# Euclid's Elements Reference Page Book IV

Def. 1. A rectilinear figure is said to be inscribed in a rectilinear figure when the respective angles of the inscribed figure lie on the respective sides of that in which it is inscribed.

Def. 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.

Def. 3. A rectilinear figure is said to be inscribed in a circle when each angle of the inscribed figure lies on the circumference of the circle.

Def. 4. A rectilinear figure is said to be circumscribed about a circle when each side of the circumscribed figure touches the circumference of the circle.

Def. 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.

Def. 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.

Def. 7. A straight line is said to be fitted into a circle when its ends are on the circumference of the circle.

(IV.2) To inscribe in a given circle a triangle equiangular with a given triangle.

(IV.5) To circumscribe a circle about a given triangle.

(IV.10) To construct an isosceles triangle having each of the angles at the base double the remaining one.

(IV.11) To inscribe an equilateral and equiangular pentagon in a given circle.

### References

1. T. L. Heath, Euclid: The Thirteen Books of The Elements, Dover, 1956
2. R. Simson, The Elements of Euclid, Books I-VI, XI, XII + Euclid's Data, Elibron Classics, 2005