The Pythagorean Theorem
Proposition XLVII proves the most famous theorem in mathematics: in a right triangle, the square on the hypotenuse equals the sum of the squares on the other two sides. Euclid's proof constructs squares on all three sides, then shows through a series of triangle congruences and area comparisons that the large square equals the sum of the two smaller squares.
The Text
What You'll Learn
Comprehension
States the theorem: square on hypotenuse = sum of squares on other sides
Cause & Consequence
Explains why the line CL is drawn parallel to AG
Meaning
Distinguishes between knowing the theorem empirically and proving it logically
Evidence
Points to a specific step in the proof
Defense
Maintains or thoughtfully revises their position under challenge
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