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Henry Clay became speaker in 1811 on his first day in the House of Representatives. It took Nancy Pelosi and John A. Boehner 20 years apiece.

“Slow learner,” Mr. Boehner said with a chuckle, seated alongside Ms. Pelosi and former Speaker J. Dennis Hastert on Friday night at a tribute to Clay, their legendary predecessor. He called Clay a role model, “the first real speaker of the House that had some power.”