XX 
ALGEBRA: DIOPHANTUS OF ALEXANDRIA 
Beginnings learnt from Egypt, 
In algebra, as in geometry, the Greeks learnt the beginnings 
from the Egyptians. Familiarity on the part of the Greeks 
with Egyptian methods of calculation is well attested. (1) 
These methods are found in operation in the Heronian writings 
and collections. (2) Psellus in the letter published by Tannery 
in his edition of Diophantus speaks of ‘ the method of arith 
metical calculations used by the Egyptians, by which problems 
in analysis are handled ’; he adds details, doubtless taken 
from Anatolius, of the technical terms used for different kinds 
of numbers, including the powers of the unknown quantity. 
(3) The scholiast to Plato’s Charmides 165 e says that ‘parts 
of XoyuTTLKrj, the science of calculation, are the so-called Greek 
and Egyptian methods in multiplications and divisions, and 
the additions and subtractions of fractions (4) Plato himself 
in the Laws 819 A-c says that free-born boys should, as is the 
practice in Egypt, learn, side by side with reading, simple 
mathematical calculations adapted to their age, which should 
be put into a form such as to combine amusement with 
instruction: problems about the distribution of, say, apples or 
garlands, the calculation of mixtures, and other questions 
arising in military or civil life. 
‘ Han ’-calculations. 
The Egyptian calculations here in point (apart from their 
method of writing and calculating in fractions, which, with 
the exception of §, were always decomposed and written 
as the sum of a diminishing series of aliquot parts or sub 
multiples) are the /mu-calculations. Hau, meaning a heap, is 
the term denoting the unknown quantity, and the calculations