The specter of violence looms over much of his speech, which is infused with words like kill, destroy and fight. For a man who speaks off the cuff, he always remembers to bring up the Islamic State’s “chopping off heads.” And he has expressed enthusiasm for torturing enemies beyond waterboarding. Last month, after several men hit a Black Lives Matter protester at one of his rallies, Mr. Trump said, “Maybe he should have been roughed up.”

“Such statements and accusations make him seem like a guy who can and will cut through all the b.s. and do what in your heart you know is right — and necessary,” said Michael Kazin, a historian at Georgetown University, echoing the slogan that Barry Goldwater used in his 1964 presidential campaign.

And Mr. Trump uses rhetoric to erode people’s trust in facts, numbers, nuance, government and the news media, according to specialists in political rhetoric. “Nobody knows,” he likes to declare, where illegal immigrants are coming from or the rate of increase of health care premiums under the Affordable Care Act, even though government agencies collect and publish this information. He insists that Mr. Obama wants to accept 250,000 Syrian migrants, even though no such plan exists, and repeats discredited rumors that thousands of Muslims were cheering in New Jersey during the Sept. 11, 2001, attacks. He promises to “bomb the hell” out of enemies — invoking Hiroshima and Nagasaki — and he says he would attack his political opponents “10 times as hard” as they criticize him.

(Mr. Trump, who also pledges to build up the military to show American toughness, will hold a rally on Monday on the aircraft carrier Yorktown in South Carolina to commemorate the anniversary of the Japanese attack on Pearl Harbor.)

And as much as he likes the word “attack,” the Times analysis shows, he often uses it to portray himself as the victim of cable news channels and newspapers that, he says, do not show the size of his crowds.

Mr. Trump declined a request to be interviewed for this article.

This pattern of elevating emotional appeals over rational ones is a rhetorical style that historians, psychologists and political scientists placed in the tradition of political figures like Goldwater, George Wallace, Joseph McCarthy, Huey Long and Pat Buchanan, who used fiery language to try to win favor with struggling or scared Americans. Several historians watched Mr. Trump’s speeches last week, at the request of The Times, and observed techniques — like vilifying groups of people and stoking the insecurities of his audiences — that they associate with Wallace and McCarthy.