Geometry - Mensuration


2000 B.C. - 600 B.C.

Geometry began as practical mensuration (this means, they assumed any two numbers could be expressed in terms of another - they didn't realize irrational numbers existed). In 2000 to 1600 B. C. there is evidence that the Babylonians had general rules for the area of a rectange, the areas of right and isosceles triangles (maybe even a general triangle), the area of a trapezoid having one side perpendicular to the parallel sides, the volume of a rectangular parallelepiped, and the volume of a right prism with a special trapezoidal base. They did not understand pi at this time, but took the circumferenc of a circle to be three times the diameter and the area as one-twelfth the square of the circumference (which equates to pi being three).

All this geometry was intuitive. There was no demonstrating or deductive reasoning. This was the time of the Ahmes Papyrus, which listed the area of isosceles triangles as 1/2 b*h, and the area of a circle as (d - 1/9d)^2, where d = diameter.

Indians had the same amount of mensurations, as did the Romans. They were interested in geometry only for its practical value. This included measurement of land, laying out of cities, engineering, warfare.


Go to outline of Euclidean geometry

Go to outline of other geometry

Return to Timeline Homepage