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ABCD added adjacent angles bases basis bear called centre chord circle circumference common consequently construction contains DEMON demonstration describe determine diameter distance divided draw draw the lines drawn equal equal angles expressed extended extremities feet figure follows formed four fourth term geometrical proportion given gles greater half height hypothenuse inches included inscribed instance Join legs length less let fall line AC manner measure meet minutes number of sides opposite parallel parallelogram perpendicular polygon ABCDEF principle PROBLEM proportion prove quadrilateral Query radii radius ratio reason rectangle regular polygon relation remaining Remark respectively right angles right-angled triangle Sect semicircle side AB side AC smaller SOLUTION square stands straight line surface tangent term three angles three sides triangle ABC triangles are equal Truth twice vertex whole
Page 144 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 124 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 111 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 106 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Page 117 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems.
Page 144 - A, with a radius equal to the sum of the radii of the given circles, describe a circle.
Page 80 - ... any two triangles are to each other as the products of their bases by their altitudes.
Page 125 - P is at the center of the circle. II. 18. The sum of the arcs subtending the vertical angles made by any two chords that intersect, is the same, as long as the angle of intersection is the same. 19. From a point without a circle two straight lines are drawn cutting the convex and concave circumferences, and also respectively parallel to two radii of the circle. Prove that the difference of the concave and convex arcs intercepted by the cutting lines, is equal to twice the arc intercepted by the radii.