Postulate 7
through any three points there is at least one plane- through any three noncollinear points there is exactly one plane.
Postulate 7 of Euclid’s geometry states that if a straight line falls on two straight lines in such a way that the sum of the inner angles on one side is less than two right angles, then these two straight lines, if extended ad infinitum, will intersect on that side where the sum of the inner angles is less than two right angles.
In simpler terms, if a line intersects two other lines and the sum of the angles on one side of the intersection is less than 180 degrees (two right angles), then the two lines will eventually intersect on that same side when extended indefinitely.
This postulate is known as the parallel postulate and it is one of the five postulates that Euclid used to lay the foundations of his system of geometry. It is also the most controversial postulate and for centuries mathematicians tried to prove it using the other four postulates, but without success. It was only in the 19th century, through the works of mathematicians such as Lobachevsky, Bolyai, and Gauss, that the idea of non-Euclidean geometries was established, showing that the parallel postulate is not necessarily true in all geometries.
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