# Book:W.S. Andrews/Magic Squares and Cubes/Second Edition

## W.S. Andrews: Magic Squares and Cubes (2nd Edition)

Published $\text {1917}$.

### Contents

Publishers' Preface
Introduction. By Paul Carus
Chapter I. Magic Squares
The Essential Characteristics of Magic Squares
Associated or Regular Magic Squares of Odd Numbers
Associated or Regular Magic Squares of Even Numbers
Construction of Even Magic Squares by De La Hire's Method
Composite Magic Squares
Concentric Magic Squares
General Notes on the Construction of Magic Squares
Chapter II. Magic Cubes. By W.S. Andrews
The Essential Characteristics of Magic Cubes
Associated or Regular Magic Cubes of Odd Numbers
Associated or Regular Magic Cubes of Even Numbers
General Notes on Magic Cubes
Chapter III. The Franklin Squares. By W.S. Andrews
An Analysis of the Franklin Squares, By Paul Carus
Chapter IV. Reflections on Magic Squares. By Paul Carus
The Order of Figures
Magic Squares in Symbols
The Magic Square in China
The Jaina Square
Chapter V. A Mathematical Study of Magic Squares. By L.S. Frierson
A New Analysis
Notes on Number Series Used in the Construction of Magic Squares
Chapter VI. Magics and Pythagorean Numbers. By C.A. Browne
Mr. Browne’s Square and lusus numerorum. By Paul Carus
Chapter VII. Some Curious Magic Squares and Combinations. By W.S. Andrews
Chapter VIII. Notes on Various Constructive Plans by which Magic Squares May be Classified. By W.S. Andrews
The Mathematical Value of Magic Squares. By W.S. Andrews
Chapter IX. Magic Cubes of the Sixth Order
A "Franklin" Cube of Six. By H.M. Kingery
A Magic Cube of Six. By Harry A. Sayles
Magic Cube of Six. By John Worthington
Chapter X. Various Kinds of Magic Squares
Overlapping Magic Squares. By D.F. Savage
Oddly-Even Magic Squares. By D.F. Savage
Notes on Oddly-Even Magic Squares. By W.S. Andrews
Notes on Pandiagonal and Associated Magic Squares. By L.S. Frierson
Serrated Magic Squares. By Harry A. Sayles
Lozenge Magic Squares. By Harry A. Sayles
Chapter XI. Sundry Constructive Methods
A New Method for Making Magic Squares of Odd Orders. By L.S. Frierson
The Construction of Magic Squares and Rectangles by the Method of Complementary Differences. By W.S. Andrews
Notes on the Construction of Magic Squares of Orders in which $n$ is of the General Form $4 n + 2$. By W.S. Andrews and L.S. Frierson
Notes on the Construction of Magic Squares of Orders in which n is of the General Form $8 n + 2$. By Harry A. Sayles
Geometric Magic Squares and Cubes. By Harry A. Sayles
Chapter XII. The Theory of Reversions. By Dr. C. Planck
Chapter XIII. Magic Circles, Spheres and Stars
Magic Circles. By Harry A. Sayles
Magic Spheres. By Harry A. Sayles
Magic Stars. By W.S. Andrews
Chapter XIV. Magic Octahedroids
Magic in the Fourth Dimension. By H.M. Kingery
Fourfold Magics. By Dr. C. Planck
Chapter XV. Ornate Magic Squares
General Rule for Constructing Ornate Magic Squares of Orders $= 0 \pmod 4$. By Dr. C. Planck
Ornate Magic Squares of Composite Odd Orders. By Dr. C. Planck
The Construction of Ornate Magic Squares of Orders $8$, $12$ and $16$ by Tables. By Frederic A. Woodruff
The Construction of Ornate Magic Squares of Order $16$ by Magic Rectangles. By W.S. Andrews
Pandiagonal-Concentric Magic Squares of Orders $4 m$, By Harry A. Sayles
Index
Diagrams of Completed Magics