Definition:Inscribe/Polygon in Polygon

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A polygon is inscribed in another polygon when each of its vertices lies on the corresponding side of the other polygon.

In the words of Euclid:

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.

(The Elements: Book $\text{IV}$: Definition $1$)

Also known as

The more archaic language inscribed within is often seen.

Also see

The second polygon also can be described as being circumscribed around the first polygon.

In the words of Euclid:

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.

(The Elements: Book $\text{IV}$: Definition $2$)