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ABCD altitude apply approaches base bisector bisects called centre chord circle circumference circumscribed coincide common construct contains conversely corresponding describe diagonals diameter difference distance divided draw drawn equal equation equilateral triangle equivalent Exercise external extremities fall figure Find four GEOMETRY given given point given straight line GIVEN—the greater half Hence hypotenuse included inscribed intersection isosceles length less limit locus mean proportional measured meet method middle points opposite sides parallel parallelogram passes perpendicular polygon position PROBLEMS PROPOSITION PROVE quadrilateral quantity radii radius ratio ratio of similitude rect rectangle regular polygon right angles right triangle segments sides similar square straight line Substituting tangent THEOREM third side triangle ABC triangle is equal turns unequal unit vertex vertices
Page 10 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 248 - The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 5 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Page 215 - 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 67 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 145 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 71 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 180 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.