8 G. H. KNIBBS. 



examination of the temples and pyramids of Egypt, has shewn 

 that their north and south lines were determined by astronomical 

 observation : their east and west lines were then set out by the 

 " Hope-Stretchers " [Harpedonaptai], using the 3. 4. 5 triangle. 

 Thus the earliest and most striking monuments of human energy 

 are indissolubly associated with mathematics. 



There are strong reasons for believing that, whenever the mind 

 of a people is wholly directed to purely practical issues, it is 

 decadent. Be that as it may, the practical Egyptian seems to 

 have remained content with his achievement ; and for something 

 like 2,000 years made no progress in mathematical knowledge : 

 like the Chinese his mind had stagnated. Nevertheless his attain- 

 ment became in time the inspiration of the Greek, who unlike his 

 predecessor, was endowed with an ardent love of science for its 

 own sake. The genius of the Greek impelled him onward to the 

 discovery of abstract relations, regardless of all question as to the 

 possibility of practical applications ; and gave birth to a geometry, 

 that in spite of its limitations as to generality, remains even to- 

 day a model of logical exposition and rigour of thought. In a 

 word the Science of Geometry and of Algebra, we owe to the Greek. 

 The lofty scorn of the Greek mind for utilitarian considerations 

 has left its impress on the world. With few exceptions that scorn 

 has been the tincture of Genius ever since. It is a significant 

 fact, and one that we do well to remember, that among the dis- 

 coveries of truths, which have conferred inestimable benefits upon 

 mankind, none can compare with those that have been vouchsafed 

 to minds untarnished with a regard for material issues. Again 

 and again have conquests in the most recondite regions of mathe- 

 matical truth, proved not only eminently practical, but even 

 essential to material advancement. To the mathematician, the 

 knowledge of this will perhaps never operate as a motive, for no 

 one can read the history of mathematics without realizing that 

 the inspiration which has guided the votaries of the "queen 

 of sciences " in their flights of genius, and has sustained them 

 in their herculean labours, was from something nobler than 



