In 1824, 1833, and 1844 he ran for president but lost each time.
ignored Texas
Yes, he was one of the candidates. He threw his votes to Quincy Adams in exchange for the position of Secretary of State.
He was never secretary of state. He was the secretary of treasury under Washington.
the sounds were so big and so impressive that he felt he should see it
presidency of the U.S.
Henry Clay and Andrew Jackson ;-)
Henry Clay of Kentucky.
ignored Texas
Henry Clay did not have a vice president, because he was never elected president of the United States. He did run for president three times, but lost each campaign.
No President of the United States ever made that statement.However, Henry Clay did.Although he never won the Presidential Election, he did run for office.
United States Senate
Yes, he was one of the candidates. He threw his votes to Quincy Adams in exchange for the position of Secretary of State.
He ran for the U.S. senate, but he lost badly. It was the only political race he ever lost, and he has said he learned a lot from it; the next time he ran for the U.S. senate, in 2004, he won.
Clay's proposal was based on the belief that a protective tariff that helped industry would eventually help every section of the country. The factories protected by the tariff would run at a profit and employ the urban population.
How does someone get chosen to run for public office
Yes. He was the Democratic nominee in 1860. (He also campaigned unsuccessfully for the Democratic nomination in the two elections before that.)
Wilson served in the office of president for eight years. I am not sure what is meant by "run in office".