Euclid — "A plane angle is the inclination of the lines to one another, when two lines mee…"
A plane angle is the inclination of the lines to one another, when two lines meet one another, but are not in the same straight line.
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
"Let the following be postulated:"
"To bisect a given rectilinear angle."
"The prime numbers are more than any assigned multitude of prime numbers."
"To draw a straight line at right angles to a given straight line from a given point on it."
"A ratio is a sort of relation in respect of size between two magnitudes of the same kind."
Verification
Unverifiable
Found in 1 providers: grok
1 source checked
Understanding this quote
What it means
An angle is formed when two lines meet at a point but don't continue in the same direction. The 'inclination' is simply how much one line tilts away from the other at their meeting point. This is geometry's foundational definition of angle — precise, stripped of assumption, built only from observable properties of intersecting lines without invoking measurement or degrees.
Relevance to Euclid
Euclid wrote this in Elements around 300 BCE, his systematic compilation of geometry. His method — defining every term before using it — was revolutionary rigor. This definition reflects his obsession with building mathematics from undeniable first principles. He trusted no prior assumption, instead constructing the entire edifice of geometry from definitions like this one upward.
The era
In Alexandria around 300 BCE, Greek thinkers were systematizing knowledge under Ptolemaic patronage. Mathematics existed but lacked unified logical foundations. Euclid synthesized centuries of scattered geometric knowledge into a deductive system. Defining 'angle' precisely mattered because competing informal definitions caused contradictions. His Elements would dominate mathematical education for over 2,000 years, shaping every subsequent civilization's approach to reasoning.
AI-generated insights based on extensive research and information for context. Factual errors? Email [email protected].