“Such a nasty woman.”

Nearing the end of a campaign of disparagement, Donald J. Trump coined a classic in the annals of insults against powerful women.

Mr. Trump’s remark — which he directed at Hillary Clinton during the third presidential debate Wednesday as she talked about a particularly nasty topic, Social Security — had all the makings of a feminist meme. It came across as impulsive and petulant, with sexist undertones, even if it lacked the sophistication of certain predecessors:

She has “the lips of Marilyn Monroe, the eyes of Caligula.” — the former French president François Mitterrand, about Margaret Thatcher

Insults are, of course, an inextricable part of politics, and not only directed at women by men. Mr. Trump has weathered his fair share this election (Senator Mark Kirk of Illinois said on Twitter this month: “DJT is a malignant clown.”) Some of the most memorable came from women: Dorothy Parker, upon hearing that Calvin Coolidge had died, reportedly said, “How can they tell?” Barbara Bush, during the 1984 Reagan-Bush campaign against Walter Mondale, described Geraldine Ferraro, the Democratic vice-presidential nominee, as an “I can’t say it, but it rhymes with rich.” Mrs. Bush later apologized and claimed the word she was looking for was “witch.”

Mr. Trump in particular is an equal opportunity insulter — just look at the things he said about his male opponents during the primaries.

But insults of powerful women by men perform a particular role, researchers say: cutting them down to size, and playing into discomfort with women in power.

Historically, there has been a high penalty for explicitly attacking women, said Kathleen Hall Jamieson, professor of communication and director of the Annenberg Public Policy Center at the University of Pennsylvania. As a result, rarely are insults of women as overt as “nasty woman” or some other Trump offerings:

“Look at that face! Would anyone vote for that? Can you imagine that, the face of our next president?” — Mr. Trump, about Carly Fiorina

Instead, insults have generally been subtler — and perhaps more pernicious, by playing into people’s stereotypes without their knowing it. Calling Mrs. Clinton “angry,” as Mr. Trump did several times Wednesday, or “emotional,” as John McCain once did, evokes negative gender stereotypes of women as hysterical and irrational, Ms. Jamieson said.
By questioning Mrs. Clinton’s “stamina,” Mr. Trump implies that she is too weak to be commander in chief. Terms of affection do something similar:

“Calm down, dear.” — Prime Minister David Cameron to Angela Eagle, a British politician

People tend to be most bothered when men and women don’t fit the stereotypes they expect — men as confident, strong leaders and women as humble, cooperative and supportive, according to research by Laurie A. Rudman, a psychologist at Rutgers.

Questioning a woman’s niceness — as some people thought Barack Obama did when he told Mrs. Clinton she was “likable enough” in a 2008 debate — serves that purpose, and also makes it hard for a woman to fight back because she will only appear less kind, Ms. Jamieson said.

While women with children have been belittled as not having enough capacity to lead while mothering, women without children also receive blistering criticism for not living up to society’s expectations of women.

“Anyone who has chosen to remain deliberately barren, they’ve got no idea about what life’s about.” — the Australian senator Bill Heffernan about Julia Gillard, who would go on to become Australia’s prime minister

Condescension is another common tool for deflating powerful women.

“Let me help you with the difference, Mrs. Ferraro, between Iran and the Embassy in Lebanon.” — George H.W. Bush mansplaining to Ms. Ferraro during a vice-presidential debate

Attacking women’s appearance serves a dual purpose: the attack itself, and the implication that a woman is valuable for her looks more than her brains. The same goes for sexual remarks, which some people heard in Mr. Trump’s use of the word “nasty,” though it’s possible he didn’t mean the word in that way at all.

Mr. Trump is an expert at targeting a woman’s looks, but he’s hardly the first to do it.

“Michelle Obama, her project is obesity. And look at her big butt.” — Representative Jim Sensenbrenner, as reported by a bystander. (Mr. Sensenbrenner later apologized.)

“Did you see Nancy Pelosi on the floor? Complete disgust. If you can get through all the surgeries, there’s disgust.” — Senator Lindsey Graham, making a plastic surgery joke

“You’re more beautiful than you are intelligent.” — the former prime minister Silvio Berlusconi of Italy, to Rosy Bindi, an opposition member of Parliament

Attacking women in power goes back centuries:

“The concubine, the she-devil, the whore.” — Eustace Chapuys, imperial ambassador to England, about Anne Boleyn

But the thing about gendered insults is that they can backfire, by rallying at least half the population. When Patty Murray was told by a state representative that she couldn’t make a difference because she was just “a mom in tennis shoes,” she turned around and used it as a campaign slogan that put her in the Senate.

Doris Burke contributed research.