Ramses II, c. 1400 B.C.) divided the land among all Egyptians 

 so as to give each one a quadrangle of equal size and to draw from 

 each his revenues by imposing a tax to be levied yearly. But 

 every one, from whose part the river tore away anything, had to 

 go to him and notify what had happened ; he then sent the overseers, 

 who had to measure out by how much the land had become smaller, 

 in order that the owner might pay on what was left in proportion 

 to the entire tax imposed. In this way, it appears to me, geometry 

 originated which passed thence to Hellas." Whether this theory 

 of the origin of geometry be entirely correct or not, it most probably 

 contains at least the germ of a very valuable truth. Geometry, 

 like astronomy, arose because of the practical needs of man, and 

 though in later years practical applications form no necessary part 

 of any science, yet it is doubtless true that all science originated 

 because certain very practical needs in the life of men had to be 

 faced. 



When one turns from the Greek traditions to the documentary 

 evidence, one finds himself on more satisfactory ground. The 

 ancient Egyptian papyrus, which is part of the Rhind collection 

 in the British Museum, was deciphered in 1877 and was found to be 

 a mathematical manual containing many problems in arithmetic 

 and geometry. It was written by a priest, Ahmes by name, who 

 lived considerably more than a thousand years before Christ, and 

 the document seems to be founded on an even older work believed by 

 Birch to date back as far as 3400 B.C. The Ahmes Papyrus re- 

 presents apparently the most advanced attainments of the Egyp- 

 tians in arithmetic and geometry. Remarkable as it is, that they 

 should have reached so great proficiency at so remote a period of 

 antiquity, it is yet even more strange that during the next two 

 thousand years they should have made so little progress. Perhaps 

 one explanation of this is that the knowledge which they held was 

 carefully guarded by the priests and was entered upon their sacred 

 books. Afterwards, as has been only too often the case, these 

 writings became sealed books and it was considered heretical to 

 augment or modify anything therein. The Book of Ahmes is 

 entitled "Directions for Knowing all Dark Things", and contains 

 a number of very interesting problems. The first part, to use 

 modern language, deals with the reduction of fractions whose 



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