This volume presents the qualitative uses of number. The basic concept of polarity leads to the precise analysis of the characteristics of the digits. The system of classification based on the characteristics of numbers is then developed from first principles. This analysis is then applied to four different qualitative classifications.

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Comparison of Pythagorean and Mathetical Views
Table of Contents
The Mathematical Analysis of Qualities
James Nohl Churchyard
First Edition © 1966
On-line Edition © 2003
 the stupa with the ten digits


Chapter Zero
gives an historical introduction to numerical qualities as discussed by the Pythagoreans, cabalists, and modern numerolgists.
Chapter One
analyzes the basic relationships among the digits.
Chapter Two
applies these relationships to classify the musical octave, colors, and the chemical elements.
Chapter three
brings the sounds of speech within the mathetical scheme.
Chapter Four
presents the basic qualities and meanings of the sounds of speech and the digits.

All these five chapters are presently implemented on this website. Reprints of the whole 1966 volume are available if you desire a physical copy to hold in your hands . There are only minor editorial differences among these two editions.


Comparison of Pythagorean and Mathetical Views

 Pythagorean Tetraktys    Mathetical Tetraktys
Pythagorean Tetraktys: Four elements composing the whole   Mathetical Tetraktys: Four elements originating from an unknown center

Table of Contents

Chapter Zero: Thesis and Introduction   Part One: Analysis - Chapter One: The Nature of Digits
Numbers and Qualities
  Figurate Numbers
  Triangular Numbers
  Square Numbers
  The Tetraktys
  Decimal Octaves
  The Digits
The Cabala
Modern Numerology
  The Generation of the Digits
  The Linear Generation
  The Binary Generation
  The Bipolar Generation
The Stupa and the Digits
The Tetraktys and the Stupa
The Bar Notation
Relative Weights of Digits and Numbers
The Four Elements and the Digits
Additive Complements
Subtractive Complements
Chapter Two: Applications of Numerical Qualities Part Two: Synthesis: - Chapter Three: Towards a Linguistic Synthesis

Laws of Three and Seven
Musical Octave
  Notes and Ratios
  Chord Structure of the Octave
  Notes and Digits
Atomic Elements
Mathetical Principles of Classification
Classification of the Simpler Phonemes
 The Pure Vowels and Digits
 The Simple Consonants
  The Labial Consonants and Numbers
  The Lingual Consonants and Numbers
Further Phonemes
 Further Vowels
 Further Consonants
Complete Table of Phonemes
Chapter Four: Numbers and Meanings   Bibliography

The Meaning of Meaning
The Meaning of the First Triad
The Meaning of the Four Elements
The Meaning of the Digits
The Meaning of the Phonemes
Synoptic Table of Meanings
Chapter Zero Bibliography
Chapter One Bibliography
Chapter Two Bibliography
Chapter Three Bibliography
Chapter Four Bibliography