In a Vienna conference room a week ago today, Jimmy Carter and Leonid I. Brezhnev sat down to summarize the relations and mutual problems of the world's two most powerful nations. What these two men with their fingers on the nuclear buttons chose to emphasize or to leave out tells much about themselves and about the fragile state of Soviet-American accord.

This initial meeting last Saturday morning in Vienna, by advance agreement, was the time and place to explain the view from the top of each man's capital. In tightly compressed remarks of about 20 minutes each - plus time for translation, Carter and Brezhnev sought to deal with the most basic questions in the superpower relationship.

Brezhnev, who led off by donning rimless glasses and reading a typewritten presentation, began by declaring that the two nations share a special relationship and a special responsibility, due to their might and their influence.

Carter, midway through his presentation from notes on yellow legal sheets, quoted with approval a statement by Brezhnev last October in Moscow to Secretary of State Cyrus R. Vance. One miscalculation, the explosion in anger or by mistake of a single nuclear weapon, would be catastrophic, Brezhnev said then and Carter repeated.

Brezhnev, a bit later in the summit talk, spoke of the major efforts needed beyond the strategic arms limitation treaty (SALT II to rid the world of the threat of nuclear war "As you said, Mr. President," the Soviet leader reiterated, "all it takes is the push of one butto."

Details of the Carter-Brezhnev presentations and byplay, as reported by Amerian officials and in unusually full accounts by Soviet officials and the Soviet press, cast additional light on a summit that was notable more for exploration of one another's positions than for any meeting of the minds.

Brezhnev's central points in his presentation to Carter were:

The historical experience of the two countries in their World War II alliance, the "pointless period" of the Cold War that hurt both nations, the "breakthroughs" of early 1970s detente and a period of retrogression in the past several years.

The "fundamental" importance of two Nixon-era agreements that are considered of minor importance, or even forgotten, in Washington because they deal in generalities. These are the 1972 "Basic Principles of Mutual Relations" and the 1973 "Agreement on the Prevention of Nuclear War." Brezhnev appealed for consistency, which the Soviets say has been lacking in their dealings with Carter, and for U.S. adherence to agreements previously concluded.

The importance of the goals, interests, policies and alliances of the two nations, which cannot be changed or encroached upon. Brezhnev reiterated Soviet solidarity with "liberation struggles" in the Third World.

While noting that assessments on regional conflicts differ, Brezhnev declared there is no hostile Soviet design against the United States or desire to prejudice legitimate American interests. These interests were not defined.

Opposition to spiraling military spending, which in Brezhnev's view is generated more by Washington than by Moscow. He accused the United States of "whipping up" the arms race, and charged "off the record" that the United States has drafted a "much larger" military budget this year. Carter responded by saying that the Soviets have had much larger military increases than the United States. Brezhnev retorted that the Soviet Union looks to the United States for leadership.

Carter's central points in his presentation to Brezhnev were:

The need for more frequent, full and many-faceted communications at the highest levels, both military and political.

The importance of SALT III negotiations, expected to follow the current SALT II, as the forum for major nuclear arms reductions. Carter advocated "maximum reductions" and at a subsequent session suggested further weapon cuts from the SALT II level as a prelude to SALT III.

The vital importance of restraint in regional conflicts and avoidance of intervention "either directly or through third parties" such as Cubans in Africa. Carter said the two nations must take into account each other's vital interests in maintaining access to crucial natural resources.

The strength and power of the two nations, which are too great for either one to be dominated by others. This appeared to be an allusion by Carter to Moscow's fears concerning its rival, Peking.

Unlike the 1961 John F. Kennedy-Nikita S. Khrushchev summit in Vienna, there was little talk of grand designs or the world strategic balance.

Unlike the Richard Nixon and Gerald Ford summits with Brezhnev in 1972-74, there were few Soviet theatrics and on major clashes on matters such as Vietnam and the Middle East. The United States and the Soviet Union have switched positions in Vietnam and in Egypt since the early 1970s.

Neither Carter nor Brezhnev, in efforts to put their best foot forward, dwelt upon those turns of history. CAPTION: Picture, President Carter and Soviet leader Leonid Brezhnev face each other across the conference table at the start of the Vienna summit at which they signed the SALT II accord setting limits on the superpowers' nuclear weapons. UPI