The extensive study of geometry in Lancashire and the northern counties generally is a fact which has forced itself upon the attention of several observers; but none of these have attempted to assign any reasons for so singular an occurrence. Indeed, the origin and progress of the study of any particular branch of science, notwithstanding their attractive features, have but rarely engaged the attention of those best qualified for the undertaking. Fully satisfied with pursuing their ordinary courses of investigation, they have scarcely ever stopped to inquire _who_ first started the subject of their contemplations; nor have they evinced much more assiduity to ascertain the _how_, the _when_, or in _what_ favoured locality he had his existence: and hence the innumerable misappropriations of particular discoveries, the unconscious traversing of already exhausted fields of research, and many of the bickerings which have taken place amongst the rival claimants for the honour of priority. Mr. Halliwell's _Letters on the Progress of Science_ sufficiently show that the study of geometry was almost a nonentity in England previously to the commencement of the eighteenth century. Before this period Dr. Dee, the celebrated author of the preliminary discourse to Billingsley's _Euclid_, had indeed resided at Manchester (1595), but his residence here could effect little in flavour of geometry, seeing, as is observed by a writer in the _Penny Cyclopaedia_-- "The character of the lectures on Euclid was in those days extremely different from that of our own time ... the propositions of Euclid being then taken as so many pegs to hang a speech upon."