Behind the television images of Arab crowds celebrating the assassination of president Anwar Sadat that are horrifying Westerners who revered him as a statesman lie deeply held personal grievances and political antagonisms that made Sadat seem very different when perceived through the Arab prism.

Pure ideology may have accounted for the outpourings of hatred in Iraq and Libya, where calls for Sadat's overthrow had been repeated often enough to make those countries prisoners of their own rhetoric. But for many Palestinians, Syrians and Lebanese, Sadat had been the perceived cause of real hardship and suffering.

Politically, the feelings of many of those dancing in the streets or firing off rifles in celebration undoubtedly boiled down to the repeated betrayals, as they saw it, that Sadat had perpetrated as leader of the most powerful Arab nation. Other Arab leaders could sell out, but theirs were betrayals of lesser impact.

Charming and suave to Westerners, especially to Americans for whom he became the polite, gallant Arab, Sadat was nothing more than a double-dealer for most of the Arab world. This may explain part of the almost complete lack of a display of compassion for the fallen leader.

Deep down, Arabs say, they were less angered at his desperate daring in travelling to Jerusalem in 1977 than at his apparent unwillingness and inability to say no to anything Israel, in the person of unbending Israeli Prime Minister Menachem Begin, demanded.

For the Palestinians, Sadat's imperturbable willingness to continue talking to a Begin so manifestly opposed to any concession on the autonomy negotiations for the future of the Israel-occupied West Bank and Gaza Strip was another sign of Egyptian egotism and treason.

Rightly or wrongly, Palestinians and also many Lebanese remain convinced that Sadat was morally responsible for the tens of thousands of mostly civilian dead in the 1975-1976 civil war in Lebanon.

They argued that Sadat, in cahoots with Israel and then secretary of state Henry Kissinger, did nothing to stop a conflict that conveniently distracted attention from the Sinai troop disengagement agreement signed in September 1975.

No matter how tortured such logic may seem to Westerners, to the Middle Eastern mind Egypt's very absence from that fighting contrasted suspiciously with Cairo's major involvement in a much less serious civil war in Lebanon in 1958.

Syrian President Hafez Assad felt twice betrayed by Sadat. Starting in 1975, Sadat had left him in the lurch by negotiating directly with Israel despite promises to work in tandem made prior to their successful partnership in the 1973 war. Then, at the end of the Lebanese civil war in 1976, their respective foreign ministers swore to uphold the "unity of unities" only to have Sadat set forth on his fateful voyage to Jerusalem the following year.

Adding to this negative image, almost the exact reverse of the one that he had projected to Westerners suddenly paying attention to the Arab side of the Middle East equation, was the manifest contempt he showed toward his Arab critics and his increasing irritation with anything approaching criticism. That telltale mark of Arab dictators in trouble long escaped his Western admirers despite periodic arrests of journalists and opposition politicians starting as long ago as 1978. Only last month when he arrested more than 1,500 opposition figures did the West seem to realize what Arabs long had been saying: that Sadat faced growing opposition.

Yet, there was something less than totally enthusiastic about these demonstrations celebrating Sadat's passing. When Sadat's predecessor, Gamal Abdel Nasser, died of natural causes, Beirut Moslems burned tires and mourned his passing in ways strangely similar to their celebration of Sadat's death as they fired their Soviet-manufactured AK47 rifles into the air for days and days. That was in 1970, before the Arab world started coming apart at the seams, before Sadat helped the process along as no Arab before him, in the view of many here.

By comparison the anti-Sadat demonstrations were limited to Palestinian and left-wing Lebanese militants and gunmen whose principal accomplishment appeared to have been to wound 18 civilians with stray bullets fired aimlessly in the air.

By today most of the demonstrations were peaceful. By tonight, the shooting and exploding of dynamite echoing through Beirut streets had nothing to do with Sadat. Rather, it was many Lebanese Moslems' way of greeting the feast of Id Al Adha that marks the end of the annual pilgrimage to Mecca.