Final answer:
The phrase originates from William Shakespeare's play Hamlet, Act 1, Scene 5, where Hamlet speaks of feigning madness to uncover the truth about his father's murder.
Step-by-step explanation:
The quotation "I perchance hereafter shall think meet to put an antic disposition on" is from William Shakespeare's play Hamlet, specifically from Act 1, Scene 5. This line is spoken by the character Prince Hamlet after he has encountered the ghost of his father, who reveals that he was murdered by Hamlet's uncle, now King Claudius. Hamlet's statement is a foreshadowing of his plan to feign madness as a way to observe the reactions of Claudius and others and to cover his actions as he seeks to confirm the truth of the ghost's claims and consider his revenge.