Question

Euclid's Construction. HELP! Will give medal!

Answer 1

Part 2:
The next paragraph is an explanation of why this construction creates an equilateral triangle. Write the explanation in your own words.
And since the point A is the center of the circle CDB, AC is equal to AB [Def. 1.15]. Again, since the point B is the center of the circle CAE, BC is equal to BA [Def. 1.15]. But CA was also shown (to be) equal to AB. Thus, CA and CB are each equal to AB. But things equal to the same thing are also equal to one another [C.N.1]. Thus, CA is also equal to CB. Thus, the three (straight-lines) CA, AB, and BC are equal to one another.