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Part I. Principles of Algebraic Symbolism: 1. On the nature of a calculus; 2. Manifolds; 3. Principles of universal algebra; Part II. The Algebra of Symbolic Logic: 1. The algebra of symbolic logic; 2. The algebra of symbolic logic (continued); 3. Existential expressions; 4. Application to logic; 5. Propositional interpretation; Part III. Positional Manifolds: 1. Fundamental propositions; 2. Straight lines and planes; 3. Quadrics; 4. Intensity; Part IV. Calculus of Extension: 1. Combinatorial multiplication; 2. Regressive multiplication; 3. Supplements; 4. Descriptive geometry; 5. Descriptive geometry of conics and cubics; 6. Matrices; Part V. Extensive Manifolds of Three Dimensions: 1. Systems of forces; 2. Groups of systems of forces; 3. In variants of groups; 4. Matrices and forces; Part VI. Theory of Metrics: 1. Theory of distance; 2. Elliptic geometry; 3. Extensive manifolds and elliptic geometry; 4. Hyperbolic geometry; 5. Hyperbolic geometry (continued); 6. Kinematics in three dimensions; 7. Curves and surfaces; 8. Transition to parabolic geometry; Part VII. The Calculus of Extension to Geometry: 1. Vectors; 2. Vectors (continued); 3. Curves and surfaces; 4. Pure vector formulae.