PHILADELPHIA — They saluted the valor and vigor of the American armed forces. They quoted Ronald Reagan and Theodore Roosevelt, iconic Republican presidents of the 20th century, as well as a beloved Republican former first lady. They talked plainly about faith, about instilling good family values, about the uniqueness of the American experiment.

Over four days here, the Democratic Party sought to flip the magnetic poles of American politics, seizing on Donald J. Trump’s unlikely rise to invade intellectual and rhetorical terrain held by the Republican Party for most of the last four decades.

While Mr. Trump’s convention in Cleveland described the United States as cheated, hapless and weak, a parade of prominent Democrats here summoned a country of limitless ingenuity, profound strength and majestic moral authority.

For the Democrats, it was a carefully calibrated, precisely drafted assault on the Republican coalition. For months, they have sought to tar Republican politicians with Mr. Trump’s essence, arguing that the New York developer and reality star was the true id of a Republican Party marbled with political extremism and racial antagonism.