Epistemological aspects of the history of classical algebra

The aim of the paper is to reconstruct the historical development of classi cal algebra from Al Khwarizmi to Lagrange and to analyse the fundamental ep istemological shifts, which occurred in the understanding of basic algebrai c concepts. The paper opens with a general characteristics of algebraic tho ught as conceptualization of motor schemes. That puts algebra into a contra st with geometry, which is based on conceptualization of the schemes of vis ual perception. From contrasting these two ways of conceptualization, the m otor and the visual, the author 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 beginni ng with Al Khwarizmi's verbal rules, through Cardano's formulas, Cartesian polynomial forms, up to Lagrange's theory of resolvents.