Propelled by the imperatives of political self-interest and the burden of the arms race on their nations, President Reagan and Soviet leader Mikhail Gorbachev demonstrated this week they have found a new way to do business with each other.

Gone was the tentativeness of Geneva or the recklessness of Reykjavik. For the first time since Gorbachev came to power and Reagan decided the time had come to do business with the Russians, both leaders came to the table ready to deal -- albeit modestly -- and ready to acknowledge where they were unable to deal.

In the joint statement they issued last night, for example, they decided to finesse the issue of Reagan's Strategic Defense Initiative (SDI) on which the Iceland summit foundered 14 months ago.

In Reykjavik, Reagan stalked out because he could not accept the Soviet demand that research on his proposed missile defense system be confined to the laboratory. The Soviets have dropped that demand, and now both leaders have reduced to writing a vague formulation on SDI that postpones the day of reckoning and allows them to disagree without disrupting their relations. It may even permit them to reach a second arms control agreement on long-range strategic weapons next year.

Nor did they find common ground this week on the difficult issues of Soviet occupation of Afghanistan or human rights, but they did not walk away in acrimony on either count. They declared they would probably meet again next summer, even if they do not have another treaty to sign.

And they signed the treaty to eliminate medium- and shorter-range nuclear missiles in a celebration of mutual satisfaction. After years of angry rhetoric in which Reagan predicted the demise of communism in the "dustbin of history" and the Soviets depicted Reagan as a nuclear-crazed cowboy, the two leaders found themselves talking in virtually the same language of hope and optimism. It often seemed during this summit that Gorbachev and Reagan could have read each other's speeches without anyone noticing the difference.

Reagan's senior advisers had said before the summit that they wanted to send a political message to the American people that the Intermediate-Range Nuclear Forces (INF) Treaty was a "first step" toward reductions in strategic arms. Yesterday those advisers said they were surprised to find Gorbachev doing their work for them from his arrival through his remarkable final news conference last night.

In a comment that could have been lifted from a dozen Reagan speeches, the Soviet leader said on his departure from the White House that the INF Treaty is "an unprecedented step in the history of the nuclear age: the signing of the treaty under which the two militarily and strategically greatest powers have assumed an obligation to actually destroy a portion of their nuclear weapons."

In a subtle -- but for the Soviets, enormously important -- gesture to the Soviet leader, Reagan's speeches in Gorbachev's presence were scrubbed clean of the confrontational anti-Soviet insults that studded his rhetoric for years. There were no comments about the failing Soviet economy, the Soviet missile defense effort or alleged Soviet violations of earlier arms control treaties.

"The president's views have changed for the better, as have mine," Gorbachev said during his marathon news conference last night when a questioner asked about the disappearance of the "evil empire" tone in the president's utterances. "I think we now have more understanding between the president and myself," Gorbachev said.

But that "understanding" came only after Reagan and Gorbachev spent years testing each other and finally making concessions.

For example, last night Gorbachev reiterated his determination to frustrate Reagan's dream of a global missile defense system, though he said he would be willing to allow the United States to squander its money in pursuit of the dream. But Gorbachev did not insist that the joint statement include new restrictions to limit the program, which Congress has curtailed until nearly the end of Reagan's term. For Gorbachev it was a concession, but a relatively painless one, to simply wait until later.

And Gorbachev put an optimistic spin on this temporizing compromise by recalling how difficult questions that held up completion of the INF Treaty were ultimately resolved. He listed several of those contentious issues -- all of them points on which the Soviets ultimately made the biggest concessions, though he didn't point that out.

Reagan, too, has come a long way in deciding to do business with Gorbachev. In the early years of his presidency, Reagan felt he had the luxury of waiting out the Soviets, a tactic that he celebrated last night as "persistence and consistency" which led to agreement on the mid-range missile treaty. The unspoken reality is that Reagan can no longer use this tactic in the far more complex phase of reducing the superpowers' strategic arsenals. He is running out of time.

While Reagan insisted for years that he wouldn't have a summit without the promise of concrete results, he has all but agreed to that now. The White House announced that Reagan would go to Moscow next summer even without final agreement on a treaty to reduce strategic weapons.

"They want a smooth roll into the history books," commented a former White House official.

More immediately, Reagan's new way of dealing with Gorbachev may prove to be the hoped-for salve to heal his wounded presidency after a year of waning influence. Polls conducted in the first two days of the summit for the White House show that Reagan's public approval rating has returned to the level it was before the Iran-contra affair brought it down last November.

The summit marked a happy political coincidence for both leaders. Reagan defended his military buildup and rigid posture as worthwhile and sought to capitalize on the leverage they created before he leaves office. Gorbachev, eager to show concrete achievements at a time when his domestic reforms have yet to produce them, likewise wanted to show he could maneuver the most stridently anti-Soviet U.S. president into a more cooperative posture.

The summit was a success because both Reagan and Gorbachev wanted it to succeed. They appeared to have come to the same conclusion -- that the time was ripe to improve Soviet-American relations, even if their biggest differences could not be resolved.