Magic Squares and Cubes

A classic treatise on magic squares and related arrangements of numbers.

• Publishers' Preface
• Introduction
• 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
  • The 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
  • 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
  • An Analysis Of The Franklin Squares
• Chapter IV. Reflections On Magic Squares
  • The Order Of Figures
  • Magic Squares In Symbols
  • The Magic Square In China
  • The Jaina Square
• Chapter V. A Mathematical Study Of Magic Squares
  • A New Analysis
  • Notes On Number Series Used In The Construction Of Magic Squares
• Chapter VI. Magics And Pythagorean Numbers
  • Mr. Browne's Square And Lusus Numerorum
• Chapter VII. Some Curious Magic Squares And Combinations
• Chapter VIII. Notes On Various Constructive Plans By Which Magic Squares May Be Classified
  • The Mathematical Value Of Magic Squares
• Chapter IX. Magic Cubes Of The Sixth Order
  • A "Franklin" Cube Of Six
  • A Magic Cube Of Six
  • Magic Cube Of Six
• Chapter X. Various Kinds Of Magic Squares
  • Overlapping Magic Squares
  • Oddly-Even Magic Squares
  • Notes On Oddly-Even Magic Squares
  • Notes On Pandiagonal And Associated Magic Squares
  • Serrated Magic Squares
  • Lozenge Magic Squares
• Chapter XI. Sundry Constructive Methods
  • A New Method For Making Magic Squares Of Odd Orders
  • The Construction Of Magic Squares And Rectangles By The Method Of "Complementary Differences"
  • Notes On The Construction Of Magic Squares Of Orders In Which N Is Of The General Form 4p + 2
  • Geometric Magic Squares And Cubes
• Chapter XII. The Theory Of Reversions
• Chapter XIII. Magic Circles, Spheres And Stars
  • Magic Circles
  • Magic Spheres
  • Magic Stars
• Chapter XIV. Magic Octahedroids
  • Magic In The Fourth Dimension
  • Four-Fold Magics
• Chapter XV. Ornate Magic Squares
  • General Rule For Constructing Ornate Magic Squares Of Orders = 0 (Mod 4)
  • Ornate Magic Squares Of Composite Odd Orders
  • The Construction Of Ornate Magic Squares Of Orders 8, 12 And 16 By Tables
  • The Construction Of Ornate Magic Squares Of Order 16 By Magic Rectangles
  • Pandiagonal-Concentric Magic Squares Of Orders 4m

1st edition 1917, 419 pages; PDF 327 pages.
word count: 72990 which is equivalent to 291 standard pages of text