DOHA, Qatar — WHEN Mohamed Morsi became Egypt’s first democratically elected president last year, it was an especially sweet victory for the Muslim Brotherhood, the region’s oldest and most influential Islamist movement. After a long history of repression, the Brotherhood had finally tasted triumph. But their short-lived rule ended Wednesday when Egypt’s army deposed Mr. Morsi.

The Brotherhood’s fall will have profound implications for the future of political Islam, reverberating across the region in potentially dangerous ways. One of the most important political developments of recent years was the decision of Islamist parties to make peace with democracy and commit to playing by the rules of the political game. Leaders counseled patience to their followers. Their time would come, they were told.

Now supporters of the Brotherhood will ask, with good reason, whether democracy still has anything to offer them. Mr. Morsi’s removal will breathe new life into the ideological claims of radicals. Al Qaeda and its followers have long argued that change can’t come through the democracy of “unbelievers”; violence is the only path. As the Qaeda leader Ayman al-Zawahri once said, “What is truly regrettable is the rallying of thousands of duped Muslim youth in voter queues before ballot boxes instead of lining them up to fight in the cause of Allah.”

Al Qaeda’s intellectual forebears emerged in the 1950s and 1960s, and were shaped by events that bear an eerie similarity to those of this week. In 1954, a popularly backed Egyptian Army moved against the Muslim Brotherhood, arresting thousands and dismantling the organization. Prison had a radicalizing effect on Sayyid Qutb, a leading Brotherhood ideologue, who experienced torture at the hands of his captors before being executed in 1966. Many of Mr. Qutb’s followers later left the Brotherhood’s embrace and went their own way, setting up militant organizations that would begin perpetrating acts of terrorism.