Introduction to Algebraic Geometry

Originally published in 1950 and written by the renowned mathematician, university professor, author and World War II codebreaker W. Gordon Welchman (1906?85), this textbook contains a treatment of projective geometry and provides a solid introduction to similar studies in space of more than two dimensions. The first three chapters analyse and establish the necessary foundations of the subject, whilst the remaining chapters are primarily concerned with the theory of conics, engaging with more complex topics such as metrical geometry, the application of matrix algebra, and invariants and covariants. The book also places much emphasis on the application of techniques rather than on the elementary principles of the subject and this is made easier by using algebraic foundations rather than purely geometrical axioms. This informative and insightful book will be of considerable value to scholars of mathematics as well as to anyone with an interest in the history of education.

Preface; 1. Introduction and definitions; 2. Algebraic systems and correspondences; 3. Rational systems of freedom one; 4. The conic; 5. Configurations; 6. Metrical geometry; 7. Homographic ranges on a conic; 8. Two conics, reciprocation of one conic into another. Particular cases; 9. Two conics. Apolarity; 10. Two-two correspondences; 11. Application of matrix algebra; 12. Invariants and covariants; List of books.