Theory of Functions of a Complex Variable

Excerpt From Theory Of Functions Of A Complex Variable. In The First Chapter, I Have Introduced The Algebra Of Complex Num Bers As An Algebra Of Number-Pairs Without Giving A General Theory Of Number Systems Of Two (Or More) Units; I Have Rather Assumed With Out Discussion The Hypotheses Characteristic Of The Theory Of Ordinary Complex Numbers. The Second Chapter Contains A Detailed Geometrical Theory Of The Elementary Rational Functions Of A Complex Variable And The Conformal Representations Determined By Them. The Transition From The Plane To The Sphere By Stereographic Projection Is Also Considered; It Is Used At Various Places In The Following Chapters. The Chapter Closes With A Discussion Of The Symmetric Invariants Of Four Points As A Function Of Their Double Ratio; This Takes The Place Of An Example (In Itself Unimportant) Of A Rational Function Of A More General Character....