(in English, apart from some introductory pages in Greek) The first part is an introduction to continued fractions, and the second a detailed rewritting of the whole paper: "A.C. Yao & D.E. Knuth, Analysis of the subtractive algorithm for greatest common divisors, Proc. Nat. Acad. Sci., vol. 72 (1979), pp. 4720-4722."