Definition:Inscribe
From ProofWiki
Circle
A circle is inscribed within a polygon when it is tangent to each of the sides of that polygon:
Note that such a polygon can also be described as being circumscribed about the circle.
Euclid's Terminology
As Euclid defined it:
- A rectilineal figure is said to be circumscribed about a circle, when each side of the circumscribed figure touches the circumference of the circle.
(The Elements: Book IV: Definition $4$)
- 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.
(The Elements: Book IV: Definition $5$)
Rectilineal Figure
As Euclid defined it:
- 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.
