Michael Stifel (Arithmetica Integra, 1544) wrote two magic squares, of orders 9 & 16 (below). These are fully magic: The rows, columns and 2 main diagonals each sum to the same "magic constant" (369 or 2056).
The latter square was originally published with several typos, corrected here.
Somehow these examples have largely escaped mention in the standard accounts of magic squares. Stifel is mentioned in the magic square writings of Günther and Cammann, but the squares themselves do not appear.
Stifel also comments on multiplicative magic squares! I did not know that these were explored so long ago.
Divers ouvrages de mathematique et de physique (Bernard Frénicle de Bessy, et. al., 1693) lists all fully magic squares of order 4. Here are a few of them:
Although original copies of this book are scarce, the 4 x 4 squares have also appeared in more readily available places:
Web pages cited in the paper
A construction of Franklin squares, by Neil Abrahams.
Benjamin Franklin, A Documentary History, by J.A. Leo Lemay (forthcoming).
How to make a Franklin square, by Paul C. Pasles.
Other relevant links
|Franklin’s Autobiography:||Poor Richard’s Almanac:|
|Project Gutenberg||1733 1753 1759 (facsimile pages)|
|earlyamerica.com||1733-59 (selected excerpts only)|
|American Philosophical Society||Athenæum of Philadelphia|
|Library Company of Philadelphia||Royal Society|
|Rosenbach Museum and Library||University of Pennsylvania|
|Historical Society of Pennsylvania||Franklin & Marshall College|