Euclid — "An obtuse angle is an angle greater than a right angle."
An obtuse angle is an angle greater than a right angle.
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Understanding this quote
What it means
An obtuse angle is any angle wider than 90 degrees but less than a straight 180-degree line. Think of scissors opened past a perfect square corner. The statement is a precise geometric definition, distinguishing one class of angles from acute (smaller than 90°) and right angles exactly. It gives geometry a shared, unambiguous vocabulary so that reasoning built on top of it cannot slip into vagueness or disagreement.
Relevance to Euclid
This line appears nearly verbatim in Book I of Euclid's Elements, his foundational treatise written around 300 BCE. Euclid structured all of geometry on definitions first, then postulates, then proofs — nothing was assumed until named. This reflects his core conviction that rigorous mathematics requires airtight, shared language before a single theorem can stand. His character was methodical and relentlessly precise; he reportedly told Ptolemy I there is no royal road to geometry.
The era
Euclid worked in Alexandria around 300 BCE during the Hellenistic period, when Ptolemy I built the Library of Alexandria to systematize Greek knowledge. Plato's Academy had elevated mathematics as the purest form of reasoning, but geometry still lacked a single, logically ordered reference. Competing definitions created confusion across city-states. Euclid's precise vocabulary unified the discipline, giving scholars from Egypt to Rome a common mathematical language that dominated education for over two thousand years.
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