Kitap 3
DEFINITIONS.
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Equal circles are those the diameters of which are equal, or the radii of which are equal.
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A straight line is said to touch a circle which, meeting the circle and being produced, does not cut the circle.
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Circles are said to touch one another which, meeting one another, do not cut one another.
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In a circle straight lines are said to be equally distant from the centre when the perpendiculars drawn to them from the centre are equal.
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And that straight line is said to be at a greater distance on which the greater perpendicular falls.
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A segment of a circle is the figure contained by a straight line and a circumference of a circle.
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An angle of a segment is that contained by a straight line and a circumference of a circle.
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An angle in a segment is the angle which, when a point is taken on the circumference of the segment and straight lines are joined from it to the extremities of the straight line which is the base of the segment, is contained by the straight lines so joined.
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And, when the straight lines containing the angle cut off a circumference, the angle is said to stand upon that circumference.
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A sector of a circle is the figure which, when an angle is constructed at the centre of the circle, is contained by the straight lines containing the angle and the circumference cut off by them.
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Similar segments of circles are those which admit equal angles, or in which the angles are equal to one another.
BOOK III. PROPOSITIONS.
PROPOSITION 1.
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To find the centre of a given circle.
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Let ABC be the given circle; thus it is required to find the centre of the circle ABC.
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Let a straight line AB be drawn through it at random, and let it be bisected at the point D; from D let DC be drawn at right angles to AB and let it be drawn through to E; let CE be bisected at F; I say that F is the centre of the circle ABC.
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For suppose it is not, but, if possible, let G be the centre, and let GA, GD, GB be joined.
