A term in use in England during the eighteenth and early in the following century. By the primitive regulations of the Grand Chapter, an applicant for the Royal Arch Degree was required to produce a certificate that he was “a Geometrical Master Mason,” and had Paseed the Chair. The word Geometrical was, in Doctor Mackey’s opinion, thus synonymous with Speculative. Later researches proved that there was actually a Degree of this name. Brother George W. Speth in 1899 (Transactions, Quatour Coronati Lodge, volume xii, page 205) mentions the ritual of the Most Excellent Order of Geometrical Master Masons as being about 1819 to 1820 but that the Degree is probably much older. He says there are nine Lectures. Much of the ritual is in very rough verse, archaic, containing allusions to matters which were in use early in the eighteenth century, such as the broached thurnell, which had disappeared from Craft Masonry long before the nineteenth century. On the other hand, much of it will be recognized by members of so-called Higher Degrees as at present in use. The Degree was given apparently after the Three Craft Degrees but is unconnected with the Royal Arch. It was conferred in a Chapter, not in a Lodge, and is Christian throughout. Both Doctor Mackey and Brother Woodford give the name Geometrical Master Masons in the Encyclopedias for which they are responsible, but neither seems to have realized that it represented an actual Degree.
the source: Mackey’s Encyclopedia of Freemasonry