1. The Simplest Geometric Manifolds I. Line-Segment, Area, Volume, as Relative Magnitudes II. The Grassmann Determinant Principle for the Plane III. The Grassmann Principle for Space IV. Classification of the Elementary Configurations of Space According to their Behavior under Transformation of Rectangular Coordinates V. Derivative Manifolds2. Geometric Transformations I. Affine Transformations II. Projective Transformations III. Higher Point Transformations IV. Transformations with Change of Space Element V. Theory of the Imaginary3. Systematic Discussion of Geometry and Its Foundations I. The Systematic Discussion II. Foundations of GeometryIndexes