ABSTRACT
Calculation using the concepts of geometry in relation to the rules of an algebra has for many years been the aim of the research of many mathematicians, Leibnitz and Carnot being two of them. W. R. Hamilton was the first to make systematic constructions and he created the quaternions. He generalized the complex numbers to that space and was obliged to abandon commutativity for the product. H. Grassmann defined the interior and exterior products of the vectors. The unification of the two former points of view was performed by W. K. Clifford in the same algebra. The algebra of space is the algebra of the three-dimensional space of euclidean geometry.
