Archimedes quotes

Give me where to stand, and I will move the earth. (Archimedes)
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. View quote
Archimedes
Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible. View quote
Archimedes
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. View quote
Archimedes
The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides. View quote
Archimedes
The centre of gravity of any cylinder is the point of bisection of the axis. View quote
Archimedes
How many theorems in geometry which have seemed at first impracticable are in time successfully worked out! View quote
Archimedes
Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes. View quote
Archimedes
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]. View quote
Archimedes
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. View quote
Archimedes
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. (Archimedes)
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. View quote
Archimedes
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. View quote
Archimedes
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. View quote
Archimedes
Do not disturb my circles! View quote
Archimedes
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]... View quote
Archimedes
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. View quote
Archimedes
Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty. View quote
Archimedes
Man has always learned from the past. After all, you can't learn history in reverse! View quote
Archimedes
Rise above oneself and grasp the world. View quote
Archimedes
There are things which seem incredible to most men who have not studied Mathematics. (Archimedes)
I have found it! or I have got it!, commonly quoted as Eureka! View quote
Archimedes
Eureka! - I have found it! View quote
Archimedes
Give me a place to stand and with a lever I will move the whole world. View quote
Archimedes
Give me a fulcrum, and I shall move the world. View quote
Archimedes