Excerpt from Uniplanar Algebra, Vol. 1: Being of a Prop?deutic to the Higher Mathematical Analysis
From the beginning, with rare exceptions, a singular logical incompleteness has characterized our text-books in elementary algebra. By tradition algebra early became a mere technical device for turning out practical results, by careless reasoning inaccuracies crept into the explanation of its principles and, through compilers, are still perpetuated as current literature. Thus, instead of becoming a classic, like the geometry handed down to us from the Greeks, in the form of Euclid's Elements, algebra has become a collection of processes practically exemplified and of principles inadequately explained.
The labors of the mathematicians of the nineteenth century - Argand, Gauss, Cauchy, Grassmann, Peirce, Cayley, Sylvester, Kronecker, Weierstrass, G.Cantor, Dedekind and others - have rendered unjustifiable the longer continuance of this unsatisfactory state of algebraic science. We now know what an algebra is, and the problem of its systematic unfolding into organic form is a definite and achievable one. The short treatise here presented, as the first part of a Prop?deutic to the Higher Analysis, endeavors to place concisely in connected sequence the argument required for its solution.
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