Regarding the contents of the book, this meant that all the subjects of higher mathematics (such as mathematical logic, group theory,
analytic, non-euclidian, and projective geometries, and integral calculus) could not be dealt with.2 The simpler manner of presentation was conditioned by the fact that neither the necessary mathematical symbols (such as the symbolism of mathematical logic used in PM or that of analytical geometry used in UA) nor the
rigorous mathematical
methods (such as axioms, definitions, and proofs) could be utilized.