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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
Proportional
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Reciprocally
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There are things which seem incredible to most men who have not studied Mathematics.
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Rise above oneself and grasp the world.
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The centre of gravity of any cylinder is the point of bisection of the axis.
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Eureka, Eureka! (I found it, I found it!).
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Give me a place to stand, and a lever long enough, and I will move the world.
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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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Man has always learned from the past. After all, you can't learn history in reverse!
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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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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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Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.
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The perimeter of the earth is about 3,000,000 stadia and not greater.
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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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Give me but a firm spot on which to stand, and I shall move the earth.
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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! [I have found it!] On discovery of a method to test the purity of gold.
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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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