Their geometry will, therefore, be Euclidean geometry, but their straight will not be our Euclidean straight.
He acted as if he had demonstrated a Euclidean proposition flawlessly.
The second stream of thought confined itself within the circle of ideas of Euclidean geometry.
In elementary geometry, however, the Euclidean idea is still held.
We are obstructed by the fact that all existing physical science assumes the Euclidean hypothesis.
He returned the proof, saying that he could not accept any of it as elucidating the exact area of a circle, or as Euclidean.
He constructed every one of his later speeches on the plan of a Euclidean solution.
The proof itself is borrowed, with slight alterations, from Cuthbertson's "Euclidean Geometry."
"City" is not necessarily descriptive: perhaps less so than the application of Euclidean axioms to advanced geometry.
That they are compatible with the Euclidean group is easy to see.
Euclidean (y-klĭd'ē-ən) 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. Compare non-Euclidean. |