JF Ptak Science Books Post 1800
"The name Magic Square, is given to a square divided into several other small equal squares or cells, filled up with the terms of any progression of numbers, but generally ah arithmetical one, in such a manner, that those in each band, whether horizontal, or vertical, or diagonal, shall always form the same sum." --from the very busy Charles Hutton's translation of Jean Etienne Montucla's edition of Jacques Ozanam Récréations mathématiques et physiques (1694, 2 volumes, revised by Montucla in 1778, 4 volumes) and the whole thing revised in an English edition of 1844 by the appropriately-names Edward Riddle, and available online at Cornell's collection of historical mathematical monographs.
That was sort of a simple introduction to magic squares, tortured by my note on the quote's parentage. Nevertheless, leafing through a copy of Ozanam's work I found a lovely little (literally speaking, as it is about 1/2 inch by an inch) 3x3 multiplication magic square for the happy sequence of 1, 2, 4 ,8, 16, 32, 64 and 256. (That means that each of the nine numbers may appear only once, and that the product (4096) must be the same for each column and row). It is a nice little problem, and I was just surprised to see it in such spare simplicity.
And since we're at it slightly, a few pages further on I found this nice series of 3x3 magic squares for numbers 1-25:
These also are a half-inch (or less) and about two inches long...they're just very attractive.
But I guess I cannot leave the subject of "pretty" magic squares without referencing a "beautiful" one, and this being one of the earliest inclusions of a magic square in Western printmaking, and surely one of the most beautifully-encumbered one in general, from Albrecht Durer's mega-popular masterwork, Melancholia (printed 1514). The magic square had been around for at least 2,000 years at this point, starting up evidently in China between 650-1000 BCE before making its way west through the Arab lands and then through India, and finally into Europe around the 13/14th century, and then into art prints with Durer in 1514.
[Detail]
I doubt that Abraham's Rees' "Magic Circle of Circles" (published ca. 1814) is "pretty", and I'm not so sure it is "beautiful", but I am sure that it is "elegant".
Ditto his "Magic Square of Squares" (published ca. 1814):
In any event these are just a few samples that I had close to the top of my head--no doubt there are endless others, but these are some that have attached themselves longest to me (with the exception of the Ozanam, which are new).
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