Archimedes

The center of gravity of any segment of an ellipsoid of revolution cut off by a plane perpendicular to the axis is on the axis of the segment, and divides the axis in a certain ratio.

On Conoids and Spheroids, Proposition 26

Give me a place to stand, and I shall move the Earth.

Letter to King Hiero II (as recounted by Pappus of Alexandria)

The ratio of the surface area of a sphere to that of its circumscribing cylinder is equal to the ratio of their volumes, i.e., 2:3.

On the Sphere and Cylinder (treatise, reflects personal discovery)

There are no small letters in mathematics.

Attributed, likely from a letter or discussion

The value of pi is approximately 3.14159.

Measurement of a Circle (treatise, reflects personal calculation)

I believe that I have found a method for measuring any given area bounded by straight lines and a parabola.

The Quadrature of the Parabola (treatise, reflects personal insight)

The center of gravity of any triangle is at the intersection of its medians.

On the Equilibrium of Planes (treatise, reflects personal derivation)

With a sufficiently long lever, one could move the world.

Letter to King Hiero II (paraphrased from Pappus)

The sand reckoning is a work in which I show you how to find a number greater than that of the grains of sand which would fill the universe.

The Sand Reckoner (treatise, reflects personal ambition)

I have often been asked to explain the principles of my burning mirrors.

Likely from a letter or discussion, regarding his war machines

The method of exhaustion is a powerful tool for determining areas and volumes.

Likely from a letter or commentary on his mathematical methods

It is not possible to construct a square equal in area to a given circle using only a compass and straightedge.

Implied by his work on pi, likely a personal conclusion

I have devised a screw for raising water, which is of great utility in Egypt.

Likely from a letter or discussion about his inventions

The properties of spirals are truly fascinating.

On Spirals (treatise, reflects personal interest)

My greatest joy is in the discovery of new mathematical truths.

Likely from a personal reflection or letter to a colleague

The study of mechanics is not merely practical, but also deeply philosophical.

Likely from a letter or introduction to a treatise

I have sent you my latest findings on the properties of floating bodies.

Hypothetical letter to a fellow scholar

The beauty of geometry lies in its absolute certainty.

Likely from a personal reflection or discussion

I am constantly seeking to refine my methods of proof.

Likely from a letter to a mathematical peer

The sun's rays, when focused, possess immense power.

Likely from a discussion about his war machines

Quotes by Archimedes