Construction of Perpendicular Line/Construction

Construction of Perpendicular Line

In the words of Euclid:

To draw a straight line at right angles to a given straight line from a given point on it.

(The Elements: Book $\text{I}$: Proposition $11$)

Construction

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

• 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 1 (2nd ed.) ... (previous) ... (next): Book $\text{I}$. Propositions