Chapter 1. Co-ordinate systems -- Chapter 2. General Description of Loci of Equations -- Chapter 3. Projections of Lines and Areas Directions of Lines -- Chapter 4. Distance of Points Equations of a Straight Line -- Chapter 5. General Equation of the First Degree -- Chapter 6. Four-point Coordinate System -- Chapter 7. Transformation of Coordinates -- Chapter 8. On Certain Surfaces of the Second Order -- Chapter 9. On Generation by Lines and Circles -- Chapter 10. Modular and Umbical Generation of Surfaces of the Second Degree -- Chapter 11. General Equation of the Second Degree -- Chapter 12. Diametral Surfaces, Diametral Planes, Conjugate Diameters -- Chapter 13. Degrees of Surfaces and Curves -- Chapter 14. Tangents Lines Planes and Cones -- Chapter 15. Method of Reciprocal Polars -- Chapter 16. General Theory of Polars and Tangent Lines -- Chapter 17. Functional and Differential Equations -- Chapter 18. Properties of Conicoids -- Chapter 19. Curves -- Chapter 20. Envelopes -- Chapter 21. Volumes, Areas of Surfaces -- Chapter 22. Curvature of Curves -- Chapter 23. Curvature of Surfaces and Lines of Curvature -- Chapter 24. Geodesic Lines .

Intending as they have done, to make the subject more accessible, at least on the earlier portions, to all classes of students, they have endeavored to explain completely all the process which are most useful in dealing with ordinary theorems and problems connected with the straight line , and plane and particular surfaces of the second degree, and in doing so, their object has been to direct the student to the selection of the method which best adapted to the exigencies of each problem.