Quotes by Archimedes

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

“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.”

“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 oppositesides respectively.”

“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 centre of gravity of any cylinder is the point of bisection of the axis.”

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

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

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

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

“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.”

“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.”