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ABCD base bisected Book called centre chord circle circumference coincide common construction described diagonals diameter difference distance divided double draw drawn equal equilateral Euclid exterior angle extremities fall figure four given point given straight line greater half Hence inscribed intersect isosceles triangle join length less Let ABC magnitudes measure meet method multiple NOTE opposite sides parallel parallelogram passes perpendicular plane PROBLEM produced proof Prop PROPOSITION prove Q. E. D. Ex quadrilateral ratio rect rectangle contained respectively right angles segment Shew shewn sides similar Similarly square suppose Take taken tangent THEOREM third touch triangle triangle ABC triangle be equal twice vertex whole
Side 42 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 17 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Side 106 - 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.
Side 178 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 188 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 78 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 91 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.