But you can buy a piece of the bridge - legally - for as little as $10. The offer is for only a small segment of the bridge's original cable, embedded in a bronze medallion. The medallions are among some 15 ''official'' mementos and souvenirs given the stamp of approval by the Brooklyn Bridge Centennial Commission. Fees being paid by manufacturers of such items go toward fireworks, a boat show, and other festivities that will mark the famous span's 100th birthday on May 24. The old bridge is currently undergoing a 10-year, $105 million restoration. This ''eighth wonder of the world,'' as some enthusiasts have called it, faces an uphill battle if it is to last even another half century. The repair effort will entail replacing the entire structure, inch by inch, cable by cable. Last month, the federal government awarded $5.4 million toward the project. Meanwhile, visitors and New Yorkers celebrating the bridge's centennial are expected to spend much smaller, but still fairly hefty, amounts on everything from lithographed buttons carrying images of the bridge to T-shirts - and bits of the bridge itself.