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CHAPTER Ⅰ．MAGIC SQUARES 1

THE ESSENTIAL CHARACTERISTICS OF MAGIC SQUARES 1

ASSOCIATED OR REGULAR MAGIC SQUARES OF ODD NUMBERS 2

ASSOCIATED OR REGULAR MAGIC SQUARES OF EVEN NUMBERS 24

THE CONSTRUCTION OF EVEN MAGIC SQUARES BY DE LA HIRE'S METHOD 43

COMPOSITE MAGIC SQUARES 55

CONCENTRIC MAGIC SQUARES 58

GENERAL NOTES ON THE CONSTRUCTION OF MAGIC SQUARES 67

CHAPTER Ⅱ．MAGIC CUBES 80

THE ESSENTIAL CHARACTERISTICS OF MAGIC CUBES 80

ASSOCIATED OR REGULAR MAGIC CUBES OF ODD NUMBERS 81

ASSOCIATED OR REGULAR MAGIC CUBES OF EVEN NUMBERS 96

GENERAL NOTES ON MAGIC CUBES 104

CHAPTER Ⅲ．THE FRANKLIN SQUARES 110

AN ANALYSIS OF THE FRANKLIN SQUARES 119

CHAPTER Ⅳ．REFLECTIONS ON MAGIC SQUARES 139

THE ORDER OF FIGURES 139

MAGIC SQUARES IN SYMBOLS 148

THE MAGIC SQUARE IN CHINA 150

THE JAINA SQUARE 155

CHAPTER Ⅴ．A MATHEMATICAL STUDY OF MAGIC SQUARES 159

A NEW ANALYSIS 159

NOTES ON NUMBER SERIES USED IN THE CONSTRUCTION OF MAGIC SQUARES 170

CHAPTER Ⅵ．MAGICS AND PYTHAGOREAN NUMBERS 181

MR. BROWNE'S SQUARE AND LUSUS NUMERORUM 197

CHAPTER Ⅶ．SOME CURIOUS MAGIC SQUARES AND COMBINATIONS 204

CHAPTER Ⅷ．NOTES ON VARIOUS CONSTRUCTIVE PLANS BY WHICH MAGIC SQUARES MAY BE CLASSIFIED 222

THE MATHEMATICAL VALUE OF MAGIC SQUARES 233

CHAPTER Ⅸ．MAGIC CUBES OF THE SIXTH ORDER 235

A "FRANKLIN" CUBE OF SIX 236

A MAGIC CUBE OF SIX 245

MAGIC CUBE OF SIX 250

CHAPTER Ⅹ．VARIOUS KINDS OF MAGIC SQUARES 258

OVERLAPPING MAGIC SQUARES 258

ODDLY-EVEN MAGIC SQUARES 271

NOTES ON ODDLY-EVEN MAGIC SQUARES 283

NOTES ON PANDIAGONAL AND ASSOCIATED MAGIC SQUARES 288

SERRATED MAGIC SQUARES 305

LOZENGE MAGIC SQUARES 308

CHAPTER Ⅺ．SUNDRY CONSTRUCTIVE METHODS 313

A NEW METHOD FOR MAKING MAGIC SUQARES OF ODD ORDERS 313

THE CONSTRUCTION OF MAGIC SQUARES AND RECTANGLES BY THE METHOD OF "COMPLEMENTARY DIFFERENCES" 325

NOTES ON THE CONSTRUCTION OF MAGIC SQUARES OF ORDERS IN WHICH n IS OF THE GENERAL FORM 4p+2 337

NOTES ON THE CONSTRUCTION OF MAGIC SQUARES OF ORDERS IN WHICH n IS OR THE GENERAL FORM 8p+2 351

GEOMETRIC MAGIC SQUARES AND CUBES 358

CHAPTER Ⅻ．THE THEORY OF REVERSIONS 373

CHAPTER ⅩⅢ．MAGIC CIRCLES, SPHERES AND STARS 406

MAGIC CIRCLES 406

MAGIC SPHERES 417

MAGIC STARS 426

CHAPTER ⅩⅣ．MAGIC OCTAHEDROIDS 440

MAGIC IN THE FOURTH DIMENSION 440

FOUR-FOLD MAGICS 455

CHAPTER ⅩⅤ．ORNATE MAGIC SQUARES 474

GENERAL RULE FOR CONSTRUCTING ORNATE MAGIC SQUARES OF ORDERS≡0(mod 4) 474

ORNATE MAGIC SQUARES OF COMPOSITE ODD ORDERS 483

THE CONSTRUCTION OF ORNATE MAGIC SQUARES OF ORDERS 8,12 AND 16 BY TABLES 492

THE CONSTRUCTION OF ORNATE MAGIC SQUARES OF ORDER 16 BY MAGIC RECTANGLES 508

PANDIAGONAL-CONCENTRIC MAGIC SQUARES OF ORDERS 4m 515

编辑手记 523