I will here introduce an explanation which is necessary for the understanding of our view on the present subject. There is a difference among ancient astronomers whether the spheres of Mercury and Venus are above or below the sun, because no proof can be given for the position of these two spheres. At first it was generally assumed that they were above the sun—note this well; later on Ptolemy maintained that they were below the sun; because he believed that in this manner the whole arrangement of the spheres would be most reasonable; the sun would be in the middle, having three stars below and three above itself. More recently some Andalusian scholars concluded, from certain principles laid down by Ptolemy, that Venus and Mercury were above the sun. Ibn Aflaḥ of Seville, with whose son I was acquainted, has written a famous book on the subject; also the excellent philosopher Abu-Bekr ibn-Alẓaig, one of whose pupils was my fellow-student, has treated of this subject and offered certain proofs—which we have copied—of the improbability of Venus and Mercury being above the sun. The proofs given by Abu-Bekr show only the improbability, not the impossibility. In short, whether it be so or not, the ancients placed Venus and Mercury above the sun, and had, therefore, the following five spheres: that of the moon, which is undoubtedly the nearest to us; that of the sun, which is, of course, above the former; then that of the five planets, the sphere of the fixed stars, and the outermost sphere, which does not contain any star. Consequently there are four spheres containing figures, i.e., stars, which were called figures by the ancients in their well-known works—viz., the spheres of the fixed stars, of the five planets, of the sun, and of the moon; above these there is one sphere which is empty, without any star. This number is for me of great importance in respect to an idea which none of the philosophers clearly stated, though I was led to it by various utterances of the philosophers and of our Sages. I will now state the idea and expound it. CHAPTER X