Archimedes Quotes
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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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Noli turbare circulos meos. or Noli tangere circulos meos.
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If two equal weights have not the same centre of gravity, the centre of gravity of both taken together is at the middle point of the line joining their centres of gravity.
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The perimeter of the earth is about 3,000,000 stadia and not greater.
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δῶς
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The centre of gravity of any cylinder is the point of bisection of the axis.
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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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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.
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The centre of gravity of any cone is the point which divides its axis so that the portion adjacent to the vertex is triple of the portion adjacent to the base.
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I am persuaded that it The Method of Mechanical Theorems will be of no little service to mathematics; for I apprehend that some, either of my contemporaries or of my successors, will, by means of the method when once established, be able to discover other theorems in addition, which have not yet occurred to me.
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Rise above oneself and grasp the world.
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The centre of gravity of a parallelogram is the point of intersection of its diagonals.
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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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There are things which seem incredible to most men who have not studied Mathematics.
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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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Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.
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In any triangle the centre of gravity lies on the straight line joining any angle to the middle point of the opposite side.
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εὕρηκα heúrēka
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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.
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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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The centre of gravity of any hemisphere is on the straight line which is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3.
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Any segment of a right-angled conoid (i.e., a paraboloid of revolution) cut off by a plane at right angles to the axis is 1½ times the cone which has the same base and the same axis as the segment
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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.