The strategic arms negotiations that the Soviet Union broke off - at least temporarily - yesterday began nine years ago in Glassboro, N.J. Since then the talks have produced unprecedented agreements but have done little to slow the arms race.

The apparent idea of President Carters novel proposal to cut substantially the Soviet and American arsenals, which the Soviets rejected yesterday, was finally to do something to stop the arms race. It was a radical idea in the context of the SALT negotiations thus far.

Beginning in the first Nixon administration, the SALT talks have been used - at first only by the Russians, subsequently by both sides - as a means of establishing a sort of contractual nuclear parity between the superpowers.

Because the two countries have different kinds of strategic weapons, radically different geographical situations and inconsistent strategic objectives, they have had a difficult time agreeing on a precise definition of parity. The Soviet side demonstrated again yesterday how serious this problem still is.

While negotiations on this problem have dragged on, both sides have continued to improve their strategic weaponry, both quantitatively (primarily on the Soviet side) and qualitatively (on both sides). The arsenals of both are now vastly superior in terms of their capacity to inflict damage than were when President Johnson first broached the idea of strategic arms talks to the Soviet premier, Alexei N. Kosygin, at their Glassboro summit.

The negotiations began after President Nixon's inauguration.The first round ended at the Moscow summit in May, 1972, when the superpowers signed two SALT documents: a treaty radically limiting both sides' antiballistic missile (ABM) systems and an "interim" limitation of offensive arms.

That interim agreement allowed the Soviets a modest numerical advantage in missle launchers that Nixon and his principal negotiator, Henry A. Kissinger, said would be offset by American superiority in the area of multiple warheads that can be launched on a single missile and fired at independent targets. But the Soviets began to close that gap, and many Americans involved in the SALT process expressed fear that the interim agreement allowed the Soviets room to achieve an unacceptable advantage.

With this background, President Ford met Leonid I. Brezhnev, in November, 1974, at Vladivostok in the Soviet Far East. They negotiated the outlines of a new, long-term limitation on missiles that would allow both sides to maintain forces composed of up to 2,400 missiles, 1,320 of them equipped with multiple, independent targetable warheads (MIRVs).

At the time this appeared to be the sort of contractual equality that had previously eluded both sides. The Soviets made what Kissinger called substantial concessions at Vladivostok by agreeing not to count in the American total U.S. atomic weapons based in Europe but capable of reaching the Soviet Union.

But before Vladivostok number could be incorporated in a final treaty, new American technological advances and the appearance of a new Soviet bomber system raised serious complications.

The United States succeeded in developing strategic, long-range cruise missiles - automatically piloted drones that could travel long distances, 2,000 miles or more, at very low altitude and strike targets with extraordinary accuracy. At first the United States took the position that since they were not ballistic missiles, they should not be counted in the SALT talks.

The Soviets, meanwhile, deployed the Backfire bomber, a plane with obvious medium-range capabilities, which the Pentagon and other analysts said might be used for long-range strategic bombing missions against the United States.

In late 1975 and early 1976 Kissinger worked out a new compromise with the Soviets taking account of these developments. He negotiated a tentative agreement allowing the United States to deploy a limited number of cruise missiles on surface ships and bombers, and also allowing the Soviets to deploy some Backfires with assurances that they would not be used as intercontinental weapons.

This agreement was rejected, in effect, by the Ford administration. Congressional and Pentagon opponents of it said Kissinger had traded away an enormously valuable card, the cruise missile, for inadequate assurances regarding Backfire.

Ford told a group of reporters in Washington last week that hesitancy in the Pentagon prevented him from converting the pact Kissinger negotiated into a final treaty. Arms control advocates have charged that Ford was intimidated by attacks on his strategic policy by Gov. Ronald Reagan, his opponent in last year's Republican Party primaries. The Kissinger proposal collapsed just as the primary season was beginning.

The Carter administration came into office pronouncing its intention to work out new SALT agreements with the Russians. The new administration worked feverishly during the last two months to formulate a new position for Secretary of State Cyrus R. Vance's trip to Moscow.

The Carter administration rejected the Kissinger compromise of early 1976, which theoritically might have been resuscitated at this time. It came up with two other ideas.

The first was the radical proposal Vance pressed in Moscow this week. Details of it were not made public, but informed sources indicated that the offer called for cuts in total missile forces on both sides to 1,800 or less - more than 24 per cent below the Vladivostok levels - coupled with unspecified restraints on cruise, Backfire and other new weapons systems.

The second, fallback position was to incorporate the Vladivostok numbers into a new treaty, setting aside the cruise, Backfire and other new weapons for the next round of SALT negotiations. The Soviets had previously rejected this idea on the ground that it allowed the United States a free hand to proceed into the next generation of weapons - cruise missiles - while the Russians were still catching up in MIRVs, the previous generation.

The Carter administration was obviously delighted with its new dual package, because it seemed to satisfy the warring elements inside the American government.

Brezhnev indicated yesterday, however, that idea which appeared so satisfactory in Washington looked much less desirable to the Soivet leadership in Moscow.