Final answer:
Athena appeases the Furies by offering them a respected role as protectors of Athens, where they would be worshipped and receive offerings, integrating them into the city's society and transitioning from an old cycle of revenge to lawful justice.
Step-by-step explanation:
When Athena and the jurors deliver their final judgement in Aeschylus's Oresteia, the Furies are still enraged over the outcome of the trial in which Orestes is acquitted for the murder of his mother. To pacify them, Athena offers the Furies a significant role within the city of Athens.
They are granted a space in Athenian society, a revered status as protectors of the city, ensuring that the land would be fruitful and the citizens would be blessed with children. Additionally, they would be worshipped and receive offerings from the Athenians. Athena’s proposal signifies respect for the ancient powers of the Furies while introducing a new order of justice. The Furies, persuaded by Athena's offer, accept the new role and harmony is restored, reflecting the transition from the older cycle of revenge to a new system of legal dispute resolution.
Learn more about Athena's Offer to the Furies