what is Euclid's proposition #5?

Answer 1

Euclid has 13 Proposition #5's. He wrote 13 books called Elements I through Elements XIII. Each has definitions and propositions.

For Elements I, Proposition #5 is "In isosceles triangles the angles at the base are equal to one another, and, if the equal straight lines are produced further, the angles under the base will be equal to one another."

Answer 2

In geometry, the parallel postulate, also called Euclid's fifth postulate since it is the fifth postulate in Euclid's Elements, is a distinctive axiom in what is now called Euclidean geometry. It states that:

If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.

Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate. A geometry where the parallel postulate cannot hold is known as a non-euclidean geometry. Geometry that is independent of Euclid's fifth postulate (i.e., only assumes the first four postulates) is known as absolute geometry (or, in some places, neutral geometry).

Answer 3

Here are the 5 postulates

Euclid's Postulates

1. For every point P and every point Q not equal to P there exists a unique line that passes through P and Q.
2. For every segment AB and for every segment CD there exists a unique point E such that B is between A and E and segment CD is congruent to segment BE.
3. For every point O and every point A not equal to O there exists a circle with center O and radius OA.
4. All right angles are congruent to each other.
5. For every line l and for every point P that does not lie on l there exists a unique line m through P that is parallel to l.



The other geometries (spherical and hyperbolic) come out if you change the 5th postulate. One assumes that no such line exists and another assumes that infinite such lines exist. So in spherical geometry it is possible to have a triangle with three right angles (the sum of the interior angles is greater than 180 degrees.)

Answer 4

Also called the parallel postulate, the postulate that is debatable. This is the postulate that "creates" other types of geometries like hpyerbolic geometry.

Answer 5

http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII5.html
http://mathforum.org/mathtools/tool/1376/
http://www.obkb.com/dcljr/euclidhs.html

These will help you.