As he starts his second term as president, with the nation prosperous and at peace and his personal popularity high, Ronald Reagan paradoxically can be more confident of his place in the history books than in the "hearts of his countrymen" during the next four years.

The achievements of the first term are almost enough in themselves to give Reagan standing as a historically significant president. The policy changes on which he campaigned and was elected in 1980, when ratified and enacted by a Congress under his domination in 1981, provided the basis for a fundamental redirection of American government.

Within a span of eight months, corporate taxes were virtually eliminated for many major firms, and individual tax rates were lowered by a quarter and permanently indexed against inflation; the growth of domestic government programs was drastically curbed by appropriations cuts and by changes in permanent law; and massive resources were shifted from the domestic budget to launch a long-term defense buildup.

In the last three years, the whole world has been trying to accommodate itself to those Reagan-initiated policy changes. The leaders of the Soviet Union, the second- most powerful nation, and of China, the most populous, have responded to Reagan's show of confidence in the dynamics of the American economy and the capability of our military technology by adjusting their diplomatic, military and -- in China's case -- domestic economic-policy doctrines. Other power centers, in Japan, West Germany and Great Britain, are seeking to conform their policies to his.

Here at home, every member of Congress, every governor, mayor and state legislator has accepted the reality that Reagan's policy choices have altered and dictated their own. The Republican Party is beginning a search for someone who can be Reagan's successor. And the opposition Democrats, having bent their lance in a futile effort to reverse his policies, now are trying to find a way to integrate and redefine them to fit their own rhetoric, values and constituencies.

By his will and his skill, Reagan has proved the contention of the late conservative philosopher, Richard Weaver, that "ideas have consequences."

Significant as this achievement is, that is not what guarantees Reagan's place in the history books. Policy revolutions inevitably run their course, and Reagan's will in time. But his impact on the presidency is permanent. It is no exaggeration to say he has rescued the office.

When Reagan was first elected in 1980, there were wise and experienced people in Washington who argued that we had entered the era of the one-term presidency. In the previous 20 years, they had seen John Kennedy murdered, Lyndon Johnson driven into political exile, Richard Nixon banished under threat of impeachment, and both Gerald Ford and Jimmy Carter defeated in their first races as incumbents.

They argued, not implausibly, that the demands of the presidency were so great and the public expectation so much larger than its limited institutional authority, that no mere mortal could "succeed" in the office. They predicted that we would continue to run people into and out of the Oval Office as fast as the Constitution allowed. Some of them were so desperate for a device to provide a degree of continuity in the office that they proposed amending the Constitution to extend the term of the president to six years.

Ronald Reagan has taken all of that well- credentialed nonsense and knocked it into a cocked hat. He has succeeded in his principal aims and has been recognized as a success by a large majority of his constituents. He has restored the presidency to its central role in our government and politics. That -- if not his individualized and almost eccentric way of managing the office -- is his historic legacy to his successors.

Ironically, by taking the oath for a second term, Reagan puts that history-book judgment at risk. For the next four years, he will not be basking in the gratitude of the nation but taking the heat for a great many short-term problems that may frustrate his efforts and break his luck.

He has given many hostages to fortune: on economics, to a business cycle he may not be able to control; on arms control, to a Soviet leadership caught up in its own perpetual crisis of succession; on peace in the Middle East, Africa and Central America to the constant threat of an assassin's bullet or a terrorist's bomb; on tax reform and the deficit, to the pressures of congressional and interest-group politics.

His domestic and international political influence, on which any further substantive accomplisment depends, faces the inevitable hazards of a lame-duck administration, already being abandoned by some of its proven officials, and, one must add, the inescapable risks of his own advancing years.

Reagan's second-term power and popularity have yet to be determined. But his place in history seems secure.