218 PHYSICAL SCIENCE IN THE MIDDLE AGES. 



concerning the particles of the four elements. He gave to each kind 

 of particle one of the five regular solids, about which the geometrical 

 speculations of himself and his pupils had been employed. The parti- 

 cles of fire were pyramids, because they are sharp, and tend upwards ; 

 those of earth are cubes, because they are stable, and fill space ; the 

 particles of air are octahedral, as most nearly resembling those of fire ; 

 those of water are the icositetrahedron, as most nearly spherical. The 

 dodecahedron is the figure of the element of the heavens, and shows 

 its influence in other things, as in the twelve signs of ,he zodiac. In 

 such examples we see how loosely space and number are combined or 

 confounded by these mystical visionaries. 



These numerical dreams of ancient philosophers have been imitated 

 by modern writers ; for instance, by Peter Bungo and Kircher, who 

 have written De Mysteriis Numerorum. Bungo treats of the mystical 

 properties of each of the numbers in order, at great length. And such 

 speculations have influenced astronomical theories. In the first edition 

 of the Alphonsine Tables, 13 the precession was represented by making 

 the first point of Aries move, in a period of 7000 years, through a 

 circle of which the radius was 18 degrees, while the circle moved 

 round the ecliptic in 49,000 years; and these numbers, 7000 and 

 49,000, were chosen probably by Jewish calculators, or with reference 

 to Jewish Sabbatarian notions. 



3. Astrology. — Of all the forms which mysticism assumed, none was 

 cultivated more assiduously than astrology. Although this art pre- 

 vailed most universally and powerfully during the stationary period, 

 its existence, even as a detailed technical system, goes back to a very 

 early age. It probably had its origin in the East ; it is universally 

 ascribed to the Babylonians and Chaldeans ; the name Chaldean was, 

 at Rome, synonymous with mathematicus, or astrologer ; and we read 

 repeatedly that this class of persons were expelled from Italy by a de- 

 cree of the senate, both during the times of the republic and of the em- 

 pire. 14 The recurrence of this act of legislation shows that it was not 

 effectual : " It is a class of men," says Tacitus, " which, in our city, 

 will always be prohibited, and will always exist." In Greece, it does 

 not appear that the state showed any hostility to the professors of this 

 art. They undertook, it would seem, then, as at a later period, to de- 

 termine the course of a man's character and life from the configuration 

 of the stars at the moment of his birth. We do not possess any of the 



»3 Montucla, i. 511. " Tacit. Ann.ii. 32. xii. 52. Hist. I. 22, II. 62. 



