ABSTRACT
Thabit ibn Qurra demonstrates a theorem that, according to him, allows one to form as many pairs of amicable numbers as one wish. This demonstration is preceded by nine lemmas or propositions and is written in the purest Euclidean style of Books VII to IX of the Elements. One finds a history of the theory of amicable numbers in Arabic mathematics nevertheless one reads that Proposition 1 is a particular case of Proposition IX of the Elements, but it is correct to say the two propositions are related, for that of Euclid treats only prime divisors and not all divisors as does that of Thabit ibn Qurra. Proposition 10 is Thabit ibn Qurra's theorem: it gives a procedure for constructing pairs of amicable numbers 'at will', which is probably to be understood as infinite in number. Euler's formulas can generate pairs of amicable numbers that were not obtained by Thabit ibn Qurra's formulas only for relatively high values of n.
