## Euclid's Elements

### Book IV

#### Book IV    Propositions

Proposition 1.
Into a given circle to fit a straight line equal to a given straight line which is not greater than the diameter of the circle.

Proposition 2.
In a given circle to inscribe a triangle equiangular with a given triangle.

Proposition 3.
About a given circle to circumscribe a triangle equiangular with a given triangle.

Proposition 4.
In a given triangle to inscribe a circle.

Proposition 5.
About a given triangle to circumscribe a circle.

Proposition 6.
In a given circle to inscribe a square.

Proposition 7.
About a given circle to circumscribe a square.

Proposition 8.
In a given square to inscribe a circle.

Proposition 9.
About a given square to circumscribe a circle.

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

Proposition 11.
In a given circle to inscribe an equilateral and equiangular pentagon.

Proposition 12.
About a given circle to circumscribe an equilateral and equiangular pentagon.

Proposition 13.
In a given pentagon, which is equilateral and equiangular, to inscribe a circle.

Proposition 14.
About a given pentagon, which is equilateral and equiangular, to circumscribe a circle.

Proposition 15.
In a given circle to inscribe an equilateral and equiangular hexagon.

Proposition 16.
In a given circle to inscribe a fifteen-angled figure which shall be both equilateral and equiangular.

Contents and Introduction     Book IV Definitions

Top of Page