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Third Article
It explains the methods of comparing the distance of terrestrial degrees with the height and depression of the fixed star called Cedy, located near the pole of the world, and then comparing those distances with the circumference, diameter, and surface area of the Earth.
O Noble One! Know that astronomers and geometers, through comparison, have stated: The measure of the belt of the earth, comprised of seas and lands, has been determined to be approximately twenty-four thousand miles. Comparing it thus, its distance across (diameter) is found to be seven thousand six hundred miles. Its radius is known to be three thousand eight hundred eighteen miles. The total surface area of the Earth has been calculated as approximately twenty-five thousand times one thousand and three hundred thirty-six fersahs.
Through comparison with these calculations, the distances of celestial bodies have also been determined.
The distance from the center of the world to the lower surface of the moon's sphere – as explained in the preceding paragraph – is roughly equivalent to thirty-two times the Earth’s radius (as established by the rule of proportion explained in previous articles). For all circles existing and posited on the spheres and the terrestrial globe are divided into three hundred sixty degrees, and each degree into sixty minutes.
Therefore, how many miles correspond to one degree of distance on the earth?
To ascertain this, geometers have made comparisons across numerous deserts, taking measurements of surface areas.
Consequently, they found that the Earth’s distance corresponding to one degree is sixty-six whole miles and 3/2 miles. They made this comparison in the following way: At a certain location on an endless desert, they erected a marker and took the altitude of the Cedy star – which they also call Sabit or Demirkazik – at night using a quadrant or astrolabe method. Subsequently, from that marked point, two groups moved along a straight line. One group moved south, the other north, and after a certain time of night, both groups took the altitude of Cedy (after which they awaited morning) and then continued on their way in a straight line during daylight. Based on the altitudes of the fixed stars at specific locations, they stopped at two places where differences appeared in their measurements: one degree short for those going south and one degree more for those going north.
They erected markers at each of these locations. Then, starting from both sides, they measured the distance between three markers, finding that the distance between the two ends was sixty-six whole miles and 3/2 miles. Subsequently, both groups (setting out again, having measured) proceeded south and north from the difference between the two places they had measured, traveling a distance equal to the number of miles measured, and stopped at the last one.
At night, when the two groups took the altitude of different stars, they found that there was again a complete degree of elevation and depression with a difference between them. [89/b] Multiplying sixty-six whole miles and 3/2 by three hundred sixty, they calculated the circumference of the circle; from there, they derived its diameter, radius, and finally, the surface area of the Earth. They obtained the same results in many places using this method.