Provide a little back ground as to the context of the origin, and happy to add them!
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It was Greek to me - Originated from "Julius Caesar." Spoken by Casca when commenting on how he didn't understand something Ciscero said because Ciscero was literally speaking in Greek. This phrase is now used to refer to how somebody may not understand what someone is talking about, like if they are using specialized jargon or simply talking in another language.
A foregone conclusion - From "Othello," a comment the titular character makes describing how an outcome was decided in advance because of a dream he had signified that it was inevitable. Usually used now to describe how something is or was unavoidable.
Break the ice - Originated from "The Taming of the Shrew," referring to how difficult it can be to break past social stiffness by starting that first conversation. It can also refer to as attempting to start a difficult task or undertaking in general rather than being limited only to a social situation.
Brevity is the soul of wit - Said in "Hamlet" by Lord Polonius, he suggests that being concise is a essential to conveying intelligence.
Green-eyed jealousy - Another "Othello" quote, Iago says this as another variation of the modern day phrase "green with envy," which refers to when someone becomes jealous.
Beware the ides of March - Said by the Soothsayer in "Julius Caesar" when he warns Caesar how he should be weary of March 15th, which turns out to be the date of his assassination.
One fell swoop - Said in "Macbeth," used by Macduff to describe how something can be done quickly in one swift action. In this case, he uses it to describe the death of his own family and servants.
Dead as a doornail - Used a few centuries before, but popularized in "Henry VI, Part 2," this phrase described how someone was 100% dead. This likely originated from the idea of hammering nails part of the way through a surface and then bending the end of it over to help secure it, making the nail useless anywhere else in the process.
Wild goose chase - Used in "Romeo and Juliet" by Mercutio, this phrase was used to refer to a horse race with a strange, difficult pattern to ride on. It now is used to refer to a long endeavor that ultimately proves pointless in the end.
Et tu, Brute? - Caesar's famous last words in the play as he witnesses Brutus, his supposed friend, finishing him off during the assassination. A variant of this phrase is usually used substituting "Brutus" with a different person's name to suggest or signify betrayal.
Good riddance - While the word "riddance" was used before then to describe getting rid of something, Shakespeare later popularized it in "Troilus and Cressida." The phrase itself is now used to describe how somebody is pleased to be rid of someone or something.