# Horn angles and Euclid's elements

• astrololo
In summary, Euclid states that the angle of the semicircle enclosed 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. This can be seen in the figure provided in the link. To prove this proposition, the given straight angle can be the same for both curved angles or different.
astrololo
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?

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.

## 1. What are horn angles in geometry?

Horn angles, also known as dihedral angles, are the angles formed between two intersecting planes in three-dimensional space.

## 2. What is the significance of Euclid's Elements in geometry?

Euclid's Elements is a mathematical treatise that laid the foundation for the formal study of geometry. It contains 13 books covering various aspects of geometry, including horn angles.

## 3. How did Euclid define horn angles?

Euclid defined horn angles as the angles formed by two intersecting planes that do not lie on the same plane. He also provided a method for measuring these angles using a protractor.

## 4. Can horn angles be measured using different units of measurement?

Yes, horn angles can be measured using different units of measurement, such as degrees, radians, or gradians. However, the most commonly used unit for measuring horn angles is degrees.

## 5. What are some real-life applications of horn angles?

Horn angles have various applications in fields such as architecture, engineering, and navigation. For example, they are used in designing and constructing buildings, bridges, and other structures. They are also used in navigation to determine the direction and orientation of objects in space.

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