Kitap 11
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When, the diameter of a semicircle remaining fixed, the semicircle is carried round and restored again to the same position from which it began to be moved, the figure so comprehended is a sphere.
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The axis of the sphere is the straight line which remains fixed and about which the semicircle is turned.
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The centre of the sphere is the same as that of the semicircle.
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A diameter of the sphere is any straight line drawn through the centre and terminated in both directions by the surface of the sphere.
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When, one side of those about the right angle in a right-angled triangle remaining fixed, the triangle is carried round and restored again to the same position from which it began to be moved, the figure so comprehended is a cone.
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And, if the straight line which remains fixed be equal to the remaining side about the right angle which is carried round, the cone will be right-angled; if less, obtuse-angled; and if greater, acute-angled.
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The axis of the cone is the straight line which remains fixed and about which the triangle is turned.
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And the base is the circle described by the straight line which is carried round.
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When, one side of those about the right angle in a rectangular parallelogram remaining fixed, the parallelogram is carried round and restored again to the same position from which it began to be moved, the figure so comprehended is a cylinder.
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The axis of the cylinder is the straight line which remains fixed and about which the parallelogram is turned.
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And the bases are the circles described by the two sides opposite to one another which are carried round.
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Similar cones and cylinders are those in which the axes and the diameters of the bases are proportional.
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A cube is a solid figure contained by six equal squares.
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An octahedron is a solid figure contained by eight equal and equilateral triangles.
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An icosahedron is a solid figure contained by twenty equal and equilateral triangles.
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