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==The Essence of Euclidean Geometry==
==The Essence of Euclidean Geometry==


Here are the Euclidean constructions, which are simply postulated, not explained in any way.
The Euclidean constructions are simply postulated, not explained in any way. You have to start somewhere.


# Join two given points with a straight line segment.
# Join two given points with a straight line segment.
Line 19: Line 19:
# Given a line segment as radius, with one end designated as the center, draw a circle.
# Given a line segment as radius, with one end designated as the center, draw a circle.


Thus:
The given points and line segment are in red, and the constructed lines and circles in black.


[[File:TAEuclideanConstructions.png]]
[[File:TAEuclideanConstructionPostulates.png]]


I am going to bypass Euclid's other assumptions until we need them.
I am going to bypass Euclid's other assumptions until we need them.