A compound-complex sentence combines the compound and the complex sentence. The compound part means that it has two or more complete sentences. The complex part means that it has at least one incomplete sentence.
Archimedes' principle. Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid. Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse.
Archimedes used the method of exhaustion to compute the area inside a circle. The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way.