Elements in Euclidean Geometry
Euclidean Geometry is the work done by the famous mathematician Euclid and is compiled in his book “Elements” consisting of 13 different elements. These Elements are collections of the various definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of these propositions.
Books 1st to 4th and 6th discuss plane geometrical figures, whereas his other books discuss the geometry of other figures. The work of Euclid laid the foundation of modern-day geometry.
For a better understanding of Geometry Euclid assumed some properties that need not be proven. All these assumptions are considered to be universal truths and they can be easily divided into two categories,
Postulates: Various Assumptions that are always true.
Axiom: Various Common Notions that are always true.
Euclidean Geometry
Euclidean geometry is the study of 2-Dimensional geometrical shapes and figures. Euclidean geometry is based on different axioms and theorems. The word geometry is derived from the Greek words ‘geo’ meaning Earth and ‘metrein’ meaning ‘To measure’. Thus, geometry is the measure of the Earth or various shapes present on the Earth.
Euclidean geometry as the name suggests was first used by the famous Greek mathematician Euclid. He described the geometry of flat objects in his book “Elements” and was the pioneer in this field. He gives various axioms or postulates that are obvious universal truths, (but they can not be proved by usual means). He stated 5 main axioms which are discussed below in the article.
In this article, we have provided the axioms and Postulates given by Euclid, and a detailed overview of Euclid’s Geometry including its definition, examples, theorem, and advantages.
Table of Content
- History of Euclid Geometry | Who was Euclid?
- What is Euclidean Geometry?
- Euclidean Geometry Definition
- History of Euclidean Geometry
- Euclid’s Definitions
- Examples of Euclidean Geometry
- Non-Euclidean Geometry
- Euclidean and Non-Euclidean Geometry Differences
- Theorems Proved by Euclid
- Euclidean Geometry in Engineering
- Properties of Euclidean Geometry
- Elements in Euclidean Geometry
- Euclid’s Axioms
- Euclid’s Postulates
- Euclidean Geometry Examples
- Euclidean Geometry Class 9
- Practice Problems on Euclidean Geometry