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For most of the 217 years since its founding under a buttonwood tree on Wall Street, the New York Stock Exchange was the high temple of American capitalism.

Behind its Greco-Roman facade, traders raised a Dante-esque din in their pursuit of the almighty dollar. Good times or bad, the daily melee on the cavernous trading floor made the Big Board the greatest marketplace for stocks in the world.

But now, even as the Dow Jones industrial average topped 10,000 for the first time since the financial crisis sent it tumbling, the exchange and its hometown face an unsettling truth: the Big Board, the symbolic heart of New York’s financial industry, is getting smaller.

Young, fast-moving rivals are splintering its public marketplace and creating private markets that, their critics say, give big banks and investment funds an edge over ordinary investors.

Some of the new trading venues — “dark pools,” the industry calls them — are all but invisible, even to regulators. These stealth markets enable sophisticated traders to buy and sell large blocks of stock in secrecy at lightning speed, a practice that has drawn scrutiny from the Securities and Exchange Commission.

These upstarts are utterly unlike the old-school Big Board, which is struggling to make its way as a for-profit corporation after centuries of ownership by its seat-holding members. Last year, its parent company, NYSE Euronext, lost $740 million.

Wall Street’s judgment has been swift and brutal. Since January 2007, the share price of NYSE Euronext has lost nearly three-quarters of its value, even though stock trading over all has soared.

While the exchange has been under assault since the beginning of the decade, its decline has accelerated in recent years as aggressive competitors have emerged. Today, 36 percent of daily trades in stocks that are listed on the New York Stock Exchange are actually executed on the exchange, down from about 75 percent nearly four years ago. The rest of are conducted elsewhere, on new electronic exchanges or through dark pools.

The old Big Board was far from perfect. Its floor brokers — who occupy a privileged, and potentially lucrative, niche between buyers and sellers — have sometimes enriched themselves at their customers’ expense.

But changes inside the exchange’s grand Main Hall are startling. For decades, the New York Exchange was the kind of place where sons followed their fathers onto the trading floor. But half of the jobs there have disappeared over the last five years. Many of the 1,200 or so remaining workers retreat quietly to their computers shortly after the opening bell clangs at 9:30 a.m.

The Big Board has been forced to close one of its five trading halls, and it has repopulated two others with business from the American Stock Exchange, which NYSE Euronext bought last year. The Main Hall — the soaring, gilded room opened in 1903 — can seem little more than a colorful backdrop for CNBC.

“It has not been pretty,” said Benn Steil of the Council on Foreign Relations in New York. “All the big established exchanges around the world have experienced the same phenomenon, but the New York Stock Exchange has taken the biggest beating.”

It is a remarkable comedown for the New York Exchange, and for New York. Once the undisputed capital of capital, the city is struggling to retain its dominance in finance as the industry globalizes. “Wall Street” seems to be no longer a place, but a vast, worldwide network of money and information.

The Big Board says that it is fighting back — and that its hybrid of computers and human traders can beat the new rivals. It slashed commissions and developed its own purely electronic exchange, Arca, in Chicago. Arca has captured about 11 percent of the market for Big Board-listed stocks. It is also winning business in areas like derivatives.

“What’s going on here is a reinvention,” said Lawrence Leibowitz, head of United States markets and global technology at NYSE Euronext. “How can you bring this institution forward into the 21st century?”

Proponents of the new exchanges and private trading systems contend that ordinary people benefit from the technologies whether they know it or not.

“Competition has benefited the average investor,” said William O’Brien, chief executive of Direct Edge, one of the new exchanges. “Their broker has so many choices available, on or off exchanges, anywhere in the world, and they can get their order executed in less than a second.”

Critics maintain that only the most sophisticated players are benefiting, able to execute their trades seconds before smaller investors and in private.

“There are tools now that certain investors have that give them an advantage over other investors,” said Joseph Saluzzi, who trades equities for institutional investors and hedge funds at his boutique brokerage, Themis Trading.

The Securities and Exchange Commission is beginning to take notice of such complaints, opening investigations into the new type of trading venues and promising action. It is worried, for example, that dark pools, with their scale unknown, could destabilize the market.

Unlike the Big Board, the new electronic exchanges are virtually unknown outside financial circles. Direct Edge, the largest, is in Jersey City. Another, the BATS Exchange, is based in Lenexa, Kan. Both are only about five years old. But each now accounts for about a 10th of daily United States stock trading.

In its fight to survive, the Big Board is building a new data center in New Jersey and another outside London. The Main Hall is being overhauled, in an attempt to lure business back to the floor. There is even a new coffee shop, Outtakes.

Even so, the world still watches — literally — what happens on the New York Stock Exchange. Twenty television networks broadcast live from the exchange, in nine languages.

But whichever way the market goes from here, many see a difficult road for the Big Board. The competition is unlikely to let up.

“There has been a sea change,” said Sang Lee of the Aite Group, a financial services consulting company. “I don’t envy what any of the exchanges have to do.”