Archimedes

Mathematics, physics, engineering

Ancient influential 47 sayings

Sayings by Archimedes

The surface of any sphere is four times its greatest circle.

c. 250 BCE — From 'On the Sphere and Cylinder'.
Humorous Unverifiable

The spiral, by a continuous motion, generates an infinite number of lines.

c. 250 BCE — From 'On Spirals', describing the properties of the Archimedean spiral.
Humorous Unverifiable

It is not possible to find a number greater than the number of grains of sand which could be contained in a sphere of the size of the universe.

c. 250 BCE — From 'The Sand Reckoner', demonstrating large number notation.
Humorous Unverifiable

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

c. 250 BCE — From 'On the Equilibrium of Planes', a fundamental result in mechanics.
Humorous Unverifiable

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.

c. 250 BCE — From 'On the Equilibrium of Planes', laying out principles of levers.
Humorous Unverifiable

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

c. 250 BCE — From 'Measurement of a Circle'.
Humorous Unverifiable

Any solid lighter than a fluid will, if placed in the fluid, be immersed in it to such an extent that the weight of the solid will be equal to the weight of the fluid displaced.

c. 250 BCE — Another phrasing of Archimedes' Principle from 'On Floating Bodies'.
Humorous Unverifiable

The surface of any segment of a sphere is equal to a circle whose radius is the straight line drawn from the vertex of the segment to any point on the circumference of its base.

c. 250 BCE — From 'On the Sphere and Cylinder'.
Humorous Unverifiable

I will show you how to calculate the number of grains of sand that would fit into the universe.

c. 250 BCE — A more informal summary of the goal of 'The Sand Reckoner'.
Humorous Unverifiable

The method of exhaustion is a powerful tool.

c. 250 BCE — Referring to the mathematical technique he used to calculate areas and volumes.
Humorous Unverifiable

It is a property of the circle that the ratio of its circumference to its diameter is the same for all circles.

c. 250 BCE — A fundamental observation about Pi.
Humorous Unverifiable

No difficulty can be too great for the human mind, if it applies itself with diligence and skill.

c. 250 BCE — A statement on intellectual perseverance.
Humorous Unverifiable

The greatest pleasure is to discover.

c. 250 BCE — Reflecting his joy in scientific inquiry.
Humorous Unverifiable

I have discovered a method by which any given solid may be weighed in water.

c. 250 BCE — Referring to his discovery of buoyancy, as told by Vitruvius.
Humorous Unverifiable

The number of grains of sand is not infinite, but finite.

c. 250 BCE — From 'The Sand Reckoner', directly refuting the idea of infinite sand.
Humorous Unverifiable

Every solid body immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

c. 250 BCE — A more precise statement of Archimedes' Principle.
Humorous Unverifiable

The cone is one third of the cylinder on the same base and of the same height.

c. 250 BCE — A known geometric theorem, often attributed to him or Eudoxus.
Humorous Unverifiable

My mind is not limited by the bounds of the earth.

c. 250 BCE — A poetic expression of his intellectual ambition.
Humorous Unverifiable

It is easier to make a thousand discoveries than to invent a single new method.

c. 250 BCE — Emphasizing the difficulty and importance of methodological innovation.
Humorous Unverifiable

The properties of bodies depend on their figures.

c. 250 BCE — A fundamental insight into the relationship between form and function in physics.
Humorous Unverifiable