Ball, W. W. Rouse (Walter William Rouse), 1850-1925 · London, Macmillan · leaf 170
magic squares, for if the consecutivenumbers, namely 1, 2, 3, &c., in a magic square are replacedby consecutive powers of any number m, namely m, m^ m^ &c.,the products of the numbers in every line will be magic. Thisis obvious, for if the numbers in any line of a square are a, a\a\… … Figure xiv. A Magic Star. passing, though I will not go into details. One instance willsuffice. Suppose a re-entrant octagon is constructed by the 10—2 148 MAGIC SQUARES [CH. VII intersecting sides of two equal concentric squares. It is requiredto place the first 16 natural numbers on the corners…
Mathematical recreations · Geometry · Astrology · Space and time · Matter · Magic squares
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