In the year 1774 the Rev. John Lawson, B.D., Rector of Swanscombe in Kent,
published _A Dissertation on the Geometrical Analysis of the Antients, with
a Collection of Theorems and Problems without solutions for the Exercise of
young Students_. This work was printed anonymously at Canterbury, but the
merits of the essay did not permit the author to remain long in obscurity;
the real writer was immediately known to most of the geometers of the day,
and the elegant character of many of the theorems and problems, led to a
general desire that their solutions should be published in a separate work.
In accordance with this intention, it was announced on a fly-sheet attached
to some copies of the work, that--
"The author of this publication being a man of leisure, and living in a
retired situation, remote from any opportunity of conversation with
mathematicians, would be extremely glad of a correspondence with any
such, who are willing to be at the expense of the same; or if this be
thought too much, will pay the postage of his answers to their letters.
But no letters, except post-paid, can be received by him; otherwise a
door would be opened for frolic, imposition, and impertinence. Any new
geometrical propositions, either theorems or problems, would be
received with gratitude, and if sent without solutions, he would use
his best endeavours to return such as might be satisfactory. Any new
solutions of propositions already in print, _especially of those
included in the present collection_, would also be very agreeable. If a
variety of such demonstrations essentially different from those of the
original authors should be communicated, he proposes at some future
time to publish them all, with a fresh collection for further exercise;
and then each author's name shall be affixt to his own solution, or any
other signature which he shall please to direct. Any person who shall
favor the publisher with his correspondence shall have speedily
conveyed to him the solutions of any propositions contained in this
collection, which he may be desirous of seeing. Letters (post-paid)
directed for P. Q., to be left at Mr. Nourse's, Bookseller, in the
{527} Strand, London, will be carefully transmitted on the first day of
each month, and all correspondents may expect answers during the course
of that month."
In consequence of this appeal, Mr. Lawson was speedily in correspondence
with several of the most able geometers then living, and amongst the rest,
Messrs. Ainsworth, Clarke, Merrit, Power, &c., appear to have furnished him
with original solutions to his collection of theorems and problems. The
manuscript containing these solutions must have been of considerable size,
since a portion of it was sent down to Manchester about July, 1777, for the
purpose of obtaining Mr. Ainsworth's remarks and corrections; and Mr.
Lawson is requested, in a letter bearing date "August 22, 1777," to "send
the next portion when convenient." Whether Mr. Lawson did so or not, I have
not yet been able to ascertain; but this much is certain, the manuscript
was never printed, and would most probably either be disposed of at the
death of its compiler, or previously transferred to the possession of some
geometer of Mr. Lawson's acquaintance. Several of the _original_ letters
which passed between the respective parties relating to this manuscript are
at present in the hands of two or three of the Lancashire geometers, but no
one seems to know anything of the manuscript itself. May I then request
that the fortunate holder of this yet valuable collection will make himself
known through the medium of the widely circulated pages of "N. & Q."