# Book IV.

## Definitions.

### I.

A rectilinear figure is ſaid to be *inſcribed in* another, when all the angular points of the inſcribed figure are on the ſides of the figure in which it is ſaid to be inſcribed.

### II.

A figure is ſaid to be *deſcribed about* another figure, when all the ſides of the circumſcribed figure paſs through the angular points of the other figure.

### III.

A rectilinear figure is ſaid to be *inſcribed in* a circle, when the vertex of each angle of the figure is in the circumference of the circle.

### IV.

A rectilinear figure is ſaid to be *circumſcribed about* a circle, when each of its ſides is a tangent to the circle.

### V.

A circle is ſaid to be *inſcribed in* a rectilinear figure, when each ſide of the figure is a tangent to the circle.

### VI.

A circle is ſaid to be *circumſcribed about* a rectilinear figure, when the circumference paſſes through the vertex of each angle of the figure.

is circumſcribed.

### VII.

A ſtraight line is ſaid to be *inſcribe in* a circle, when its extremities are in the circumference.

*The Fourth Book of the Elements is devoted to the ſolution of problems, chiefly relating to the inſcription and circumſcription of regular polygons and circles.*

A regular polygon is one whoſe angles and ſides are equal.