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ABCD altitude Apply approaches base bisecting bisector called centre chord circle circumference circumscribed coincide common construct contains CONVERSELY describe diagonals diameter difference distance divided Draw drawn equal equally distant equilateral triangle equivalent Exercise extremities fall figure Find Find the area four GEOMETRY given given circle given point given straight line given triangle GIVEN—the greater half Hence hexagon homologous hypotenuse inscribed intercepted intersection isosceles length less limit locus measured meet method middle points opposite sides parallel parallelogram passes perpendicular plane polygon position PROBLEMS PROPOSITION PROVE quadrilateral quantity radii radius ratio rectangle regular regular polygon right angles right triangle ruler segment similar square straight line Substituting symmetry tangent THEOREM triangle ABC triangles are equal turned unequal variable vertex vertices
Side 248 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Side 63 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC. In BC take any point D, and join AD; and at the point A, in the straight line AD, make (I.
Side 49 - If, from a point within a triangle, two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle.
Side 148 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Side 47 - ... the third side of the first is greater than the third side of the second.
Side 149 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Side 47 - If two triangles have two sides of one equal respectively to two sides of the other...
Side 100 - At a given point in a straight line to erect a perpendicular to that line. Let AB be the straight line, and let c D be a given point in it.