1, can you pass any two points? Straight line connection.

2. Can any line segment be used? The limit is extended to? Straight line.

3. Given an arbitrary line segment, can you use it? Is the endpoint a circle? , line segment as radius? A circle.

4. All straight? Everyone is equal.

5, if two straight lines intersect with the third straight line, and in the same? Inside the side? Sum? Twice in a row? So these two straight lines are here? The edges must intersect.

Euclidean geometry axioms are several geometric axioms established by Euclid, also known as Euclid geometry. Its establishment adopts the method of analysis and synthesis, which is not only the connection between the premise and conclusion of a single proposition, but also the connection of all geometric propositions into a logical network.

Euclid listed some recognized facts as definitions and axioms, and used these definitions and axioms to study the properties of various geometric figures by formal logic, thus establishing a set of geometric argumentation methods to demonstrate propositions and obtain theorems from axioms and definitions, forming a strict logical system.

Historical influence

Euclid, a great mathematician in ancient Greece, is famous for his masterpiece Elements of Geometry. This book is the most famous, complete and widespread mathematical work in the world, and it is also the most valuable work of Euclid.

In Elements of Geometry, Euclid systematically summarized the geometric knowledge gained by ancient working people and scholars in practice and thinking. Euclid listed some recognized facts as definitions and axioms, and used these definitions and axioms to study the properties of various geometric figures with the help of formal logic.

Thus, a set of geometric demonstration methods based on axioms and definitions is established, and a strict logical system-geometry is formed. And this book became the cornerstone of European geometry. ?

For more than two thousand years, The Elements of Geometry has been the main teaching material for studying geometry. Many great scholars, such as Copernicus, Galileo, Descartes and Newton. , studied the elements of geometry, and absorbed rich nutrition from it, thus making many great achievements. ?