Discussion and Homework
Fourth Reading Assignment

Notes for the Reading

Elements XII.2: Circles are to one another as the squares on the diameters.
Elements III.33: On a given straight line to describe a segment of a circle admitting an angle equal to a given rectilineal angle.

Questions for Discussion

It might help if you label the parts of the diagram as you go through the reading. Label lengths, and "areas" in the diagram.

  1. What is the lunule in the diagram on page 60 of which we are finding the area?
  2. What is a segment of a circle and what is its base? Describe these in the diagram on page 60.
  3. What does the expression "similar segments of circles have the same ratios as the squares of their bases" mean in terms of the diagram and areas of parts of the diagram?
  4. How would a Greek of this era know that the triangle in the semicircle is a right triangle?

A pdf version of this page and the accompanying reading assignment.

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