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

x CONTENTS
LECTURE IV
DOCTRINAL INTERPRETATIONS
PAGES
A Mother of Doctrines Mistaken for Her Eldest ChildInfinitely Many Interpretations of One Doctrinal
Function-Ordinary Geometry but One of Them-Other
Interpretations Geometric, Algebraic and MixedIdentity of Form with Diversity of Content-Distinction
of Logical and Psychological-Projective Geometry the
Child of Architecture-A Science Born of an Art-Infinite
Points and the Meeting of Parallels-Pole-to-Polar
Transformations-Logical Use of Pathological Configurations................................... 60-72
LECTURE V
ANOTHER GEOMÉTRIC INTERPRETATION
Brief Introduction to the Method of Descartes and FermatInversion Geometry and Inversion Transformation-The
Infinite Region of Inversion Space a Point-Bundles of
Circles and Clusters of Spheres-Pathocircles and
Pathospheres-One-to-One Correlation............... 73-85
LECTURE VI
NON-GEOMETRIC INTERPRETATION
Not All that Glitters is Gold-A Diamond Test of Harmony
-Two-dimensional Doctrine of Number Dyads and
Systems Thereof-The Three Dimensional Analogue... 86-1o3
LECTURE VII
ESSENTIAL DISCRIMINATIONS
Distinction of Doctrine and Method-Analytic Geometry
and Geometric Analysis-The Twain Begotten of Converse Transformations-An Infinite Family of Sisters