PRESIDENT REAGAN was at his best in his appearance before the European Parliament. It was the occasion for underlining the record of transatlantic striving since the defeat of Nazi Germany, and he did it with modesty and some eloquence and a nice touch of history. His hecklers provided (noisy) evidence of American success in helping Europe -- Western Europe -- to make itself unprecedentedly united, stable and democratic in the years since Europeans "wept in the rubble." The president offered his familiar views about Soviet power -- in a tone sufficiently restrained to satisfy the broad European desire for no jostling.

In almost simultaneous counterpoint, Mikhail Gorbachev was offering the Kremlin's perspective on the same sweep of history. His speech bristled with the pride in Soviet arms and the bitterness toward the West that commonly mark the Soviet attitude toward World War II. Even on a day that was bound to be given over to nationalistic celebration, however, the new Soviet leader was careful, as was President Reagan, to keep a door open for dealings with the other great power.

Forty years later, the continent that was the center stage of the war remains the great prize in the rivalry between the United States and the Soviet Union, the place -- Eastern Europe as well as Western Europe -- regarded as most worthy of being influenced by one or the other. For all of this time, the first aim of Soviet policy has been to weaken Europe's confidence in America; the first aim of American policy has been to strengthen Europe's confidence. Fortunately, over the decades, America has kept the advantage. At least in the latter stages of the round that took place in the last week, we would say, Mr. Reagan more than held his own.

Beyond the atmospherics, Europeans are deeply interested in how the Soviet-American arms control talks at Geneva fare. The picture of Soviet- American reaching for agreement is a source of reassurance to them, and any accord would be warmly welcomed. At the moment, the two sides have laid out initial positions that, from all accounts, are miles apart, and are arguing them out before the publics of Europe and, of course, the United States.

The steadiness of Western public opinion is crucial to the administration's bargaining strategy in Geneva now. It is precisely what President Reagan hopes has been earned by the 40-year record of American constancy that he celebrated in Europe this week.