The quotient-difference (=QD) algorithm developed by the author may be considered as an extension ofBernoulli's method for solving algebraic equations. WhereasBernoulli's method gives the dominant root as the limit of a sequence of quotientsq 1 () =s 1 (+1) /s 1 () formed from a certain numerical sequences 1 () , the QD-algorithm gives (under certain conditions) all the rootsλ σ as the limits of similiar quotient sequencesq σ () =s σ (+1) /s σ () . Close relationship exists between this method and the theory of continued fractions. In fact the QD-algorithm permits developing a function given in the form of a power series into a continued fraction in a remarkably simple manner. In this paper only the theoretical aspects of the method are discussed. Practical applications will be discussed later.