To pursue this study, it is necessary to obtain geometrical arguments, in which we can believe without doubting. I will make then a figure of the earth, and I will place E in the centre of it, and I will describe another circle from the north of it to the south, and draw a straight line from the Arctic (Celestial) Pole to the Antarctic (Celestial) Pole through the centre and circumference of the earth, and place A at the zenith of the firmament, and B in the northern pole of the circle, and C down below it, and D in its south (celestial) pole164.
Therefore, whosoever being in position E (at the equator), should take the astrolabe in his handfor with it will be obtained full certain knowledge of this matterand placing his face along the middle line of the astrolabe which he holds suspended by a thread from his thumb, and beholding the Arctic (Celestial) Pole through the two holes of its two plates, would find that pole level with the earth; and if you travel three score six and two-thirds of a mile165 from E to B and then place the astrolabe opposite the Arctic (Celestial) Pole, and look through it as you did before, you would find it has an elevation of one degree above the horizon166 and one of the three hundred and sixty degrees of the astrolabe proves it to be so.
Again, if you move another three score six and two-third miles from that towards B, and place the astrolabe opposite the same pole167, and look as before, you will find it has an elevation of two degrees,168 and so on, always, from E to B, for every three score six and two-thirds miles until one would reach B, one would find the same pole increasing in height by one degree. The amount of all those miles put together in accordance with the amount of the three hundred and sixty degrees which are in the circumference of the sphere of the earth, make 24,000 miles169, which is the circumference measurement, including the water and the land of the globe. And the alkoterra,170 i.e., the diameter of the earth's globe, is eight thousand miles171, and, accordingly, it is four thousand miles to the centre of the earth, and three thousand to every thousand of these is the extent that should be therein i.e., in the circumference172.