Like Monroe's speech to Congress in 1823, President Polk's 1845 speech is pretty long and talks about a lot of different topics. In one section, though, Polk reiterates the administration's commitment to the main principles of the Monroe Doctrine: nonintervention in Europe, and no more European colonies in the Americas.

Polk leads into this section discussing the Oregon territory and proposals to split the land with Britain (hint: he's not a fan). He uses the opportunity to talk about U.S. expansion and "rising greatness as a nation," and how they're "attracting the attention of the powers of Europe."

He continues on:

It is well known to the American people and to all nations that this Government has never interfered with the relations subsisting between other governments… We may claim on this continent a like exemption from European interference. The nations of America are equally sovereign and independent with those of Europe… We must ever maintain the principle that the people of this continent alone have the right to decide their own destiny… The American continents, by the free and independent condition which they have assumed and maintain, are henceforth not to be considered as subjects for colonization by any European powers. (Source)

Did you notice how he directly quoted Monroe in that last line (4)?

Twenty years after the fact, Polk clearly aims to "reaffirm the principle avowed by Mr. Monroe." The speech shows the lasting impact that the Monroe Doctrine had American foreign policy, and how much its ideas were supported, at least by the government. Polk's wording also illustrates how the ideas of the Monroe Doctrine were presented, with a focus on freedom and protecting the American system of government—which are obviously better than stuffy old monarchies.