Coming now to the fixed stars, their number, and brightness, Alfraganus does not copy Ptolemy’s great catalogue, but informs us that learned men (“sapientes”) did number all the fixed stars as far south as they could see in the 3rd climate, and divided them according to magnitude into six classes. “To the first class they assigned the bright and shining stars such as Canis (Sirius) and Procyon, Vultur Cadens (Vega) and Cor Leonis (Regulus). Stars a little less bright they called second magnitude: such are Alfarcatein and Benet Naax,” Arab constellations which the Latin version describes as the two bright stars of Ursa Minor, and those brilliant ones in the tail of Ursa Major. Thus they proceeded with the other magnitudes, the smallest measured being of the sixth magnitude. The number of stars in each class is given, and the total of 1022;[66] then a list of the 15 first-magnitude stars, which are the same as Ptolemy’s (See p. 155). This is followed by a list of the Arab “Mansions of the moon.” ------------------------------------------------------------------------ [66] The Catalogue of Hipparchus is said to have contained 1080 stars, but Ptolemy’s has only 1022. ------------------------------------------------------------------------ [Illustration: Fig. 36. Method (erroneous) of estimating planetary distances, described by Alfraganus. The distance _E A_ being known, and _E p_ being assumed equal to it, the distance _E a_ can be calculated from the known ratio _E a_: _p a_.] So far (with the exception of the mansions of the moon) the Arab writer has followed the Greek, but we have now reached a point where he diverges. Ptolemy, he says, only tells us the distances and sizes of the sun and moon, and said nothing about the other heavenly bodies; but if we suppose the greatest distance of the moon to be the same as the least distance of Mercury, and from this calculate his greatest distance (for the ratio is known), and if we proceed in the same way with Mercury and Venus, we shall find that the greatest distance of Venus equals the least distance of the sun as given by Ptolemy. Ptolemy’s least distance for the sun, which was totally wrong, was 1160 Earth-radii: the greatest distance of Venus, calculated in this way from Ptolemy’s figures, was 1150. Alfraganus takes this unlucky coincidence as an indication that there is only just sufficient space between each sphere and the next to allow their respective epicycles to pass one another, and upon this entirely erroneous assumption he proceeds to lay down the distances of each planet from the earth, and finally of the stars, which are all supposed to be at the same distance, equal to the greatest distance of Saturn. Who first suggested this method of estimating distances we do not know: the first mention of it occurs in Europe in the fifth century A.D. The following table shows the distances obtained in this way:— GREATEST DISTANCE.