"Makes the reader feel the inspiration that comes from listening to a great mathematician." Bulletin, American Mathematical Society
A distinguished mathematician and educator enlivens abstract discussions of arithmetic, algebra, and analysis by means of graphical and geometrically perceptive methods. His three-part treatment begins with topics associated with arithmetic, including calculating with natural numbers, the first extension of the notion of number, special properties of integers, and complex numbers. Algebra-related subjects constitute the second part, which examines real...

This text begins with the simplest geometric manifolds, the Grassmann determinant principle for the plane and the Grassmann principle for space; and more. Also explores affine and projective transformations; higher point transformations; transformations with change of space element; and the theory of the imaginary. Concludes with a systematic discussion of geometry and its foundations. 1939 edition. 141 figures.