# 260 BCE

## Mechanical advantage

## The book of science

Tom Sharp

Archimedes mechanics |

## Mechanical advantage

- 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.

## Eureka

- 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’ inventions

- 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.

## The new

- 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.

Archimedes valued the math more than its practical applications. For Galileo and Kepler, the math explained the data, but for Newton, the mathematical model came first.

Galileo explained and extended the work of Archimedes, working out the dynamic theory of simple machines for his work

On Mechanicsin 1600.See also in

The book of science:Windmill—Hero of Alexandria (Heron)Planetary orbits—Johannes KeplerKinematics—Galileo GalileiPrincipia Mathematica—Isaac NewtonPi—Johann Heinrich Lambert, Ferdinand von LindemannRoots blower—Philander Roots, Francis Marion RootsReadings on wikipedia: