Introduction

This is a picture of a pair of compasses and a ruler.

How to draw a line

Using a ruler (based on Book I, Postulate 1), we can draw a segment of a straight line.

We will use the notation ${\displaystyle {\overline {AB}}}$ for the line segment the starts at A and ends at B. Note that we don't care about the segment direction and therefore ${\displaystyle {\overline {AB}}}$ is the same as ${\displaystyle {\overline {BA}}}$.

Line segment ${\displaystyle {\overline {AB}}}$

Line segment ${\displaystyle {\overline {BA}}}$

How to draw a circle

• Using the compass (based on Book I, Postulate 3).

We use the notation ${\displaystyle \circ A,{\overline {AB}}}$ for the circle whose centre is the point A and its radius length equals that of the segment ${\displaystyle {\overline {AB}}}$.

Note that in other sources, such as Euclid's Elements, a circle is described by any 3 points on its circumference, ABC.

The center-radius notation was chosen because of its suitability for constructing circles with a ruler and a compass.