June 22. 1850.] 



NOTES AND QUERIES. 



59 



these unlettered students being able to derive any 

 material advantages from their publication : and 

 hence arises another weighty reason why Simpson's 

 writings were so eagerly studied, seeing they con- 

 tained the leading propositions of some of the most 

 interesting researches of the Alexandrian School. 

 After the death of Simpson, the Rev. John 

 Lawson, who appears to have inherited no small 

 portion of the spirit of his predecessors, began to 

 take the lead in geometrical speculations ; and 

 having himself carefully studied the principal writ- 

 ings of the ancient geometers, now formed the 

 happy project of unfolding these treasures of anti- 

 quity to the general reader, by presenting him with 

 English translations of most of these valuable re- 

 mains. With this view he published a translation 

 of Vieta's restoration of Apollonius on Tangencies 

 in 1764, and to this, in the second edition of 1771, 

 was added the Treatise on Spherical Tangencies, 

 by Fermat, which has since been reprinted in the 

 Appendix to the Ladies' Diary for 1840. In 1767 

 appeared Emerson's Treatise on Conic Sections; 

 a work which, notwithstanding its manifest defects, 

 contributed not a little to aid the student in his 

 approaches to the higher geometry, but whose pub- 

 lication would probably have been rendered un- 

 necessary, had Dr. Simson so far loosened himself 

 from the trammels of the age, as to have written 

 his own admirable treatise in the English language. 

 The frequency, however, with which Mr. Emerson's 

 treatise has been quoted, almost up to the present 

 date, would appear to justify the propriety of in- 

 cluding it amongst the means by which the study 

 of geometry was promoted during the last genera- 

 tion. The success which attended Mr. Lawson's 

 first experiment induced him to proceed in his 

 career of usefulness by the publication, in 1772, 

 of the Treatise on Determinate Section ; to which 

 was appended an amended restoration of the same 

 work by Mr. William Wales, the well-known geo- 

 meter, who attended Captain Cook as astronomer, 

 in one of his earlier voyages. In 1773 appeared 

 the Synopsis of Data for the Construction of Tri- 

 angles, which was folIowe<l in 1 774 by his valuable 

 Dissertations on the Geometrical Analysis of the 

 Ancients; and although the author used an unjus- 

 tifiable freedom with the writings of others, Dr. 

 Stewart's more especially, it is nevertheless a work 

 which probably did more to advance the study of 

 the ancient geometry than any other separate 

 treatise which could be named. As these publica- 

 tions became distributed amongst mathematicians, 

 the Mugazinns, the Diaries, and various oilier 

 periodicals, began to show the results of the activity 

 which had thus been created ; geometrical (jues- 

 tions became much more abundant, and a numer- 

 ous list of contributions appeared which aiford 

 ample proof that tiieir al)le authors had entered 

 deeply into the s]jirit of the ancient geometry. 

 During the year 1777 Mr. Lawson i.ssued the first 



portion of Dr. Simson's restoration of Euclid's 

 Porisms, translated from the Opera Reliqua of that 

 distinuuished greometer: and though the work was 

 not continued, sufficient had already been done to 

 furnish the generality of students with 'a clue to 

 the real nature of this celebrated enigma of anti- 

 quity. 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 Pergceus on In- 

 clinations gave publicity to a valuable relic which 

 would otherwise have remained buried in the Latin 

 obscurity of Dr. Horsley's more elaborate pro- 

 duction. 



During the greater portion of the time just re- 

 viewed, 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 asso- 

 ciated 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 mathema- 

 tical 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 oifering 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 col- 

 lecting 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 tiie ancients to the very greatest minds, 

 (became) familiar to men whose condition in li'e 

 was, to say the least, most unpropitious for the suc- 

 cessful 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 

 improbaljle that other reasons, equally cogent, or 

 perhaps corrective of several of the preceding, may 

 be advanced by some of your more learned cor- 

 respondents, whose experience and means of re- 

 j ference are superior to my own. Should any .such 



