IAMBLICHUS 
117 
(2) The method of calculating the pythmen is like the opera 
tion of ‘ casting out nines ’ in the proof which goes by that 
name, where we take the sum of the digits of a number and 
divide by 9 to get the remainder. The method of verification 
by ‘ casting out nines ’ came to us from the Arabs, who may, 
as Avicenna and Maximus Planudes tell us, have got it from 
the Indians; but the above evidence shows that, at all events, 
the elements from which it was built up lay ready to hand 
in the Pythagorean arithmetic.