Euclid’s Axioms
Euclid’s Axioms which are used to study Euclidean Geometry are:
- Things which are equal to the same thing are equal to one another.
- If equals are added to equals, the wholes are equal.
- If equals are subtracted from equals, the remainders are equal.
- Things which coincide with one another are equal to one another.
- The whole is greater than the part.
- Things which are double of the same things are equal to one another.
- Things which are halves of the same things are equal to one another.
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