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Axioms, Euclidean geometry

In the historical process of the development of geometry - pay someone to do my homework , relatively simple, descriptive statements were chosen as axioms on the basis of which the remaining facts could be proven.

Axioms are therefore of experimental origin, i.e. they also reflect certain simple, descriptive properties of real space - math homework solver . Axioms are thus fundamental statements about the basic concepts of a geometry, which are added to the geometric system under consideration without proof and on the basis of which all further statements of the system under consideration are proved.

Axioms of incidence (linkage)

I1 - One and only one straight line passes through every two different points.

I2 - At least two points lie on each straight line.

I3 - There are three points that do not lie on a straight line.

Axioms of arrangement

A1 - Of any three points on a straight line that are different in pairs, one lies and only one lies between the other two.

A2 - For two points of a straight line there exists on this straight line such a third point that the second lies between the first and the third point.

A3 - Let the straight line g lie on the plane ABC - , where A, B and C do not lie on a straight line, and pass through none of the points A, B and C.

If g contains a point on the line AB, it also contains a point on the line BC or the line AC.

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