Euclid — "Things which are equal to the same thing are also equal to one another."
Things which are equal to the same thing are also equal to one another.
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 Euclid
"What has been affirmed without proof can also be denied without proof."
"Things which coincide with one another are equal to one another."
"An obtuse angle is an angle greater than a right angle."
"If a straight line touch a circle, and from the point of contact there be drawn across in the circle a straight line cutting the circle, the angles which it makes with the tangent will be equal to the…"
"A figure is that which is contained by any boundary or boundaries."
Verification
Confirmed
Found in 3 providers: grok,deepseek,gemini
3 sources checked
Understanding this quote
What it means
If two things are each equal to a third thing, they must be equal to each other. This is the transitive property of equality — one of the most basic rules of logical reasoning. It means you can chain comparisons: if A matches C and B matches C, then A and B match. Simple as it sounds, it underpins virtually all mathematics and formal logic, letting complex proofs be built from simple, undeniable relationships.
Relevance to Euclid
This is literally Common Notion 1 from Book I of Euclid's Elements, written around 300 BCE — the most reprinted textbook in history after the Bible. Euclid built all of geometry from just five postulates and five common notions like this one. His defining achievement was showing that vast mathematical truth could be derived purely from a handful of self-evident starting points, and this axiom was his very first foundational brick.
The era
Euclid worked in Alexandria around 300 BCE during the Hellenistic era, as Greek thinkers were formalizing the concept of mathematical proof. Earlier Babylonian and Egyptian math was purely practical — measuring land, trading grain. Building on Aristotle's logic, Greek philosophers demanded rigorous deductive chains. Euclid's axioms arrived precisely when civilization needed a universal language of reasoning, standardizing how knowledge could be justified and reliably transmitted across generations.
AI-generated insights based on extensive research and information for context. Factual errors? Email [email protected].