Geometric Construction/Examples/Bisection of Angle
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Example of Geometric Construction
From Euclid's The Elements:
Proposition $10$ of Book $\text{I} $: Bisection of Angle
Let $\angle BAC$ be the given angle to be bisected.
Let $D$ be an arbitrary point on $AB$.
From Proposition $3$: Construction of Equal Straight Lines from Unequal, let $AE$ be cut off from $AC$ such that $AE = AD$.
From Euclid's First Postulate, let the line segment $DE$ be constructed.
From Proposition $1$: Construction of Equilateral Triangle, let an equilateral triangle $\triangle DEF$ be constructed on $AB$.
From Euclid's First Postulate, let the line segment $AF$ be constructed.
Then the angle $\angle BAC$ has been bisected by the straight line segment $AF$.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): construction
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Euclidean construction
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): construction
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Euclidean construction