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

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 - ALL HERITORS OF THEIR
MOTHER S FORM-THEIR COMMON CHARACTER AND
INDIVIDUALITIES-EXCESSIVE MEANING OF CONTENT
— GENERIC AND SPECIFIC MEANINGS OF EUCLIDEAN
AND NON-EUCLIDEAN-THREE PROPERTIES COMMON
TO POSTULATE SYSTEMS-FERTILITY AND COMPENDENCE AND COMPATIBILITY.
IN this lecture and the next one, I invite you to join
me in considering a variety Qf kindred matters closely
connected with the preceding lectures. Some of these
matters are suggested in the foregoing lengthy title.
In course of the discussion some of the unanswered questions you have asked and some others that you are no
doubt prepared to ask will, I hope, receive suitable
answers. I say " some " of them, for I trust we are not
so stupid as to be able to answer all the questions we are
able to ask. Let us begin with one of the questions that
must be asked and can be answered satisfactorily.
A Word about Analytic Geometry and Geometric
Analysis.-In Lecture V, I gave a little introduction to
what is called the analytic or algebraic geometry of the
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