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