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i know that Euclid wrote the book "Elements." he came up with The concepts of incidence (i.e. a point lies on a line), betweeness (i.e. a point is between two other points), and congruence (i.e. line segments are congruent). check out this website. http://www.libraryofmath.com/euclidean-geometry.html
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Which of the following are the tools which allowed the Greeks to exploit the five basic postulates of Euclidian geometry?
Straightedge Compass
How many lines can be drawn through two fixed points?
In Euclidian or plane geometry, there can be only one line through two fixed points. Lines cannot actually be drawn; if you see it it is not a geometric line. If the points are on a curved surface as in a geometry that is non-Euclidian, then there can be infinitely many lines connecting two points.
Why are postulates not proved in geometry?
postulates cannot be proved, they are the base of geometry and there isn't anything to prove it with. if the postulates were wrong then all of euclidian geometry would be wrong. that is like saying how do we know the English language is correct, it is the basis for communication and if it wasn't, then how would speaking the language work?
Why is the parallel axiom in Euclid's geometry false in non-Euclidian geometry?
Euclid's parallel axiom is false in non-Euclidean geometry because non-Euclidean geometry occurs within a different theory of space. There may be one absolute occurrence in non-Euclidean space where Euclid's parallel axiom is valid. Possibly as some form of infinity.
How many distinct lines can be drawn through 2 points?
In plane (Euclidian) geometry there is only one line through two points. On a sphere, every meridian intersects the north and south poles.
