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Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.
Archimedes
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Archimedes
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Archimedes of Syracuse
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Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible.
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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.
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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.
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Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.
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Rise above oneself and grasp the world.
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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.
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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.
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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.
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How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!
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