ents with
a clue to the real nature of this celebrated enigma of antiquity. The last
of these worthy benefactors to the non-academic geometers of the last
century was Mr. Reuben Burrow, who by publishing in 1779 his _Restitution
of Apollonius Pergaeus on Inclinations_ gave publicity to a valuable relic
which would otherwise have remained buried in the Latin obscurity of Dr.
Horsley's more elaborate production.

During the greater portion of the time just reviewed, Mr. Jeremiah
Ainsworth was resident in the neighbourhood of Manchester, and so early as
1761 was in correspondence with the editors of the _Mathematical Magazine_.
He subsequently associated with Mr. George Taylor, a gentleman of kindred
habits, then resident in the immediate vicinity, and these worthy veterans
of science, as time wore on, collected around them a goodly array of pupils
and admirers, and hence may truly be said not only to have laid the
foundation of the "Oldham Society," but also to have been the fathers of
the Lancashire school of geometers. Such then was the state of affairs in
the mathematical world at the period of which we are speaking; all the
works just enumerated were attracting the attention of all classes of
students by their novelty or elegance; Dr. Hutton and the Rev. Charles
Wildbore had the management of the _Diaries_, each vieing with the other in
offering inducements for geometrical research; whilst both, in this
respect, for a time, had to contend against the successful competition of
Reuben Burrow, the talented editor of Carnan's _Diary_: correspondents
consequently became numerous and widely extended, each collecting around
him his own select circle of ardent inquirers; and thus it was, to use the
words of Mr. Harvey, and answer the questions proposed, that inquiries
which had hitherto been "locked up in the deep, and to them unapproachable
recesses of Plato, Pappus, Apollonius and Euclid * * porisms and loci,
sections of ratio and of space, inclinations and tangencies,--subjects
confined among the ancients to the very greatest minds, (became) familiar
to men whose condition in life was, to say the least, most unpropitious for
the successful prosecution of such elevated and profound pursuits."

The preceding sketch is respectfully submitted as an attempt to answer the
queries of PEN-AND-INK, so far as Lancashire is concerned. It is not
improbable that other reasons, equally cogent, or perhaps corrective of
several of the pre