East Germany's winning ways; The Miracle Machine, by Doug Gilbert. New York: Coward, McCann, Geoghegan. $10 .95.

At the Montreal Games in 1976 the East German team took 40 gold medals, six more than the United States. If the US does not participate in the Olympic Games in Moscow this summer, East Germany is likely to sweep the awards again. The East German athletes may triumph even if the US doesm participate.

In "The Miracle Machine" Canadian journalist Doug Gilbert shows how a country the size of the state of Virginia, with a population of only 17 million, has vaulted itself into international dominance in track and field and swimming, as well as winter sports.

It all began, Gilbert tells us, as part of a post-World War II rebuilding program. Manfred Ewald, then Minister of Sport in East Germany, and others began a slow but extremely systematic national effort to rebuild their war-torn country, not through economic revitalization, social renovations, or political endeavors, per se, but through sport. Mass sport. Everyone participating. Huge arenas, gymnasiums, rinks, and other facilities were built by the state. Academic progrms in sport science, sport medicine, coaching techniques, and other related activities were launched.

After 30 years of slow but steady progress, the program is now reaping awards.

Gilbert explains that it is the nature of the East German political system that has allowed for such unprecedented growth and success: Facilities are funded by the state, therefore centralized, therefore widely available.

Indeed, when one reads about the selection processes, the training techniques , and the seemingly total dedication to excellence in competitive athletics, one is struck not so much by how successful the East German system has been, but by how successful the US has been with something quite less than an organized state-supported effort.