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Give me but one firm spot on which to stand, and I will move the earth.
On the action of a lever
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Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.
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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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First then I will set out the very first theorem which became known to me by means of mechanics, namely that
Any segment of a section of a right angled cone (i. e., a parabola) is four-thirds of the triangle which has the same base and equal height,
and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]...
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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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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.
Archimedes
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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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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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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.
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The centre of gravity of any cylinder is the point of bisection of the axis.
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The centre of gravity of a parallelogram is the point of intersection of its diagonals.
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I thought fit to... explain in detail in the same book the peculiarity of a certain method, by which it will be possible... to investigate some of the problems in mathematics by means of mechanics. This procedure is... no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards... 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.
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Give me the place to stand, and I shall move the earth.
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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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Give me a place on which to stand 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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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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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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The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.
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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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Quote of the day
Wisdom too often never comes, and so one ought not to reject it merely because it comes late.
Felix Frankfurter
Archimedes
Creative Commons
Born:
287 BC
Died:
212 BC
(aged 75)
Bio:
Archimedes of Syracuse was an Ancient Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity.
Known for:
Archimedes Palimpsest
The Sand Reckoner
On the Sphere and Cylinder
Measurement of a Circle
Most used words:
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method
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middle
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point
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cone
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opposite
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portion
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triangle
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stand
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straight
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segment
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