The monograph is devoted to the analysis of the development of scientific knowledge from the VI century. BC e. to the XVI century. It traces how during this period the understanding of science, its subject and research methods, ideas about the ideals of scientific knowledge changed. The author's focus is on the formation and development of the first scientific programs, within the framework of which the methodological principles of nature research and the fundamental concepts of scientific thinking were formed - the concepts of number, space, motion, finite and infinite, continuous, etc. The book shows how, with the change in historical conditions in the Middle Ages and the Renaissance, the key concepts of scientific programs that developed in antiquity are revised, and thereby the prerequisites for the natural sciences of the New Age are prepared.