Preliminary engineering work will begin next month on a 13-mile, two-station extension of the Bay Area Rapid Transit into the Livermore Valley, directors decided. The move represents the first extension of the 71-mile system since it was completed in 1976. Most of the construction will be funded from a half-cent sales tax approved last year by voters in Alameda County and from state and federal highway grants. Seven of the transit district's directors approved the extension plan, which had been considered and studied for 13 years. "This is a historic point," BART President John Glenn said. The new line will run east from San Leandro to a station in Castro Valley and then to another station in Dublin.