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A B C alternate angles applied base bisect bisector called centre CHAPTER chord circle circumference coincide common Consequently Construct converse corresponding determined diagonals diameter difference direction distance divided draw drawn equal equidistant evident example EXERCISE extremities fall figure four given point given straight line greater half height Hence inches inscribed instance intersect isosceles triangle joining length less line drawn line joining magnitudes mark means measure meet middle point moving opposite opposite sides parallel parallelogram pass perimeter perpendicular placed plane polygon position PROBLEM produced properties proportion propositions proved quadrilateral radius ratio rectangle regular polygon remainder represented respectively right angles segment sides similar square statements Suppose surface tangent termed Theo THEOREM third touch triangle true twice units vertex vertical whole
Pagina 242 - 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.
Pagina 240 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Pagina 240 - 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.
Pagina 242 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Pagina 242 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Pagina 241 - If the first has to the second the same ratio which the third has to the fourth...
Pagina 240 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Pagina 242 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Pagina 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.