So Madame L was not surprised to find, when she Googled this word, that "termagant" has come to mean a harsh-tempered or overbearing woman.
But Madame L was surprised to find on Wikipedia that the original meaning of the word "termagant" was a made-up god in Christian morality plays, supposedly worshiped by Muslims, who were also believed to worship Muhammad the prophet as a god.
Do read the Wikipedia article for more fascinating information about this. Here's how it came to refer to women, according to Wikipedia:
As a result of the theatrical tradition, by Shakespeare's day the term had come to refer to a bullying person. Henry IV contains a reference to "that hot termagant Scot". In Hamlet, the hero says of ham actors that "I would have such a fellow whipped for o'er-doing Termagant, it out-Herods Herod". Herod, like Termagant, was also a character from medieval drama who was famous for ranting. In similar vein Beaumont and Fletcher's play A King and No King contains the line "This would make a saint swear like a soldier, and a soldier like Termagant."
Mainly because of Termagant's depiction in long gowns, and given that female roles were routinely played by male actors in Shakespearean times, English audiences got the mistaken notion that the character was female, or at least that he resembled a mannish woman. As a result, the name "termagant" came increasingly to be applied to a woman with a quarrelsome, scolding quality, a sense that it retains today.