- Archimedes' principle: buoyancy, and its relation of being equal to the weight of the fluid it displaces.
(It was this discovery that led Archimedes to reportedly exclaim "Eureka!")
- Archimedes' Screw: a machine used for transferring water from a low-lying body of water into irrigation ditches.
- Hydrostatics: the science of fluids at rest.
- Levers: Archimedes gave a detailed explanation of the principle involved with levers in his work On the Equilibrium of Planes.
(He did not however invent the lever itself.)
- Infinitesimals: the idea of objects so small that there is no way to see or measure them.
- Claw of Archimedes: a weapon that Archimedes is said to have designed in order to defend the city of Syracuse.
Also known as "the ship shaker," the claw consisted of a crane-like arm from which a large metal grappling hook was suspended so that when the "claw" was dropped onto an attacking ship, the arm would swing upwards, lifting the ship out of the water and possibly sinking it.
- Heat Ray: a weapon that Archimedes is said to have used during the Siege of Syracuse.
The "Archimedes heat ray" was supposedly a device used to focus sunlight onto enemy ships, causing them to catch fire.
(The credibility of this device has long been a subject of debate.)