ix 
TABLE OF CONTENTS 
PART I 
Illustrations, Geometrical Interpretations and Applications 
of Invariants and Covariants 
PAGE 
§ 1. Illustrations from Plane Analytics 1 
§2. Projective Transformations 4 
§ 3. Homogeneous Coordinates of a Point in a Line 8 
§ 4. Examples of Invariants 9 
§ 5. Examples of Covariants 11 
§ 6. Forms and Their Classification 14 
§ 7. Definition of Invariants and Covariants 14 
Exercises 15 
§ 8. Invariants of Covariants 16 
§ 9. Canonical Form of a Binary Cubic. Solution of Cubic Equations 17 
§ 10. Covariants of Covariants 18 
§11. Intermediate Invariants and Covariants 19 
Exercises 20 
§ 12. Homogeneous Coordinates of Points in a Plane 20 
§ 13. Properties of the Hessian 23 
§ 14. Inflexion Points and Invariants of a Cubic Curve 26 
Exercises 28 
PART II 
Theory of Invariants in Non-symbolic Notation 
§ 15. Homogeneity of Invariants 30 
§ 16. Weight of an Invariant of a Binary Form 31 
§ 17. Weight of an Invariant of any System of Forms 32 
Exercises 33 
§ 18. Products of Linear Transformations 33 
§ 19. Generators of all Binary Linear Transformations 34 
§ 20. Annihilator of an Invariant of a Binary Form 34 
Example and Exercises 36 
§ 21. Homogeneity of Covariants 37 
§ 22. Weight of a Covariant of a Binary Form 38 
§ 23. Annihilators of Covariants 39 
Exercises 40