  This is a translation of Leonhard Euler's ``De quadratis magicis'' . It is
E795 in the Enestrom index. This paper studies how to construct magic squares
with certain numbers of cells, in particular 9, 16, 25 and 36. It considers
some general rules for making squares of even and odd orders. Euler uses
Graeco-Latin squares and constrains the values that the variables can take to
make magic squares. I think this is where the terms ``Latin'' and
``Graeco-Latin'' square comes from, since he uses Latin letters in one square
and Greek (i.e. ``Graeco'') letters in another for each construction. (This
paper was published before Euler's only other paper ``Recherches sur une
nouvelle espece de quarres magiques'' E530 about Latin squares was, in 1782.)
