Archimedes

Eureka! Give me a place to stand on, and I will move the Earth. The lever — the simplest of machines — contains within it the whole secret of mechanical advantage.

Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. I wrote this not as a boast but as a demonstration of the lever's principle, which I have proved geometrically: the ratio of weight to weight is inversely proportional to the ratio of arm to arm. I also demonstrated it practically: I launched a fully loaded ship...

The centre of gravity of any parallelogram lies on a diagonal. I proved this. Then I spent three years building war machines to defend Syracuse. Do not tell me that pure mathematics and practical engineering are separate disciplines. They are the same mind in different clothes.

Mathematics reveals its secrets only to those who approach it with pure love and for its own sake. Whoever asks what is this useful for has already misunderstood what kind of thing mathematics is. It does not justify itself by application. It justifies itself by being true.

I can calculate the number of grains of sand needed to fill the universe. This is not madness — it is the point. The universe is not so large that mathematics cannot measure it, and number is not so small that it cannot contain the universe. The Sand-Reckoner was my proof of both.

I discovered the method of exhaustion — approaching a curved area with inscribed and circumscribed polygons until the gap between them was less than any assignable quantity. This is not approximation. It is infinitely precise reasoning about infinite smallness. Newton and Leibniz called it something else. I called it geometry.

Domenico Fetti painted me seventeen centuries after my death, staring at a diagram, absorbed. I appreciate the instinct. I was never more alive than when working on a problem.

The story they tell is that I ran naked through the streets shouting Eureka. I may have been excited when I discovered the principle of displacement — that a body immersed in fluid...

The Archimedes screw was used in Egypt to raise water from the Nile for irrigation — perhaps I designed it during my time in Alexandria, perhaps I only improved an existing device. Diodorus Siculus credits me with it; I will not argue the point either way.

The principle is elegant: a helix within a cylinder, turned by a handle. Water enters at the bottom,...

Eureka — I have found it. I stepped into the bath and observed the water rise. I had been tasked with determining whether King Hiero's crown was pure gold or alloyed with silver without damaging it. The solution presented itself: a body submerged displaces a volume of water equal to its own volume. Gold and silver have different densities; the same weight...

Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty. Do not disturb my circles. I shall prove it by exhaustion — if I must exhaust myself in the doing.

I have discovered a truly marvellous proof of this, which this margin is too narrow to contain. The surface area of a sphere is four times that of a great circle — I demand this carved on my tomb.

Do not disturb my circles. These were my last recorded words, spoken to the Roman soldier who interrupted my work. I say this not as a boast but as a summary of how I lived: the diagrams drawn in sand were more real to me than the city burning outside.