β Eureka, Eureka! that is: I found it, I found it! β -Archimedes

β Many people believe that the grains of sand are infinite in multitude. Others think that although their number is not without limit, no number can ever be named which will be greater than the number of grains of sand. But I shall try to prove to you that among the numbers which I have named there are those which exceed the number of grains in a heap of sand the size not only of the earth, but even of the universe. β -Archimedes

β Do not disturb my circles! β -Archimedes

β In any triangle the centre of gravity lies on the straight line joining any angle to the middle point of the opposite side.β -Archimedes

β Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.β -Archimedes

β Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible.β -Archimedes

β The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.β -Archimedes

β Fellow, stand away from my diagram.β -Archimedes

β 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.β -Archimedes

β The center 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.β -Archimedes

β There are things which seem incredible to most men who have not studied Mathematics.β -Archimedes

β It follows at once from the last proposition that the center 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.β -Archimedes

β Man has always learned from the past. After all, you canβt learn history in reverse!β -Archimedes

β Give me a place outside the earth on which to rest my lever, and I will move the world.β -Archimedes

β Rise above oneself and grasp the world.β -Archimedes

β Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.β -Archimedes

β 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.β -Archimedes

β Two magnitudes whether commensurable or in-commensurable, balance at distances reciprocally proportional to the magnitudes.β -Archimedes

β The center of gravity of any cylinder is the point of bisection of the axis.β -Archimedes

β 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.β -Archimedes

β 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.β -Archimedes

β I am persuaded that 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.β -Archimedes

β If two equal weights have not the same center of gravity, the center of gravity of both taken together is at the middle point of the line joining their centers of gravity.β -Archimedes

β First then I will set out the very first theorem which became known to me by means of mechanics 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. β -Archimedes

β How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!β -Archimedes