The First Proof
Proposition I shows how to construct an equilateral triangle on a given line segment. Using only the postulates (draw circles, draw lines), Euclid constructs two circles that intersect at a point. He then proves, using the definition of a circle and Axiom I, that all three sides must be equal. This simple proof demonstrates the method that will be used throughout the Elements.
The Text
What You'll Learn
Comprehension
Identifies the datum (given: line AB) and quaesitum (sought: equilateral triangle)
Cause & Consequence
Explains why circles are used: all radii of a circle are equal
Meaning
Articulates what makes this a proof rather than just a claim
Evidence
Points to a specific step in the proof
Defense
Maintains or thoughtfully revises their position under challenge
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