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

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.

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

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

Rise above oneself and grasp the world.

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

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.

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.

Eureka! (I have 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

Spoken of the young Archimedes: . . . [he] was as much enchanted by the rudiments of algebra as he would have been if I had given him an engine worked by steam, with a methylated spirit lamp to heat the boiler; more enchanted, perhaps for the engine would have got broken, and, remaining always itself, would in any case have lost its charm, while the rudiments of algebra continued to grow and blossom in his mind with an unfailing luxuriance. Every day he made the discovery of something which seemed to him exquisitely beautiful; the new toy was inexhaustible in its potentialities.

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.

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

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

Eureka! [I have found it!] On discovery of a method to test the purity of gold.

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

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

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.

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.

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.

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.

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!).

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