Andrews, William Symes: Magic Squares and Cubes ©1917 Open Court Publishing Hardcover, 419 pages

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Comments: A very mathematical book on Magic Squares. From the preface, "The essays which comprise this volume appeared first in The Monist at different times during the years 1905 to 1916...The first edition contained only the first eight chapters, and these have now been carefully revised."

Contents (from book ToC):

v Publisher's Preface
vii Introduction (Paul Carus)

1 Chapter I Magic Squares (W.S. Andrews)
1 The Essential Characteristics of Magic Squares
2 Associated or Regular Magic Squares of Odd Numbers
18 Associated or Regular Magic Squares of Even Numbers
34 Construction of Even Magic Squares by De La Hire?s Method
44 Composite Magic Squares
47 Concentric Magic Squares
54 General Notes on the Construction of Magic Squares

64 Chapter II Magic Cubes (W.S. Andrews)
64 The Essential Characteristics of Magic Cubes
65 Associated or Regular Magic Cubes of Odd Numbers
76 Associated or Regular Magic Cubes of Even Numbers
84 General Notes on Magic Cubes

89 Chapter III The Franklin Squares (W.S. Andrews)
96 An Analysis of the Franklin Squares (Paul Carus)

113 Chapter IV Reflections on Magic Squares (Paul Carus)
113 The Order of Figures
120 Magic Squares in Symbols
122 The Magic Square in China
125 The Jaina Square

129 Chapter V A Mathematical Study of Magic Squares (L.S. Frierson)
129 A New Analysis
137 Notes on Number Series Used in the Construction of Magic Squares

146 Chapter VI Magics and Pythagorean Numbers (C.A. Browne)
158 Mr. Brown’s Square and Iusus Numerorum (Paul Cams)

163 Chapter VII Some Curious Magic Squares and Combinations (W.S. Andrews)

178 Chapter VIII Notes on Various Constructive Plans by which Magic Squares May be Classified (W.S. Andrews)
187 The Mathematical Value of Magic Squares (W.S. Andrews)

189 Chapter IX Magic Cubes of the Sixth Order
189 A "Franklin? Cube of Six (H.M. Kingery)
196 A Magic Cube of Six (Harry A. Sayles)
201 Magic Cube of Six (John Worthington)

207 Chapter X Various Kinds of Magic Squares
207 Overlapping Magic Squares (D.F. Savage)
217 Oddly-Even Magic Squares (D.F. Savage)
225 Notes on Oddly-Even Magic Squares (W.S. Andrews)
229 Notes on Pandiagonal and Associated Magic Squares (L.S. Frierson)
241 Serrated Magic Squares (Harry A. Sayles)
244 Lozenge Magic Squares (Harry A. Sayles)

248 Chapter XI Sundry Constructive Methods
248 A New Method for Making Magic Squares of Odd Orders (L.S. Frierson)
257 The Construction of Magic Squares and Rectangles by the Method of Complementary Differences (W.S. Andrews)
267 Notes on the Construction of Magic Squares of Orders in which n is of the General Form 4p + 2 (W.S. Andrews and L.S. Frierson)
277 Notes on the Construction of Magic Squares of Orders in which n is of the General Form 8p + 2 (Harry A. Sayles)
283 Geometric Magic Squares and Cubes (Harry A. Sayles)

295 Chapter XII The Theory of Reversions (Dr. C. Planck)

321 Chapter XIII Magic Circles – Spheres – and Stars
321 Magic Circles (Harry A. Sayles)
331 Magic Spheres (Harry A. Sayles)
339 Magic Stars (W.S. Andrews)

351 Chapter XIV Magic Octahedroids
351 Magic in the Fourth Dimension (H.M. Kingery)
363 Fourfold Magics (Dr. C. Planck)

376 Chapter XV Ornate Magic Squares
376 General Rule for Constructing Ornate Magic Squares of Orders = 0 [mod 4] (Dr. C. Planck)
383 Ornate Magic Squares of Composite Odd Orders (Dr. C. Planck)
390 The Construction of Ornate Magic Squares of Orders 8 12 and 16 by Tables (Frederic A. Woodruff)
404 The Construction of Ornate Magic Squares of Order 16 by Magic Rectangles (W.S. Andrews)
410 Pandiagonal-Concentric Magic Squares of Orders 4m (Harry A. Sayles)

415 Index
419 Diagrams of Completed Magics