Zenith, on the other side the moon is 70 degrees from the Zenith; if we add together these two angles, we shall see that the moon is 108 degrees from the North Pole, as seen at Greenwich, G. This 108 degrees is the measure of the angle PGM, GP being supposed to be directed to the celestial North Pole. At the same time, observations are going on at the Observatory C, at the Cape of Good Hope, where they cannot see the North Pole, but they can see the South Pole, and therefore they must refer their observations there to the South Pole; suppose that there they find the angular distance of the moon from the South Pole to be 7312 degrees, this is the measure of the angle P'CM, CP' being supposed to be directed to the celestial South Pole, and therefore parallel to GP.
Now, we have got these two measures from which we see, that by the combinations of the Zenith distances at Greenwich, the moon is seen at 108 degrees from the North Pole; and by a similar combination of the Zenith distances at the Cape of Good Hope, the moon is seen 7312 degrees from the South Pole. If we were observing a star S at an immense distance, we should get this relation between the two angular measures; that the sum of the two angular measures, one from the South Pole and the other from the North Pole, must be 180 degrees; inasmuch as the two directions GP and CP' are exactly opposite, and the two directions GS and CS, on account of the immense distance of a star, are exactly parallel; and therefore, in turning a line first from the position GP to GS, and then from the position GS or CS to CP', we have turned it exactly half round. But the thing which we have found out with regard to the moon is this: that the sum of the two angular measures is
