ii. A rectilineal figure is said to be inscribed in a circle when its angular points are on the circumference. Reciprocally, a rectilineal figure is said to be circumscribed to a circle when each side touches the circle.
iii. A circle is said to be inscribed in a rectilineal figure when it touches each side of the figure. Reciprocally, a circle is said to be circumscribed to a rectilineal figure when it passes through each angular point of the figure.
iv. A rectilineal figure which is both equilateral and equiangular is said to be regular.
Observation.—The following summary of the contents of the Fourth Book will assist the student in remembering it:—
1. It contains sixteen Propositions, of which four relate to triangles, four to squares, four to pentagons, and four miscellaneous Propositions.
2. Of the four Propositions occupied with triangles—
(α) One is to inscribe a triangle in a circle.
(β) Its reciprocal, to describe a triangle about a circle.
(γ) To inscribe a circle in a triangle.
(δ) Its reciprocal, to describe a circle about a triangle.