Download MAGIC SQUARES AND CUBES, Second Edition, Revised and by W. S. Andrews PDF
By W. S. Andrews
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Extra resources for MAGIC SQUARES AND CUBES, Second Edition, Revised and Enlarged
Example text
Associated 8X8 magic squares may be constructed in great variety by the method now under consideration, and the different com- / J2. J IJ' 2J 2/ 22- 7 12 26 0 ? 9 f31 s- 034- '" Fig. 84. 3& Fig. 85. binations of numbers from I to 8 given in Fig. 86 will be found useful for laying out a large number of A primary squares. Fig. 87 shows the fixed numbers in the diagonal columns of these 8 X 8 A primary squares, and also designates by letters tIle 8pecific rows of figures which may be used for the different horizontal columns.
11/ "" z, JiI JO JS" JI J~ 01.. Jol Fig. 59. 2 S. oFI i IS /;9 2-2 /;1. y 27 oJl .... I Fig. 60. " 19 Totals = 260. 29 MAGIC SQUARES. shown in the annexed examples. Fig. 55 illustrates two different forms from which the magic square Fig. 56 is constructed. Fig. 57 shows three different forms which are used in connection with the square in Fig. 58, and in a similar manner Figs. 59 and 60 show four different diagrams and the square derived therefrom. The , ,OD 1- 99 /1. $ 4. 1 7~ JJ ". /" IZ 29 72.
51 (First Part). diagrams in the order A, D, and C, which ha~'e each a different form of irregularity, and after numbering them in arithmetical sequence from I to 36, as shown in Pig. 49, copy the numbers in diagrammatic order into the cells of a 6 X 6 square. It must be remembered that the cells in the corner diagonal 23 MAGIC SQUARES. columns of these even magic squares may be correctly filled by writing the numbers in arithmetical order according to the rule previously given, so in beginning any new even square it will be found helpful to first write the numbers in these columns, and they will then serve as guides in the further development of the square.