THE LANCASHIRE GEOMETERS AND THEIB WRITINGB. 



137 



derable portion of his geometrical writings relate to the Con- 

 struction of Triangles from given data, as may be seen by a 

 reference to the Lady's Diary for the years 1774 — 1784, and 

 his analyses of these and similar problems afford abundant 

 proofs of his intimate acquaintance with the best forms of the 

 Greek Geometry. The same fact is also obvious from his 

 Rationale of Circulating Numbers, (Lond. 1777,) where he 

 gives corrected solutions to a number of geometrical and other 

 questions which had been incorrectly treated in Malton's 

 Geometry^ the Town and Country Magazine, the Lady's 

 Diary, and ebewhere ; and at the close of the work " some 

 new Geometrical Propositions" are added, which are the 

 more deserving of notice since they make a nearer approach 

 to systematic investigation than any other portion of the 

 Lancashire geometry with which I am acquainted; Swale's 

 ApoUonius, the Lineal Sections, and the "Modern Geometry" 

 in the Student alone excepted. 



Of the many Geometers of the Lancashire School, none 

 have become so much distinguished as Wolfenden and Butter- 

 worth. They both belonged to the Oldham Mathematical 

 Society, and throughout the course of their long lives resided 

 in the immediate locality. Both of them were nursed and 

 reared in poverty ; — both had to struggle with its difficulties 

 through life ; — and both in old age would have had to endure 

 its keenest privations had not the pecuniary assistance of 

 the members of the " Manchester Literary and Philosophical 

 Society" softened the rigours of stern necessity, and freed 

 the last days of these "noblemen of nature" from all anxiety 

 respecting the ordinary necessaries of life. The nam.es of 

 Messrs. Hodgkinson, Binney, and Moore stand prominent in 

 this act of mercy, and I have the satisfaction of knowing that 

 their efforts in behalf of "scientific men in humble life" have 

 not been unappreciated by many whose thanks have formed 

 their only means of recompense. 



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