Finally, extend the definition of "hyperbolic angle" to that subtended by any interval on the hyperbola. Suppose formula_12 are positive real numbers such that formula_13 and formula_14, so that formula_15 and formula_16 are points on the hyperbola formula_17 and determine an interval on it. Then the squeeze mapping formula_18 maps the angle formula_19 to the "standard position" angle formula_20. By the result of Gregoire de Saint-Vincent, the hyperbolic sectors determined by these angles have the same area, which is taken to be the magnitude of the angle. This magnitude is formula_21.