Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.

— Archimedes

## The most breathtaking Archimedes quotes that are little-known but priceless

Man has always learned from the past. After all, you can't learn history in reverse!

Give me a place to stand, and a lever long enough, and I will move the world.

Give me but a firm spot on which to stand, and I shall move the earth.

Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible.

### Rise above oneself and grasp the world.

Eureka! Eureka! Supposed to have been his cry, jumping naked from his bath and running in the streets, excited by a discovery about water displacement to solve a problem about the purity of a gold crown.

Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.

### Eureka! (I have found it!).

It follows at once from the last proposition that the centre of gravity of any triangle is at the intersection of the lines drawn from any two angles to the middle points of the opposite sides respectively.

The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.

I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.

The perimeter of the earth is about 3,000,000 stadia and not greater.

The centre of gravity of any cylinder is the point of bisection of the axis.

Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.

### Eureka! I've got it.

There are things which seem incredible to most men who have not studied Mathematics.

Archimedes to Eratosthenes greeting. ... certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced. On floating bodies I, prop 5.

How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

### Eureka, Eureka! (I found it, I found it!).

### Many people believe that the grains of sand are infinite in multitude .

.. Others think that although their number is not without limit, no number can ever be named which will be greater than the number of grains of sand. But I shall try to prove to you that among the numbers which I have named there are those which exceed the number of grains in a heap of sand the size not only of the earth, but even of the universe

Having been the discoverer of many splendid things, he is said to have asked his friends and relations that, after his death, they should place on his tomb a cylinder enclosing a sphere, writing on it the proportion of the containing solid to that which is contained.

The diameter of the earth is greater than the diameter of the moon and the diameter of the sun is greater than the diameter of the earth.

Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.