Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

POSTULATE PROPERTIES 13S
attempts, pretty successfully, to avoid philosophic questions, may yet be recommended to philosophical students
as a collection of essays affording an introduction to a
variety of important elementary topics of modern mathematics: namely, Veblen's The Foundations of Geometrywhich does not deal with the foundations of geometry in
general, but gives the reader a finely histological view of
the ultimate tissues and minute logical structure of the
first parts of Euclidean metric geometry; Non-Euclidean
Geometry, by Professor F. S. Woods-resembling Veblen's
essay in spirit and method, hardly surpassed as an introduction, for beginners, to the geometries of Lobachevski
and Riemann; Modern Pure Geometry, by Professor T. F.
Holgate-not postulational or rigoristic like the articles
just now mentioned, and not concerned with pure geometry in general, but giving such an acquaintance with pure
projective geometry as one gains of an immense city by
riding about in it on the top of a comfortable 'bus; an
exceedingly enlightening essay by Professor E. V. Huntington, dealing postulationally and very refreshingly with
The Fundamental Propositions of Algebra; an interesting
and instructive article by Professor G. A. Miller treating
The Algebraic Equation in part historically, in part critically, in a manner a little too mature, perhaps, and a bit
sketchy for beginners; The Function Concept and the
Fundamental Notions of the Calculus, by Professor G. A.
Bliss-an essay chiefly notable, I think, as showing how
swiftly and quickly a competent reader may be conducted into the presence of the cardinal concepts of the
calculus and be given some sense of their power; and
three instructive and stimulating essays by Professors
J. W. A. Young, L. E. Dickson and D. E. Smith concerned, respectively, with The Theory of Numbers, Con