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Horn angles and Euclid's elements

  1. Jun 17, 2015 #1
    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?
  2. jcsd
  3. Jun 18, 2015 #2


    Staff: Mentor

    Thread moved, as it is more of a question for clarification than a homework problem.
  4. Jun 18, 2015 #3


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    Homework Helper

    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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