30 A SHORT HISTORY OF SCIENCE 



Egyptians added 5 days at the end of each year. According to 

 their legend the god Thot won these days at play from the moon 

 goddess. An edict of 238 B.C. introduced the leap-year, but the 

 innovation was afterwards forgotten. The Egyptian records 

 number more than 350 solar, and more than 800 lunar eclipses 

 before the Alexandrian period. 



THE AHMES PAPYRUS. - - Our most important source of in- 

 formation in regard to early Egyptian mathematics is the so-called 

 Ahmes manuscript, dating from some time between 1700 and 

 2000 B.C. "Direction for attaining knowledge of all dark things" 

 are the opening words of this oldest known mathematical treatise. 

 Rules follow for computing the capacity of barns and the area of 

 fields. The text consists, however, rather of actual examples than 

 of rules, the inferring of these being left to the reader. Reference 

 is made to writings some 500 years older, presumably based in 

 their turn on centuries of tradition. 



In the computations fractions are used as well as whole numbers, 

 but fractions other than f are expressed in terms of fractions 

 with unit numerators. The problem of decomposing other frac- 

 tions into a limited number of such reciprocals is interestingly 

 treated, examples occurring of considerable complexity. It 

 would appear that such decompositions, effected by special de- 

 vices or hit upon accidentally, were gradually tabulated as rec- 

 ords of mathematical experiment. 



The problems discussed by Ahmes include a class equivalent 

 to our algebraic equations of the first degree with one unknown 

 quantity, - - the first known appearance of this important idea. 

 Thus, for example : - 



"Heap (or quantity) its f , its |, its y, its whole makes 33." In 



2 r a* 

 our notation -x + - H h x = 33. 



o Zi i 



The solution requires the number to be found which multiplying 

 1 + i + ^ + y shall produce 33. The result appears in the suffi- 

 ciently intricate form 



