Geometric Construction/Examples/Perpendicular through Point

Example of Geometric Construction

From Euclid's The Elements:

Proposition $11$ of Book $\text{I} $: Construction of Perpendicular Line

Let $AB$ be the given straight line segment, and let $C$ be the given point on it.

Let a point $D$ be taken on $AB$.

We cut off from $CB$ a length $CE$ equal to $DC$.

We construct an equilateral triangle $\triangle DEF$ on $DE$.

We draw the line segment $FC$.

Then $FC$ is the required perpendicular to $AB$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): construction
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): construction