Archimedes of Syracuse

Mathematics Greek -287 – -212 332 quotes

A brilliant ancient Greek mathematician, physicist, engineer, inventor, and astronomer, known for his work on buoyancy and levers.

Quotes by Archimedes of Syracuse

There are no numbers sufficiently large to be uncounted.

The Sand Reckoner

The area of a segment of a parabola is 4/3 of the area of the triangle with the same base and height.

Quadrature of the Parabola, Proposition 17

The value of pi (π) is between 3 10/71 and 3 1/7.

Measurement of a Circle, Proposition 3

All bodies tend to move towards the center of the Earth.

On Floating Bodies, Book I, Postulate 2

The center of gravity of a parallelogram is at the intersection of its diagonals.

On the Equilibrium of Planes, Book I, Proposition 10

If magnitudes are in equilibrium at certain distances, they are inversely proportional to the distances.

On the Equilibrium of Planes, Book I, Postulate 1

If unequal weights are at equal distances, they will not be in equilibrium, but the one which is heavier will incline.

On the Equilibrium of Planes, Book I, Postulate 2

If unequal weights are at unequal distances, but the greater weight is at the lesser distance, and the lesser weight at the greater distance, they may be in equilibrium.

On the Equilibrium of Planes, Book I, Postulate 3

The area of a circle is equal to the area of a right-angled triangle whose sides about the right angle are equal to the radius and circumference of the circle respectively.

Measurement of a Circle, Proposition 1

The spiral of Archimedes is a curve generated by a point moving uniformly along a line which itself revolves uniformly about a fixed point.

On Spirals, Definition 1

The tangent to a spiral at any point makes an angle with the radius vector to that point equal to the angle whose tangent is the ratio of the circumference of the circle described with the radius vector as radius to the arc of the spiral from the pole to the point.

On Spirals, Proposition 18

The volume of any segment of a paraboloid of revolution cut off by a plane perpendicular to the axis is one and a half times the volume of the cone which has the same base and the same axis.

On Conoids and Spheroids, Proposition 21

The volume of any segment of a hyperboloid of revolution cut off by a plane perpendicular to the axis is to the cone which has the same base and the same axis as the sum of the square on the radius of the base and the square on the radius of the section made by the plane to the square on the radius of the base.

On Conoids and Spheroids, Proposition 25

The method of exhaustion can be used to find the areas and volumes of various geometric figures.

Various works, implicitly

The center of gravity of a segment of a parabola is on its axis, and its distance from the vertex is 3/5 of the axis.

On the Equilibrium of Planes, Book II, Proposition 8

The center of gravity of a segment of a sphere is on its axis, and its distance from the center of the sphere is such that...

On Floating Bodies, Book II, Proposition 5

The principle of the lever is fundamental to understanding mechanical advantage.

On the Equilibrium of Planes, Book I

The use of infinitesimals, though not rigorously defined, can lead to correct results.

The Method of Mechanical Theorems

The problem of squaring the circle is impossible using only a compass and straightedge.

Implicit in his work on pi, though not explicitly stated as an impossibility proof

The universe is finite, but its size is immense.

The Sand Reckoner