EAST AND WEST 137 



tury b.c. They compiled lists of stars and were soon able to predict 

 eclipses. 



That early knowledge was not only abundant, but highly 

 systematized. In the case of Egypt we are especially well informed 

 because we have two early papyri, each of which might be called 

 a treatise. The earliest, the Golenishchev papyrus of Moscow, 

 dates from the middle of the nineteenth century b.c. but is copied 

 from an older document of the end of the third millennium; the 

 second, the Rhind papyrus, kept in London and New York, dates 

 from the middle of the seventeenth century b.c. but is a copy of 

 a text which may be at least two centuries older. The second of 

 these texts has been studied with extreme care by a number 

 of investigators. The latest edition of it by Arnold Buffum Chace, 

 chancellor of Brown University, Ludlow Bull, H. P. Manning, and 

 R. C. Archibald (1927-29) is at once so complete and so attrac- 

 tive that I am sure it will turn the hearts of many men and women 

 to the study of Egyptian antiquities. I imagine that the first re- 

 action of some people, if they were shown these sumptuous 

 volumes, would be one of wonder that so much time and money 

 should have been spent on an early text of so little scientific value 

 from the point of view of our present knowledge, but I am sure 

 that it would not take long to convert them to an entirely different 

 attitude. For just think what it means. Here we have a mathe- 

 matical treatise which was written more than thirteen centuries 

 before the time of Euclid! To be sure it does not compare with 

 the latter's Elements, and we are not surprised that more than 

 a millennium of additional efforts were needed to build up the 

 latter, but it contains already such elaborate results that we must 

 consider it, not as a beginning, but rather as a climax, the climax 

 of a very long evolution. The Egyptian mathematicians of the 

 seventeenth century were already able to solve complicated prob- 

 lems involving determinate and indeterminate equations of the 

 first degree and even of the second; their arithmetical ingenuity 

 was astounding; they used the method of false position and the 



