Madison Square Garden turned 100 yesterday and celebrated by welcoming back a long-lost naked lady.

In defiance of politicians' traditional abhorrence of having their photographs taken with their hands on women or cash boxes, New York Mayor Edward Koch helped pull on the golden rope that unveiled a bronze (and naked) statue of Diana.

Although naked status of women or naked live women, for that matter, have never been the Garden's stock and trade, Carey pointed out that politicians haven't always fared that well there either.

"Where the politicians stand up, we boo," Carey said of the Garden crowd's attitude. "When the champions take the line, we cheer."

"Let's keep it that way," said the governer, who ran some notably unsuccessful track races at the Garden, but has come up a winner ever since he started running in street clothes.

To help the Garden begin its celebrations which will include a giant dinner and television spectacular of hype later in the anniversary year, a number of other athletes put on their street clothes.

Phil Esposito, Dave Maloney and Mike McEwen of the Stanley Cup finalist New York Rangers appeared. Jack Dempsey, 84 next month, limped in on a cane and was able only to half rise from his chair when master of ceremonies Howard Cosell introduced him.

The only black man crowded into the small reception area where people waited for 40 minutes until Carey arrived was Joe Frazier, who won with Muhammad Ali on March 8, 1971, fought what many boxing fans call "The fight of the century."

"What I remember about that fight," Frazier said when reporters asked him, "is that he (Ali) got hurt in every round."

Frazier, who is trying to rally his career as a singer after doing badly in some early rounds, said for him, "Madison Square Garden is No. 1."

When Madison Square Garden left Madison Square in 1925, a New York Herald Tribune editorial declared, "What passes is not a building, but a state of mind."

The wrecker's ball got the building (and 43 years later it demolished another Madison Square Garden), but the state of mind didn't die. When Rod Steiger told his brother Marlon Brando to throw a fight in "On The-Waterfront" it was in the locker rooms of the Garden. When performers of all kinds - from six-day bike riders to ice skaters to hockey and basketball stars - made the big time, they played the Garden.

It got its name 100 years ago yesterday when William H. Vanderbilt took control of a former railway station that had become P. T. Barnum's Hippodrome, then Gilmore's Garden, then changed its name to Madison Square Garden in an attempt to capture some of the glamor of what was then a choice New York address.

Madison Square has fallen on hard times since the glorious days when O. Henry described it unblushingly as "the center of the universe" and its hotels, townhouses and famous brothels, named, also unblushingly, the Louvre, were among the most elaborate New York offered.

Now unremarked by guidebooks and long accustomed to bright lights and gay crowds, the square has been kept alive in American minds by its 100-year-old namesake, which survived by leaving home.

Four buildings have carried the Garden's name.

The first, unheatable in winter and therefore an expensive proposition for its owners, was replaced on the same site by the Stanford White Building.

Of all the happenings in its elegant halls - from the opening Viennese concert attended by 17,000 people paying as much as $50 in 1890, to the May 5, 1925, fight between Johnny Dundee and Sud Terris that closed it - probably none is as well remembered as White's murder.

On June 25, 1906, White, who gave parties and kept lodgings at the Garden and often created its roof-garden shows, was watching chorus girls in pink tights dance around a giant bottle of champagne as a vocalist sang "I could love a thousand girls," when millionaire Harry K. Thaw walked up to White's table and shot the architect twice through the head.

It would have been hard to invent a crime better designed to boost newspaper circulation. Sex, money, fame, and glamor were mixed in nice proportions. Thaw supposedly killed White because he had become crazed upon learning that his wife, Evelyn Nesbit Thaw, has been seduced by White. Never mind that the seduction was before she was married. Never mind that Mrs. Thaw told her husband of her seduction three years before he shot White. At the 11-week trial Mrs. Thaw told in graphic detail of all her cavorting on a red-velvet swing with White, and trial reporters outdid one another in their efforts to describe and praise her beauty. Thaw was not convicted.

The third Garden was the first to be built away from Madison Square. Legendary promoter Tex Rickard persuaded friends he called "my 600 millionaires" to finance the new arena as Eighth Avenue and 50th Street after the New York Life Insurance Company foreclosed its mortgage on Stanford White's Garden. Rickard told the world he didn't consider choosing a new name.

Neither did Irving Felt when he decided to move the Garden into the air rights above Pennsylvania Station.

Garden III closed in 1968, with the dogs. The last act in its arena was the crowning of ch. Steingray of Derryabah, a lakeland terrier, the Best of Show. Garden IV opened a few days later with a gala starring Bob Hope and Bing Crosby. In deference to the Garden's tradition as a sports arena, Hope and a long-retired Rocky Marciano did a skit in boxing trunks.

Diana and the Garden have not been together since the arena left Madison Square in 1925, with ring announcer Joe Humphreys (who could be heard without a microphone) breaking into tears as he recited some doggeral about Diana.

Stanford White commissioned Augustus Saint-Gaudens to sculpt Diana the huntress for the top of the elegant column that rose about 100 yards above the street and made his Garden the second tallest building in 1890 New York.

On opening night, 10 searchlights were trained on Diana as she swiveled on ball bearings so that her bow always aimed into the wind.

The searchlights left no doubt that Diana was doing her hunting in the nude.

In its more serious early efforts to promote physical culture, the Garden has had its share of trouble with law enforement over the women performing in tights.

The police, however, were less of a threat to Diana than the writers. "Where babyhood once disported itself, today elderly gentlemen, delmonico elegants, Casino Johnnies and every variety of local dude linger in listless idleness," the New York Mercury lamented of the Garden.

Despite the enthusiastic cheers that came with the unveiling, not every eye cast skyward from Madison Square was concupiscent.

Benny Leonard, the lightweight champion, considered Diana his good-luck charm. Each time he entered the Garden for one of his many fights, Leonard cast a glance at his charm.

"When the going was not so good for me," Leonard wrote later, "I thought of her while resting in my corner and always managed to rally."

Leonard sought to buy Diana and find a home for her, as did many other admirers from her years atop the Garden. One suggested installing her in City Hall Park as a balance to the statue of Civic Virtue there.

The Philadelphia Museum of Art got Diana, and she presides over its great stair. Philadelphia, whose newspaper once denounced the statue as typical of "the depraved artistic taste of New York," doesn't want to let Diana go, so the Garden is settling for a cast half the size of the original 13-foot Diana.

The Garden's new sculpture will not turn in the wind, but by a motor inside the main entrance. Her bow will point over the heads of all entrants. Her once-controversial body is no longer at such elevation that anyone today must follow the example of those men of the 1890 who brought their field glasses to Madison Square, the better to study Saint-Gaudens, sculptural achievement. CAPTION: Picture, Jack and Deanna Dempsey, by AP