Archimedes — "The center of gravity of any triangle is the point of intersection of its median…"
The center of gravity of any triangle is the point of intersection of its medians.
Get This Quote & Author's Image Illustrated On:
Click any product to generate a realistic preview. Up to 3 at a time.
* Initial load can take up to 90 seconds — revising the preview in another color is nearly instant.
Kitchen
Apparel
Other
More from Archimedes
"I have found the solution to a problem that has puzzled many."
"Every magnitude is comparable with every other magnitude of the same kind."
"The cone is one third of the cylinder on the same base and of the same height."
"The spiral, by a continuous motion, generates an infinite number of lines."
"Every solid body immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body."
Details
From 'On the Equilibrium of Planes', a fundamental result in mechanics.
Date: c. 250 BCE
GeneralVerification
Unverifiable
Found in 1 providers: grok
1 source checked
Understanding this quote
What it means
Every triangle has a natural balancing point — its centroid — where weight distributes equally in all directions. This point always lies exactly where the three medians intersect: lines drawn from each corner to the midpoint of the opposite side. Cut any triangle from uniform material and you can balance it perfectly on a pin placed at this single point. It connects abstract geometry directly to physical equilibrium.
Relevance to Archimedes
Archimedes built his engineering legacy on mastering equilibrium. His treatise On the Equilibrium of Planes formally proved this centroid theorem using geometric reasoning about levers. He designed catapults and war machines defending Syracuse, where knowing balance points was life-or-death practical knowledge. His law of the lever — give me a place to stand and I will move the earth — shares the same intellectual DNA: finding the exact point where forces balance.
The era
Archimedes lived in Hellenistic Syracuse (c. 287–212 BC), when Greek mathematics — systematized by Euclid a generation earlier — was the pinnacle of human knowledge. City-states competed through engineering as much as armies. Rome was expanding aggressively, and Archimedes died during its siege of Syracuse. In this climate, geometry was simultaneously philosophical discipline and military technology: the same mind that proved triangle centroids also built the claws and catapults that held Rome at bay for years.
AI-generated insights based on extensive research and information for context. Factual errors? Email [email protected].