President Reagan returned yesterday to the images and ideology of his political past as he presented a vision of a peaceful and prosperous future in which the United States remains the "last, best hope of man on Earth."

This description of America, originally Abraham Lincoln's, was first used by Reagan in 1964 in the closing passage of the speech that made him famous: his nationally televised appeal in behalf of Republican presidential candidate Barry Goldwater.

Many of Reagan's phrases in his second and final Inaugural Address echoed the speeches for which he is best remembered. Speaking of the need for "hard decisions" and who should make them, Reagan repeated words he used for his inauguration as governor of California in 1967: "If not us, who? If not now, when?"

And in calling upon his countrymen to "challenge the limits of growth," Reagan returned to the theme of everyday Americans as heroes that provided the focus of his first presidential inaugural speech four years ago.

"We must think anew and move with a new boldness, so every American who seeks work can find work; so the least among us shall have an equal chance to achieve the greatest things: to be heroes who heal our sick, feed the hungry, protect peace among nations and leave this world a better place," Reagan said.

But the speech Reagan gave yesterday was in other respects vastly different from his first inaugural.

"There's a considerable difference in being president for a few minutes and for four years," said Ben Elliott, chief of the speechwriting team that prepared drafts for Reagan that were reworked in longhand by the president.

Reagan's speech, which was interrupted 11 times by applause, united the rhetoric of free enterprise he has been using since the early 1950s, when he was a touring speaker for General Electric, with the favorite issues of his presidency: limits on domestic government spending, continuance of a strong defense and constitutional amendments banning abortion and mandating a balanced federal budget.

As the United States and Soviet Union prepare to resume arms-control negotiations that he said offered the promise of the elimination of nuclear weapons, Reagan was unrelenting, though careful in his rhetoric, in his portrayal of the rival superpower.

"There are those in this world who scorn our vision of human dignity and freedom," he said. "One nation, the Soviet Union, has conducted the greatest military buildup in the history of man, building arsenals of awesome offensive weapons."

Reagan was equally unrelenting in making the case for the futuristic and much-criticized proposal to protect the United States by "a security shield . . . that will destroy nuclear missiles before they reach their target." This idea, formally known as the Strategic Defense Initiative and often called "Star Wars," has captivated Reagan, and aides said he insisted on including a central reference to it in his inaugural speech.

Apart from these specifics, Reagan's address yesterday recapitulated the basic ideas of individualistic freedom from which he has rarely deviated in 20 years of public life.

The economy should be "freed from government's grip," he said. People must be "free to follow their dreams." The United States "must remain freedom's staunchest friend, for freedom is our best ally and it is the world's only hope to conquer poverty and preserve peace."

The speech was laced with inspirational phrases designed to identify Reagan with the aspirations and values of an America that Reagan said has "lighted the world with our inventions, gone to the aid of . . . mankind wherever in the world there was a cry for help, journeyed to the moon and safely returned."

Other evocative Reaganisms sprinkled throughout the speech included depictions of America as "a rising nation," "poised for greatness," and a country on the verge of "a new American emancipation."

In Reagan's view, the United States remains "a nation still mighty in its youth and powerful in its purpose."

"Let history say of us, these were golden years when the American revolution was reborn, when freedom gained new life and America reached for its best," the president said.

Reagan yesterday was preoccupied with American history as well as his own.

"History is a ribbon, always unfurling; history is a journey," he said. "And as we continue our journey we think of those who traveled before us."

The next passage of the speech, originally scheduled for delivery on the West Front of the Capitol, called for Reagan to say that "we stand again at the steps of this symbol of our democracy."

Reagan read this line, became aware of what he had said and made a typically impromptu revision, adding with a smile, "or we would have been standing at the steps if it hadn't gotten so cold. Now we're standing inside this symbol of our democracy."

The president made several other changes in the speech, none of them similarly conspicuous to the television audience. Aides said they were made because Reagan anticipated that he would be speaking outside in the cold before an audience in no condition for prolonged oratory.

Reagan, sometimes accused during his presidency of giving insufficient attention to homework, has always lavished attention on his major ceremonial speeches, and yesterday's was no exception.

He took original drafts, prepared by a speechwriting team of Elliott, Peggy Noonan and Anthony Dolan, to Palm Springs, Calif., with him late last month and worked out his own version in longhand. After further revisions and inserts, including the presidential defense of "Star Wars," the draft was completed late last week.

What Reagan wanted to focus on most, Elliott said, was the idea "that the future is rich in possibilities, that the American revolution is reborn."

It was this idea, restated in different ways throughout the speech, that won a positive response from some Democrats normally critical of the president.

"President Reagan, in a moving and inspirational address, has restated America's mission," said Sen. Alan Cranston (D-Calif.), the Senate minority whip.

Sen. Joseph R. Biden Jr. (D-Del.) called the speech "brilliant" and compared it to the 1961 Inaugural Address of President John F. Kennedy.

"He was optimistic, exciting," Biden said of Reagan's speech. "He said we're not abandoning the past but we're setting out on a new course."

Sen. Daniel Patrick Moynihan (D-N.Y.) said he found Reagan's delivery "subdued, very subdued" and added: "It's almost as though Reagan was saying it's not going to be as much fun as the other time around."

Moynihan was among many in the Rotunda who couldn't hear a word of what the president said. Reinforcing the view of Reagan aides that it was a television speech, Moynihan slipped out to an anteroom to watch the performance on TV.

The symbols of the past that mean so much to Reagan were resonant in the speech's final passage, which bore the evocative imprints of speechwriter Noonan as well as the president.

"A general falls to his knees in the hard snow of Valley Forge; a lonely president paces the darkened halls and ponders his struggle to preserve the Union, the men of the Alamo call out encouragement to each other; a settler pushes west and sings a song, and the song echoes out forever and fills the unknowing air," the president said.

"It is the American sound: hopeful, big-hearted, idealistic -- daring, decent and fair," Reagan said. "This is is our heritage, that is our song. We sing it still."

It was old music for Reagan, who has played these tunes many times in a long career.

"For all our problems, our differences, we are together as of old, as we raise our voices to the God who is the author of this most tender music," the president said in a quiet voice.

"And may he continue to hold us close as we fill the world with our sound -- in unity, affection and love."