Lever, pulley, and screw. Archimedes was the first to prove the mechanical advantage of the lever— that the input force is multiplied by its distance from the fulcrum divided by the output force’s distance. The load on a pulley is divided by the number of rope sections that lift the load. The mechanical advantage of a screw is the ratio of the circular distance it turns to the distance the load moves.
As Galileo figured, to determine whether the king’s crown was made of pure gold, Archimedes probably used the principle in hydrostatics known as Archimedes’ principle— he weighed the crown under water on a scale balanced with the proper amount of gold.
Archimedes used infinitesimals with the method of exhaustion to limit the value of π. Archimedes used an infinite geometric series to determine the areas of parabolic segments. Archimedes invented a system of counting to prove the number of grains of sand in the world is finite. Archimedes explained how to build orreries, mechanical models of the solar system with differential gearing. Archimedes might have invented Archimedes’ screw to pump bilge water from the large ship Syracusia, which he designed. Archimedes invented the heat ray, designed the Claw of Archimedes, and improved the catapult to defend Syracuse from the Romans. Archimedes designed block-and-tackle pulley systems to help sailors, and he invented the first odometer.
1. Discovering something new is hardly good enough; “new” has no meaning without an explanation and can be perceived only in relation to the “known.” 2. It’s difficult to explain things to those who don’t know much, and many who supposedly know, often ignoring and taking the known for granted, are oblivious. Recent news reports claim that modern humans inherit traces of Neanderthal genes, but this ignores the base commonality. In fact, 99.7% of the base pairs of the modern human are identical to the base pairs of the Neanderthal. The human shares around 94% of base pairs with the chimpanzee, although a dispassionate analysis might find it should be more. 3. The new and improved modern human has made great advances in ignorance, egotistic attitudes, and self-deception.