# Definition:Euclid's Definitions - Book IV

Jump to navigation
Jump to search

## Euclid's Definitions: Book $\text{IV}$

These definitions appear at the start of Book $\text{IV}$ of Euclid's *The Elements*.

- 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. - 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. - 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. - A rectilineal figure is said to be
**circumscribed about a circle**, when each side of the circumscribed figure touches the circumference of the circle. - 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. - 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. - A straight line is said to be
**fitted into a circle**when its extremities are on the circumference of the circle.

## Sources

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