Principle of buoyancy (upthrust equals the weight of fluid displaced) (3rd century BC)
Set out in On Floating Bodies; linked with the story of testing King Hiero's crown
Science · Maths, astronomy, medicine & more
Archimedes
c. 287–212 BC · Greek (Syracuse, Sicily)
Mathematics — geometry and mechanics
Archimedes of Syracuse was the greatest mathematician of antiquity and a brilliant engineer. He calculated areas and volumes by methods anticipating integral calculus, bounded pi, and founded statics and hydrostatics with the law of the lever and the principle of buoyancy, while his war machines held off the Romans. He was killed by a Roman soldier when Syracuse fell in 212 BC during the Second Punic War.
How to spot them
- ▸'Eureka!' in the bath and King Hiero II's golden crown
- ▸'Give me a place to stand and I will move the Earth' — the law of the lever
- ▸Archimedes' screw, the claw of Archimedes, burning mirrors
- ▸Sphere inscribed in a cylinder on his tomb, rediscovered by Cicero
- ▸The Archimedes Palimpsest containing The Method
Key discoveries & works
Law of the lever (3rd century BC)
Proved in On the Equilibrium of Planes; basis of the boast about moving the Earth
Screw pump for raising water (3rd century BC)
A helical screw inside a tube, still used for irrigation and drainage
Measurement of a Circle (3rd century BC)
Shows pi lies between 223/71 and 22/7 using polygons of 96 sides
On the Sphere and Cylinder (3rd century BC)
Proves a sphere has two-thirds the volume and surface area of its circumscribing cylinder
The Sand Reckoner (3rd century BC)
Estimates the number of grains of sand needed to fill the universe, using a new system for huge numbers
The Method of Mechanical Theorems (3rd century BC)
Explains how he found results by 'weighing' thin slices; survived only in a palimpsest identified in 1906
Quadrature of the Parabola (3rd century BC)
Shows a parabolic segment has 4/3 the area of an inscribed triangle, by the method of exhaustion
Key ideas
- Method of exhaustion: approximating curved areas and volumes with ever-finer polygons, anticipating integral calculus
- Founded mathematical statics (centres of gravity, the lever) and hydrostatics (buoyancy)
- Handled arbitrarily large numbers systematically in The Sand Reckoner
Quick-fire facts
- •Born and died in Syracuse, Sicily; in The Sand Reckoner he names his father as the astronomer Phidias
- •Vitruvius tells how he leapt from his bath shouting 'Eureka!' ('I have found it') after realising how to test whether Hiero II's crown was pure gold
- •Plutarch says he was killed by a Roman soldier during the capture of Syracuse in 212 BC; 'Do not disturb my circles' is a later embellishment
- •He asked for a sphere inscribed in a cylinder to be placed on his tomb; Cicero found the neglected tomb in 75 BC
- •His defensive machines, including the 'claw' that lifted ships, held off the Roman general Marcellus
- •The Archimedes Palimpsest, a 10th-century copy overwritten as a prayer book, was identified by J. L. Heiberg in 1906
- •The Archimedes cattle problem is a famous number puzzle whose smallest solution is enormous
- •His portrait appears on the Fields Medal
Drill it — 9 cards
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Sources
- MacTutor History of Mathematics, University of St Andrews — Archimedes of Syracuse
- Reviel Netz and William Noel — The Archimedes Codex