History of Science and Engineering Annotation << Back HISTORY OF CONVERGENT SEQUENCES METHODS AND SUB-SEGMENTS G.I. Sinkevich The idea of nested intervals or an equivalent idea of convergent sequences originated in antiquity. Archimedes calculated in excess and defi ciency, with two sequences of values, ambient and nested. The notion of a point lying in the sequence of nested segments, stated J. Buridan. A calculation of an unknown quantity by means of approximation with excess and defi ciency used P. Fermat, J. Gregory, I. Newton, C. Maclaurin, K. Gauss, J.-B. Fourier. This logic structure had transformed into a ground method of analysis in the XIX century in works of B. Bolzano, A.- L. Cauchy, P. Lejeune-Dirichlet, E. Heine, G. Cantor, J.G. Darboux. Some concepts of a real number formed in the seventies of the XIX century. Cantor’s construction founded on the concept of limit point and the principle of nested segments. We will consider just a genesis of this idea from antiquity to XX c. Keywords: Convergent sequences; nested intervals; Archimedes; Buridan, Maclaurin; Cantor; Kolmogorov. Contacts: E-mail: Galina.sinkevich@gmail.com Pp. 03-14.