Archimedes Quotes

The centre of gravity of a parallelogram is the point of intersection of its diagonals.

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.

Give me but a firm spot on which to stand, and I shall move the earth.

Noli turbare circulos meos!

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

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

Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.

Give me a lever long enough and a place to stand and I will move the entire earth.

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

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.

Give me a place to stand, a lever long enough and a fulcrum. and I can move the Earth

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]...

The centre of gravity of any cylinder is the point of bisection of the axis.

δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω. [Dôs moi pâ stô, kaì tàn gân kinásō.]

Give me a lever long enough and a fulcrum on which to place it and I'll move the world