AbstractsMathematics

"The imaginary expression which occurs in common Algebra, and in all the higher departments of mathematical science, has been one of the most perplexing problems which the human mind has encountered in any age. It was studied by the early mathematicians and became a field of speculation, but developed no marked results, for it was generally considered algebraically and in the interpretation is a symbol of an impossible operation. But many of the problems arising from algebraic-geometrical analysis involving imaginaries was of such importance to mathematical and physical science that great attempts were made to establish their solution. It was known that the imaginary occurred in mathematical functions having real values, and so was supposed to have some real meaning" – Introduction, p. 1.