# 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.*

### Euclid's Elements Reference Page

### References

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

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