Geometrical Mean

Geometrical Mean of two numbers is a number, whose square is the product of the given numbers. It is thus obtained by multiplying the two given numbers together and taking the square root of the product. The geometrical mean of 4 and 49 is thus 14. In algebra the geometrical mean of two numbers a and b is Vab. In Pure Geometry the geometrical mean of two lines is a line the square on which is equal in area to the rectangle contained by the two given lines. Euclid gives a construction for obtaining this mean.