Andrew H. Frost and Charles A. M. Fennell

“ MAGIC SQUARE, a square divided into equal squares, like a chess-board, in each of which is placed one of a series of consecutive numbers from 1 up to the square of the number of cells in a side, in such a manner that the sum of the numbers in each row or column and in each diagonal is constant.
Fig. 1. From a very early period these squares engaged the attention of mathematicians, especially such as possessed a love of the marvellous, or sought to win for themselves a superstitious regard. ”

“ From a perfect magic ring of n2 cells containing one number each, n2 distinct magic squares can be read off; as the four numbers round each intersection of a zonal circle and a transverse circle constitute corner numbers of a magic square. The shape of a magic ring gives it the function of an indefinite extension in all directions of each of the aforesaid n2 magic squares. ”

“ Nasik Cubes.—A Nasik cube is composed of n3 small equal cubes, here called cubelets, in the centres of which the natural numbers from 1 to n3 are so placed that every section of the cube by planes
Fig. 25—Nasik Cube. perpendicular to an edge has the properties of a Nasik square; also sections by planes perpendicular to a face, and passing through the cubelet centres of any path of Nasical summation in that face. Fig. 25 shows by dots the way in which these cubes are constructed. ”