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Euclid's fifth postulate: If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.
It can be rewritten: If two lines are drawn which intersect a third at angles of 90 degrees, the two lines are parallel and will not intersect each other.
It has also been rewritten as Playfair's axiom:In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.
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What is euclids theory?
need a simple explanation of Euclids theory.
Through a point not on the line exactly one line can be drawn parallel to the?
... given line. This is one version of Euclid's fifth postulate, also known as the Parallel Postulate. It is quite possible to construct consistent systems of geometry where this postulate is negated - either many parallel lines or none.
Title of thirteenth book in euclids elements?
compositions
What is midpoint postulate?
midpoint postulate
Are two lines that are parallel to the same line parallel to each other?
Yes they are. It is delineated in something called the parallel postulate, and the axiom is also called Euclid's fifth postulate. This is boilerplate Euclidean geometry, and a link can be found below if you'd like to review the particulars.
