In my March 31, 2013 post, "RN: The Memoirs of Richard Nixon, Volume 2:17", I talked about Nixon's discussion of the 1973 attack on Israel by Syria and Egypt. The U.S. was providing military supplies to Israel, whereas Arabs received Soviet support. But Nixon's strategy was to wait until there was a stalemate and both sides were tired of fighting before proposing a cease-fire.
What happened instead was that
Israel made significant military gains in the conflict, bringing Syria
and Egypt to the bargaining table. There was no stalemate, per se, for
Israel had the upper hand. The Arabs proposed a cease-fire agreement in
which Israel would withdraw to its pre-1967 borders. While Nixon in
the past did not rule that out, in his attempt to cultivate
relationships with Arab countries, Nixon found the Arab cease-fire
proposal to be unrealistic. For one, the Israelis valued the territory
that they gained after 1967, regarding it as necessary in terms of their
national security as well as "their leverage in any negotiations" (page
488). Second, the Israelis were the victors in 1973, so why would they
agree to give up the territory that they got after 1967, as if the
Arabs had won? Both sides agreed on a cease-fire that did not require
Israel to return to its pre-1967 borders, yet both sides suspected the
other of violating the cease-fire. In any case, Nixon says on page 502
that the Arabs recognized that military victory against Israel was "now
beyond their reach for at least the next several years", and so Egypt
and Syria were open to negotiation. On pages 501-502, Nixon rejoices
that, under his Administration, the U.S. was able to support Israel,
without utterly alienating the Arabs.
On pages 501 and 502-503, Nixon talks some about detente.
Israeli Prime Minister Golda Meir told President Nixon that she thought
that Europeans were naive about detente and the Soviet threat, but that
Nixon had a more realistic perspective about it. Nixon says that he
never said that the Soviets were "good guys", for he recognized that the
U.S. and the U.S.S.R. would act according to their self-interests. But
Nixon thought that detente could prevent "unnecessary confrontations"
with the Soviets: "All we can hope from d[e]tente is that it will
minimize confrontation in marginal areas and provide, at least,
alternative possibilities in the major ones" (page 501).