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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.
Is hyperbolic parallel postulate a postulate of Euclid?
No, the hyperbolic parallel postulate is not one of Euclid's original five postulates. Euclid's fifth postulate, known as the parallel postulate, states that given a line and a point not on that line, there is exactly one line parallel to the original line that passes through the point. Hyperbolic geometry arises from modifying this postulate, allowing for multiple parallel lines through the given point, leading to a different set of geometric principles.
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
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.
Why does a triangles angles always add up to 180 degrees?
It is a consequence of Euclids's parallel postulate.
What is euclids theory?
need a simple explanation of Euclids theory.
How could drawing a line on a sphere refute Euclids second postulate that a line segment may be extended indefinitely.?
Because it will eventually complete a Circle, like the dachshund that met its end going round a lamp-post.
Who are euclids parents?
eetrgrv
If there is a line and a point not on the line then there is exactly lines trough the point parallel to the given line?
This is 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.
Is hyperbolic parallel postulate a postulate of Euclid?
No, the hyperbolic parallel postulate is not one of Euclid's original five postulates. Euclid's fifth postulate, known as the parallel postulate, states that given a line and a point not on that line, there is exactly one line parallel to the original line that passes through the point. Hyperbolic geometry arises from modifying this postulate, allowing for multiple parallel lines through the given point, leading to a different set of geometric principles.
An axiom or a is an accepted statement of fact?
A postulate is assumed to be a fact and used to derive conclusions. However, there is no assurance that the postulate is itself true and so all the derived conclusions may depend on a proposition that is not necessarily true. Euclid's fifth, or parallel) postulate in geometry is a notable example.
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.
Books written by euclid?
euclids elements
What were euclids favorite areas of mathematics?
geometry
What was euclids major maths discoveries?
geometry
Non-Euclidean geometry was discovered when in seeking cleaner alternatives to the fifth postulate it was found that the negation could also be true?
true
