In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with a room's walls extended infinitely far, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry. 

When working exclusively in two-dimensional Euclidean space, the definite article is used, so, "the" plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, or, in other words, in the plane. 

Euclid set forth the first great landmark of mathematical thought, an axiomatic treatment of geometry. He selected a small core of undefined terms (called "common notions") and postulates (or axioms) which he then used to prove various geometrical statements. Although the plane in its modern sense is not directly given a definition anywhere in the "Elements", it may be thought of as part of the common notions. Euclid never used numbers to measure length, angle, or area. In this way the Euclidean plane is not quite the same as the Cartesian plane.
How is a plane described in mathmatics?
Who set fourth the first great landmark of mathmatical thought?
What was it?
In what aspects of mathematics are performed in two-dimensional space in other words in the plane?
Did Euclid ever use numbers to measure length, angle or area?
Is that the same as a Cartesian plane?
How can a plane arise?
What article is used when working exclusivley in two-dimensionial Euclidean space?
Then what does the plane refer to?
What did Euclid use to prove various geometric statements?
a plane is a flat, two-dimensional surface that extends infinitely far
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far
Euclid
Euclid set forth the first great landmark of mathematical thought,
an axiomatic treatment of geometry
Euclid set forth the first great landmark of mathematical thought, an axiomatic treatment of geometry
geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, or, in other words
Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, or, in other words
No
 Euclid never used numbers to measure length, angle, or area.
no
Euclid never used numbers to measure length, angle, or area. In this way the Euclidean plane is not quite the same as the Cartesian plane
as subspaces of some higher-dimensional space
Planes can arise as subspaces of some higher-dimensional space
the definite article is used
When working exclusively in two-dimensional Euclidean space, the definite article is used
the whole space
"the" plane refers to the whole space
He selected a small core of undefined terms (called "common notions") and postulates (or axioms)
 He selected a small core of undefined terms (called "common notions") and postulates (or axioms) which he then used to prove various geometrical statements.