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Index
»
Geometry
»
Chapter 1
»
Level 1
level: Level 1
Questions and Answers List
level questions: Level 1
Question
Answer
David Hilbert (1862- 1943), a german mathemetician and developer of the axiomaic approach to mathimatics.
David Hilbert
Points, lines, and planes
Undefined terms
Is a statment accepted without proof.
Postulate
A line contains atleast two points
Postulate1:
A plane contains atleast three points not all on one line
Postulate 1a:
Space contains atleast four point not all in one plane.
Postulate1b:
Through any two points different points, exactly one line exists.
Postulate2:
Through any three points that are not on one line, exactly one plane exists.
Postulate3:
If two points lie in a plane, the line contianing them lies in that plane.
Postulate4:
If two planes intersect, then their intersection is a line.
Postulate5:
If two lines intersect, then their intersecting is exactly one point.
Theorem 1-1:
Exactly one plane contains a given line and a given point one the line.
Theorem1-2:
If two lines intersect, then exactly one plane contains both lines.
Theorem 1-3