# Euclidean

or Eu·clid·i·an

[ yoo-klid-ee-uhn ]

1. of or relating to Euclid, or adopting his postulates.

Euclidean

/ yo̅o̅-klĭdē-ən /

1. Relating to geometry of plane figures based on the five postulates (axioms) of Euclid, involving the derivation of theorems from those postulates. The five postulates are: 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment, a circle can be drawn having the line segment as radius and an endpoint as center. 4. All right angles are congruent. 5. (Also called the parallel postulate. ) If two lines are drawn that intersect a third in such a way that the sum of inner angles on one side is less than the sum of two right triangles, then the two lines will intersect each other on that side if the lines are extended far enough.
2. Compare non-Euclidean

## Word History and Origins

Origin of Euclidean1

1650–60; < Latin Euclīdē ( us ) of Euclid (< Greek Eukleídeios ) + -an

## Example Sentences

Unless, of course, you look beyond Euclidean geometry, as Steve Curry did.

The next source from which we learn anything of this part of the subject is the pseudo-Euclidean Introductio Harmonica.

So in the Euclidean Sectio Canonis the propositions which deal with the 'movable' notes, viz.

It was developed with rigorous mathematical logic and Euclidean conclusiveness.

The real basis of the non-Euclidean geometry is dimension as direction.

But they constitute the substance of non-Euclidean geometry; they are its blood and sinews.