“Ballet,” Brodovitch’s only book, includes 104 pictures — shot in New York in the late 1930s — of the Ballets Russes companies that were formed after Diaghilev’s 1929 death. The poet and dance critic Edwin Denby, whose essayis reprinted in the new edition, wrote, “There are many fine moments that seemed like the bright afterglow of the 30-year-long Diaghilev epic and at the end of an atmosphere in dancing we came to know as Ballets Russes or Russian ballet.” Denby also describes the artistic ambition with which “Ballet” was conceived. Brodovitch, he wrote, “was trying to catch the elusive stage atmosphere that only ballet has, as the dancers in action created it.” He wanted to render ballet magic in visual terms, Denby added, to show “the unconscious grace and spontaneous animation all through that turns a choreography from a lesson into a dance.”