- Proposition 1.
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To fit into a given circle a straight line equal to a given straight line which is not greater than the diameter of the circle.
- Proposition 2.
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To inscribe in a given circle a triangle equiangular with a given triangle.
- Proposition 3.
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To circumscribe about a given circle a triangle equiangular with a given triangle.
- Proposition 4.
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To inscribe a circle in a given triangle.
- Proposition 5.
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To circumscribe a circle about a given triangle.
Corollary. When the center of the circle falls within the triangle, the triangle is acute-angled; when the center falls on a side, the triangle is right-angled; and when the center of the circle falls outside the triangle, the triangle is obtuse-angled.
- Proposition 6.
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To inscribe a square in a given circle.
- Proposition 7.
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To circumscribe a square about a given circle.
- Proposition 8.
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To inscribe a circle in a given square.
- Proposition 9.
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To circumscribe a circle about a given square.
- Proposition 10.
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To construct an isosceles triangle having each of the angles at the base double the remaining one.
- Proposition 11.
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To inscribe an equilateral and equiangular pentagon in a given circle.
- Proposition 12.
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To circumscribe an equilateral and equiangular pentagon about a given circle.
- Proposition 13.
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To inscribe a circle in a given equilateral and equiangular pentagon.
- Proposition 14.
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To circumscribe a circle about a given equilateral and equiangular pentagon.
- Proposition 15.
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To inscribe an equilateral and equiangular hexagon in a given circle.
Corollary. The side of the hexagon equals the radius of the circle.
- Proposition 16.
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To inscribe an equilateral and equiangular fifteen-angled figure in a given circle.
Corollary. And, in like manner as in the case of the pentagon, if through the points of division on the circle we draw tangents to the circle, there will be circumscribed about the circle a fifteen-angled figure which is equilateral and equiangular.
