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## Chapter Abstracts

## Hippocrates' Quadrature of the Lune

• Since the dawn of agriculture humans have had a grasp of measurement and basic geometric concepts like area, and the early Egyptians knew some of the properties of specific shapes such as right triangles but did not develop the higher theories that examine these relationships.

• One of the first mathematicians was Thales, and later Pythagoras, who stated what is now know as the Pythagorean Theorem.

• The Pythagorean theorem states for any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs (a² + b² = c²).

• Hippocrates was a teacher who advanced mathematics by demonstrating how to build a logical theorem.

• Hippocrates's great advance was devising a way to "square" a figure with curved sides, specifically a "lune," or crescent. His theory and proof are fairly simple and are based on properties of triangles and...

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