THE LANCASHIBE OEOMETEBS AND THEIR WRITINGS. 



131 



inquiries almost indefinitely ; but owing to the want of some 

 ffeneral principle, by which one construction can be derived 

 from another, nearly all such speculations terminate in iso- 

 lated problems, which, however much they may exercise the 

 ingenuity of the student, are rarely found to repay the time 

 and labour expended upon them.* 



The publication of Newton's Arithmeiica Universalis and 

 the Appendix to Simpson's Algebra no doubt furnished the 

 incentives to such a course of stud}', and almost every mathe- 

 matical periodical for nearly a century testifies to the ardour 

 with which the subject was cultivated. The fact of having 

 solved all Newton's problems geometrically was made a 

 matter for self-congratulation by Mr. Reuben Burrow, The 

 Rev. John Lawson, Professor Ley bourn, and Mr. John Farey 

 published Synopses of Data for the Construction of Triangles, 

 pointing out what had been efiected and what still remained 

 to be done in certain cases; yet, with perhaps one or two 

 exceptions, no general principles have been elicited. Each 

 geometer commences his analysis de novo for each isolated 

 problem, and after deducing the construction for the difference 

 from that for the sum, or vice versa, most frequently abandons 

 one method of investigation to adopt another equally unpro- 

 fitable. The germs of many of the beautiful theories which 

 form so conspicuous a feature in the writings of the Conti- 

 nental Geometers, are to be found in several of our early 

 English periodicals. The leading properties of Transversals, 

 Poles and Polars, Radical Axes, Poles of Similitude, the 

 Complete Quadrilateral, Conjugate Section, &c. &c., occur 

 in the Diaries and elsewhere, as has been frequently pointed 

 cut in my contributions to the ^•History of Mathematical 

 Periodicals" in the Mechanics^ Magazine^ 



Where it was or by whom Mr. Jeremiah Ainsworth received 



• A variety of interesting and valuable observations on tliis subjeet may be 

 found in Nos. IX. and X. of tlie late Professor Davies'a "Qkovietry and Geometers,''^ 

 published in the Phil. Ma^. for April and June, 1852. 



