A Treatise on the Line Complex

Originally published in 1903, this book contains a summary of the contemporary research on the theory of line-geometry. Jessop illustrates the text with many diagrams and various examples of how line theory can be applied. This book will be of particular value to anyone with an interest in the history of mathematics.Introduction; 1. System of coordinates; 2. The linear complex; 3. Synthesis of the linear complex; 4. Systems of linear complexes; 5. Ruled cubic and quartic surfaces; 6. The quadratic complex; 7. Special varieties of the quadratic complex; 8. The cosingular complexes; 9. Polar lines, points, and planes; 10. Representation of a complex by points of space; 11. The general equation of the second degree; 12. Connexion of line-geometry with sphere-geometry; 13. Connexion of line-geometry with hypergeometry; 14. Congruence of lines; 15. Congruences of the second order without singular curves; 16. The congruence of the second order and second class; 17. The general complex; 18. Differential equations connected with the line complex; Miscellaneous results and exercises; Index.