Final answer:
The ancient scientist known for the water displacement method is Archimedes, who made significant contributions to mathematics, physics, and engineering, and formulated the renowned Archimedes' principle.
Step-by-step explanation:
The ancient scientist famous for the water displacement method and often associated with the famous exclamation Eureka is Archimedes. Born in Syracuse around 287 BCE, Archimedes is known for formulating principles in fields like mathematics, physics, and engineering. One of his most notable contributions is Archimedes' principle, which is a method for determining the volume of an object by the amount of water it displaces. This principle helped lay the foundations for the study of hydrostatics, the branch of physics concerned with the properties of fluids at rest. Archimedes' insights and discoveries have had a lasting impact, influencing various disciplines throughout history.