbal rules, through Cardano's formulas, Cartesian polynomial forms, up to Lagrange's theory of resolvents.