He measured the radius of the earth twice...

He measured the radius of the earth twice, once from a mountain peak in the Hindukush mountains in Afghanistan and the other time from the peak of a high mountain next to a flat plain when he was travelling to India. According to the figure in order to measure the radius of the earth through this method one should climb to the peak of a high mountain which overlooks a flat plain.

(Mountain is indicated with the height of AH in figure (1) but as we know the irregularities on the surface of the earth are insignificant in respect to the largeness of the earth but in order to make the mountain recognizable in the figure we drew it bigger than its real size.

The horizon should be drawn on top of the mountain (But how?) Abu Raihan then by using an instrument similar to today's telescope overlooked the surface of the earth and measured the angle(-< ) between the horizon (AH) and the tangent line to the earth's surface (AC) which was a small angle about 30 minuted (half a degree). By measuring the height of the mountain's peak (AH) and using the following equations, he measured the radius of the earth.

In the right triangle of (OAC), the equation could be written as: Therefore, by measuring the angle (-<) and the height of the mountain (h) the radius of the earth could be measured, through Abu Raihan's method. Have you ever considered how the height of a mountain could be measured? Abu Raihan Biruni in his book entitled Ghanoon Masoudi which is an astronomical book, described the measuring method of a mountain's height. Figure (2) shows this method which is still used today.

[^1]: Uyan ul Anbaa, Vol. 1, page 314-315. [^2]: History of Literature, by Dr. Safa…