56 THE WORLD MACHINE 



We have in the fable, then, either an evidence of the extreme 

 slowness of mental development, or else an indication of the 

 stage attained by the Greeks of Thales' time. 



The construction of the Pyramids indicated a very consider- 

 able knowledge of geometry. Its birth must have been far 

 back. Herodotus would have it that it was the invention of 

 the Egyptian king who wished to give an equal measure of 

 land to each of his subjects. Those who dwelt along the Nile 

 suffered from the erosions of the river's annual flood, but in 

 unequal degree. There was need, therefore, of an annual 

 equalisation. This was the work of the harpedonapta or " rope- 

 stretchers/' These may have been the first surveyors. Pro- 

 bably their art had existed in a rude form for many thousands 

 of years. There is in the British Museum a hieratic papyrus 

 dating from before 1700 B.C., and founded upon an older work, 

 believed to date from before 3400 B.C. This manuscript treatise 

 of old Ahmes implies a rudimentary knowledge of proportion, 

 squares the circle with very fair approximation, and contains 

 many rules of much practical value. It contains no theorems. 



Apparently, then, we might believe that, among the Egyptians 

 at least, abstract reasoning that is, mathematical generalisa- 

 tions did not exist at this period ; and we know of no other 

 people then flourishing who were further advanced. The fact, 

 however, is by no means certain. We know that among the 

 ancient Egyptians learning was confined very largely to the 

 priesthood. They guarded their treasure jealously. Know- 

 ledge did not ope her ample page to the vulgar. So it was 

 even among the earlier Greeks. The Pythagoreans constituted 

 a sort of secret society, and in times, of distress or disorder 

 they were mobbed and their homes burned. 



It may very well be, then, that the manuscript of Ahmes 

 does not represent the intelligence of the time any more, let us 

 say, than Mr. Gladstone's theories of creation and allied subjects 

 represented the intelligence of his day. The mode of tradition 

 may have been almost exclusively, as we know it was largely, 

 oral. When the curtain lifts upon Greek geometry, we find 

 it far advanced. Euclid is its culmination. Behind him we 

 know of a long line of geometers. They in turn may have 

 been the successors of a still longer line, reaching far into the 

 mists of antiquity. The fact may always be that there came 

 at this period a sudden flowering of the human intellect, like 



