Who first discovered that a body immersed in fluid is buoyed up with a force equal to the weight of the displaced fluid?

The principle that a body immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced is known as Archimedes' principle, named after the ancient Greek mathematician and physicist Archimedes. This discovery is foundational in the fields of fluid mechanics and physics.

Archimedes formulated this principle during his studies on buoyancy, illustrating that the upward buoyant force on an object in fluid is equal to the weight of the fluid that the object displaces. This principle is not only pivotal in understanding how objects float or sink in water but also has practical applications in various industries, including engineering, design, and shipbuilding.

In contrast, figures like Newton and Galileo contributed significantly to the fields of physics and mathematics but are not associated with this particular discovery. Newton’s work focused more on gravitation and motion, while Galileo is known for his contributions to the scientific method and kinematics. Einstein’s theories revolutionized the understanding of relativity and energy but do not pertain to fluid buoyancy. Thus, Archimedes stands out as the correct answer, embodying the concept central to this question.