Euclid — "And the whole is greater than the part."
And the whole is greater than the part.
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More from Euclid
"A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line."
"The greatest of the parts is called the antecedent, and the less the consequent."
"To describe a circle with any centre and radius."
"The properties of figures are derived from their definitions and postulates."
"In isosceles triangles the angles at the base are equal to one another, and, if the equal straight lines be produced further, the angles under the base will be equal to one another."
Details
Common Notion 5 from 'The Elements'. A foundational axiom with broad philosophical implications.
Date: c. 300 BCE
PhilosophicalVerification
Confirmed
Found in 3 providers: grok,deepseek,gemini
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Understanding this quote
What it means
Any complete entity necessarily exceeds any of its constituent pieces. What seems obvious — a pie is larger than a slice, a country larger than one city — is actually a foundational logical axiom. Euclid wasn't stating the obvious for its own sake; he was building a rigorous system where even self-evident truths needed to be formally declared before you could use them as the basis for proving more complex things.
Relevance to Euclid
This is literally Euclid's Common Notion 5, one of five self-evident truths he listed at the opening of Elements, his 13-book geometric masterwork written around 300 BCE in Alexandria. It reveals his defining character trait: refusing to assume anything without stating it explicitly. Where others relied on intuition, Euclid formalized even obvious truths as foundational axioms, building an unbroken logical chain from simple declarations to complex theorems.
The era
Euclid wrote Elements around 300 BCE in Alexandria, Egypt, then the intellectual capital of the Hellenistic world under Ptolemy I. Greek thinkers had recently developed formal logic through Aristotle, and mathematics was transitioning from practical Babylonian and Egyptian calculation toward abstract proof-based reasoning. Establishing obvious-seeming axioms explicitly was a radical act of rigor — creating a model of deductive reasoning that would dominate Western mathematics, science, and philosophy for over two thousand years.
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