And the chilling memory of the 241 American servicemen slaughtered by a Muslim suicide truck bomber at the US Marine base in Beirut in 1983 sent US negotiator Richard Holbrooke back to Sarajevo to ask Alija Izetbegovic to order Arab fighters out of his country. The Bosnian president rather optimistically gave them 30 days to leave.
In Beirut, where the bloodbath in Bosnia has been watched on television with both horror and the condescension of shared guilt, the Lebanese did not know whether to laugh or cry. Wasn't Sarajevo already worse than Beirut? In 15 years of civil war and "ethnic cleansing" in Lebanon, 150,000 men, women and children were killed. In just four years of war in the former Yugoslavia, about 200,000 have died.
But the parallels should be troubling the most powerful force in Nato. Back in 1982, the American Marines arrived in Beirut at the head of an all-Nato force of French and Italian troops and - later - 100 British soldiers. They came, they said, to protect the Palestinians after the massacre at the Sabra and Chatilla camps by Israel's Christian Lebanese allies. In 1982, Washington believed it had secured the agreement of both Syria and Israel to withdraw their armies from the country. The Americans were told that local militias would be disarmed and "foreign fighters" would be expelled. They promised to re-arm the government army.
Just like Bosnia. Most frightening of all parallels is the American failure to plot an escape route. The Marine presence in Beirut - only 2,000 strong - was open-ended, while the Nato deployment, with 20,000 US troops, is limited to just a year. But the American failure to bring peace to Lebanon forced the Marines to stay longer - until they became so deeply involved in the civil war that they were themselves attacked by that lonely, smiling suicide bomber.
Can Nato really pull out of Bosnia if it fails, if the war re-ignites, or if those ambiguous, frighteningly complex paragraphs of the Dayton agreement prove too difficult for its troops to put into practice? The US failure in Lebanon forced President Reagan to search for new policy interests in the region; will the current US administration have to find new goals in the Balkans if it faces humiliation there?
The Americans also have a habit of declaring their desire to assist one political group or ethnic community while ending up supporting another. The Marine deployment in Beirut was intended to ensure the protection of Palestinians and the withdrawal of foreign forces from Lebanon. But it ended up supporting a Lebanese government that loathed the Palestinians, and opening a defence alliance with the Israelis who had invaded Lebanon.
The Bosnian government has now been told it will control a unified Sarajevo, that the frontiers of Bosnia are inviolate, that courts and civil society will be resurrected after three years of massacre. But the Americans are relying on their Croat friends to hold the Bosnian federation together; which is why the US ambassador to Zagreb denied that the Croats had "ethnically cleansed" 200,000 Serbs out of Krajina last summer - even when the Croats were driving the Serbs out, murdering elderly survivors and burning every village. The Muslim-Croat alliance in Bosnia may look good on paper, but it is as brittle as gold leaf.
And if the Croats grow tired of Izetbegovic's puppet show in Sarajevo, they can turn out the lights. What will the Bosnian Muslims do when they realise that the American peace is founded on the good offices of their two enemies, the Croats and the Serbs?
In Beirut, 13 years of winter storms have bathed the scorched ruins of the US Marine base, but the burn-marks can still be seen on the concrete, the faded signs for drinks in the Marine mess still visible behind the long, wet grass and rubble. Somehow, they seem more powerfully symbolic today than they have for many years. The Lebanese discovered the price of civil war - just as the Bosnians will now discover it: that their future is decided not by themselves but by outside powers. And the outside powers must reckon with the fury of those they came to help if their promises turn to dust.