Euclid's Elements
Book IV
DEFINITIONS

1. 
A rectilineal figure is said to be inscribed in a rectilineal figure when the respective angles of the inscribed figure lie on the respective sides of that in which it is inscribed. 
2. 
Similarly a figure is said to be circumscribed about a figure when the respective sides of the circumscribed figure pass through the respective angles of that about which it is circumscribed. 
3. 
A rectilineal figure is said to be inscribed in a circle when each angle of the inscribed figure lies on the circumference of the circle. 
4. 
A rectilineal figure is said to be circumscribed about a circle when each side of the circumscribed figure touches the circumference of the circle. 
5. 
Similarly a circle is said to be inscribed in a figure when the circumference of the circle touches each side of the figure in which it is inscribed. 
6. 
A circle is said to be circumscribed about a figure when the circumference of the circle passes through each angle of the figure about which it is circumscribed. 
7. 
A straight line is said to be fitted into a circle when its extremities are on the circumference of the circle. 
Contents and Introduction
Book IV Propositions
