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 fifteenangled figure which shall be both equilateral and equiangular.
Contents and Introduction
Book IV Definitions
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