THE LANCASHIRE GEOMETERS AND THEIR WRITINGS. 



157 



of research ; and such is undoubtedly the only legitimate 

 course which the student can pursue with advantage. 



Dr. Stewart's determination of the Suris Distance, and 

 Sir John Leslie's Geometry of Curve Lines, present two 

 memorable instances of Geometry as applied to subjects for 

 which it is ill-adapted ; but, on the other hand, the pages of 

 our Mathematical periodicals furnish numerous instances of 

 complicated and lengthy co-ordinate discussions, the results 

 of which are seen at a glance from the simplest principles 

 of ordinary geometry. In all geometrical researches a quick 

 perception of the proper system of investigation to be adopted 

 ought to be especially the aim of the student: — each method 

 has its own peculiar advantages ; and that only ought to be 

 adopted which conducts us most naturally to the required 

 result. Both methods of investigation will thus assist in 

 furthering the progress of Geometrical Science, and all idea 

 of antagonism between the supporters of the ancient and 

 modern practices will thus be rendered impossible; for it is 

 as absurd to imagine that the modern geometrical methods 

 will ultimately be abandoned for those of the Greeks, as it 

 would be to suppose that the Astronomer will forsake his 

 formulae and return to graphical delineation, or the "rule 

 of thumb." The change in the modes of conducting geo- 

 metrical inquiries is without doubt both permanent and real ; 

 the works of Chasles and Mulcahy are undoubtedly but the 

 avant couriers of a numerous and progressive race ; nor will 

 the expectations of those Lancashire Geometers soon be 

 realised who hope to witness the re-establishment of the 

 Ancient Analysis upon the ruins of the Geometric Suj)erieure, 



