Horn angles and Euclid's elements

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SUMMARY

The discussion centers on Euclid's proposition from Book 3, Proposition 16, which states that the angle of a semicircle formed by the straight line BA and the circumference CHA is greater than any acute rectilinear angle, while the angle formed by the circumference CHA and the straight line AE is less than any acute rectilinear angle. The participants clarify that BA represents the diameter, indicating that the semicircle's arc is 180 degrees, while the arc enclosed by AE is zero degrees. The conversation emphasizes the geometric principle that a right angle drawn from any point on a circle is tangent to the circle.

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astrololo
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We have the following statement by Euclid : "I say further that the angle of the semicircle contained by the straight line BA and the circumference CHA is greater than any acute rectilinear angle, and the remaining angle contained by the circumference CHA and the straight line AE is less than any acute rectilinear angle." (Book 3 proposition 16)

The figure is in this link : http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII16.html

So, I was wondering, could somebody give me an example of where it is true ? For this proposition to be true, must the given straight angle be the same for both curved angles ? Or different?
 
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Thread moved, as it is more of a question for clarification than a homework problem.
 
In this part, I believe BA still is referring to the diameter. So he is stating that the arc of the semicircle enclosed by BA = 180 degrees, and the arc of the circle enclosed by AE is zero.
Essentially restating his point that a right angle from any point on a circle is tangent to the circle.
 

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