Euclid, continuous fractions, Dick paths

It is classical that continuous fractions, rational approximations of functions of one variable, orthogonal polynomials, are all related to the Euclidean division of polynomials and to the combinatorics of Dyck and Motzkin paths. I shall show that the theory of symmetric functions allows to handle the different determinants arising in these theories, and give as well their combinatorial descriptions in terms of paths. A key point is division by 1, i.e. what you can do with a pair of series, one of them being supposed equal to 1 without loss of generality.