Today's history lesson starts in 1840, when Washington area businessmen for the first time developed a strategy of seeking federal backing for a convention center in the nation's capital.

That was a couple of decades before the Board of Trade was organized after the Civil War. But the basic strategy has remain unchanged for 137 years, during which Congress has turned deaf ears on an idea for which the Board of Trade today is a principal advocate.

If the local business community is determined to stick with an approach which for so long has failed to be successful, the history books do offer some here. It took only a century and a quarter to obtain a full code of laws for the District of Columbia.

But the concept of a government-aided convention center has been kicked around for a longer period of time and one day, business leaders who beleive such a complex is vital to the community's health may have to consider a totally new strategy.

As Congress and the White House have demonstrated year after year, affairs of the District of Columbia are not treated as hot priority items. If history has any lesson for individuals interested in promoting the central city's economic future, it may be that those persons will have to seize the initiative themselves.

Some new ideas have emerged in recent weeks. Retail executive John W. Hechinger ha proposed private construction of a convention center on Hechinger land in Northwest Washington. His plan is to donate the site and lease the center to the city.

Architect and planner Arthur Cotton Moore subsequently suggested covering Robert F. Kennedy Stadium and connecting it to the D.C. Armory with an enclosed hall, providing more space for exhibits than proposed at Mt. Vernon Square at less than one-fourth the cost.

Hechinger's idea has been rejected out of hand by city planners and the business community in which Hechinger long has been a maverick. Moore's plan has not received much attention.

Another possibility that has not been discussed would be the formation of a new company, perhaps called the Washington Convention Center Corp. in which local and national business could invest. The land projected for a Mt. Vernon Square center is estimated to cost between $20 million and $25 million, and the new corporation might buy the land as its demonstration of business confidence in the center's future success.

In other cities, notably Detroit and St. Louis, the private sector has committed its money to such downtown renewal ventures. It has been said that such efforts cannot be duplicated here because of the absence of major business enterprises.

While metropolitan Washington does not have the concentration of business to match a Detroit ot St. Louis, many big companies are based here - firms that to date have not been vocal in support of a convention center.

TWhat could be losty, for example in seeking investments of a million dollars each by Washington Gas Light Co., Potomac Electric Power Co., Chesapeake & Potomac Telephone Co. (owned by American Telephone & Telegraph), Mariott Corp., Martin Marietta Corp., Fairchild Industries, Southern Railway, Woodward & Lothrop, and other area firms? Or from national companies with large operations here, such as Xerox or International Business Machines Corp.?

To be fair, there have been some changes over the years in proposals for a D.C. cenvention center. When 300 businessmen formed a National Fair Association in 1878, with a charter from Congress, they sought in vain for money from the U.S. Treasury to build a large public auditorium.

Similar ideas were suggested in later decades and in the 1920s, about 800 businessmen purchased stock in a 6,000-seat Washington Auditorium which never attracted much bussiness and which failed with the Depression. But that facility, if it hadn't been torn down, would be inadequate for business conventions of the 1970s.

Today, the business community is seeking approval from Congress only to permit the city government to borrow money from the Tresury for initial work on a convention center at Mt. Vernon Square, estimated to cost $110 million. Top officials of the elected city government are on record in support of the project but the District Building's own lobbying efforts have been characterized as too little and to late, all too often.

Sen. Patrick J. Leahy (D-Vt.), chairman of the Appropriations Subcommittee on D.C., has said flatly that such a center "is not needed to maintain and permit growth in the city's current position in the tourist and convention market."

Leahy has managed to block congressional approval of the proposed initial $27 million in spending for the center to complete planning and acquire land in a three-block site.

Leaders of the business community have vowed to fight for the spending plan as proposed. Clarence A. Arata, who will retire at the end of this month as executive vice president of the Board of Trade after 39 years promoting Washington business, says at least that is his intention.

"We're still trying to convince Leahy and giving (Rep. William) Natcher (head of the House Appropriations Suncommittee) all the support we can give him . . . in his stand . . . After Congress returns in January, the iogiam may be broken," says Arata, who plans to remain active in the convention center project after he retires from an active role at the Board of Trade.

Natcher has argued that since the city has a good record of repaying Treasury debts and since the city wants to spend money for the center. Congress should not stand in the way. Natcher has been quoted as saying he is "not going to give an inch" in the confrontation with Leahy.

Arata scoffs at suggestions by opponents of the proposed convention center that the business community has not really demonstrated financial support for the project. "What everybody seems to forget," he notes, are proposed hotel occupancy taxes and a corporate income tax subcharge that would be earmaked solely for a convention center. The taxes, proposed by the business community are designed to bring in an estimated $18 million over three years.

More significant perhaps Arata believes the business community would support an increased surcharge on corporate taxes to yield $6 million a year for the center. When added to the proposed hotel tax that would add up to $9 million a year or $36 million by 1981, when the proposed center would open for business.