Dear Bill Casselman,

I worked on trisecting a square. Perigal was the first one to find a minimal 6-piece solution probably arround 1835-1840, but he only publish later in 1891. Thus Phillip Kelland was probably the first one who publish this technique for a gnomon in 1855. I've upload in wikisource his full publication for "Geometric dissections and transpositions". Here it is:

Moreover, at the end of this paper: "L. J. Rogers (1897). Biography of Henry Perigal in appendix of On certain Regular Polygons in Modular Network. Proceedings London Mathematical Society. Volume s1-29, pp. 732-735.", I've found an interesting biography of Perigal (look at the four last pages):

Best regards,
Christian Blanvillain