Mr. T. S. Davies's Notes on Geometry and Geometers. 29 



In my copy the full title nins thus : — " The Mathematical Repo- 

 sitoiy : containing many ingenious and useful Essays and Ex- 

 tracts, with a collection of Problems and Solutions, selected from 

 the correspondence of several able Mathematicians, and the works 

 of those who are eminent in the Mathematics. London, 1795 ;" 



and as all "Letters for the use of No. II must come to 



hand before the first of January 1796,'' it seems almost certain 

 that the first number was pubhshed about the beginning of 

 October, 1795. 



The "Mathematical Companion" was projected by several 

 active members of the Spitalfields Mathematical Society, and, 

 with the exception of the last number, was edited by its members 

 Messrs. Davis and Hampshire from its commencement in No- 

 vember 1797, to its close in November 1826. On its projection 

 it was proposed to designate it " A Companion to the Gentleman's 

 Diary, or a Preparation to that useful work," and the first number 

 was actually printed with that title ; but since the then Editor of 

 the " Gentleman's Diary," the Rev. Charles Wildbore {jwt Dr. 

 Hutton), had not been consulted respecting the new publication, 

 he declared in the Diary for 1798 that he "would discourage it 

 all in his power," and consequently the second number was 

 issued as the " Gentleman's Mathematical Companion," to which 

 the title of the first number was altered on its being reprinted in 

 1809. The reasons for this change are fully stated in the " Ad- 

 vertisement" prefixed to the reprint of 1809, and must have been 

 overlooked by Professor Davies when writing the remarks con- 

 tained in " Geometry and Geometers, No. VIII." The " open 

 field" alluded to is also liable to correction, for Mr. Whiting's 

 " Scientific Receptacle" and " Geometrical Delights" had ap- 

 peared at intervals for several years previously to the appearance 

 of the Repository, Mr. Leybourn himself being a joint proprietor 

 in the latter work with Messrs. Whiting and Davis. 



The whole of No. VII. of this series of papers is devoted to 

 an analysis of Mr. Swale's merits as a geometer, and to a short 

 notice of his "Geometrical Amusements," the "ApoUonius," 

 and his manuscript remains. Had the hand of death not so 

 prematurely arrested his progress, we should have had much 

 more on this interesting topic, since the j\ISS. could have fur- 

 nished much av.;ilable matter for Mr. Davies's versatile and dis- 

 cursive genius ; and it is much to be regretted that the task, if 

 ever it be accomplished, should have devolved upon others so 

 much less able and experienced. Most of the inferences and de- 

 ductions respecting Mr. Swale's speculations in mathematical 

 publications, &c. have been confirmed to me in private corres])ond- 

 ence with his son, the ])resent Mr. J. H. Swale ; nor will any one 

 who is at all acquainted with his father's writings, hesitate for a 



