7 8 MATHEMATICAL SCIENCES. 



so much importance, practical science was generally made subordinate to 

 speculative science. Thus the theory of the calculus, the formulae of 

 algebra, the projections of lines through space, the problems of triangulation, 

 were by preference applied to astronomical observations, so that the tran- 

 scendental mathematics were always inseparable from astronomy. 



It was as follows that Claudius Ptolemaous, a Greek or Egyptian astro- 

 nomer, constituted the mundane system in a " Cosmography " written in 

 Greek, which became one of the bases of mathematical and astronomical 

 science in the Middle Ages : " The world is divided into two vast regions ; 

 the one ethereal, the other elementary. The ethereal region begins with the 

 first mover, which accomplishes its journey from east to west in twenty-four 

 hours ; ten skies participate in this motion, and their totality comprises the 

 double crystalline heaven, the firmament, and the seven planets." According 

 to Ptolemaeus, the double crystalline heaven was placed between the first 

 mover and the firmament. The elementary region, comprising the four 

 elements of fire, air, water, and earth, reigned beneath the cavity of the sky, 

 and was subject to the influence of the moon. The terrestrial globe, 

 composed of earth and water, existed motionless in the centre of the world, 

 and was surrounded by the element of air, in which was mingled that of fire. 



This system was not, however, exclusively adopted by all the philosophers. 

 Some of them accorded their preference to the system of Aristarchus of 

 Samos, who did not place the earth in the centre of the world, and who 

 attributed to it a rotary motion around the sun, which was suspended motion- 

 less amidst the planets and the planetary circles. According to Aristarchus 

 of Samos, Mercury, the planet which is nearest the sun, completed his motion 

 around it in three months, whilst Venus took seven months and a half to 

 execute hers. The earth, apart from its motion round the sun in the space 

 of a year, effected a second motion, revolving upon its own axis, in the space 

 of twenty-four hours, thus causing the succession of day and night. The 

 monthly motion of the moon around the earth was accomplished in about 

 twenty-seven days. The fourth planet, Mars, took two years to accomplish 

 his revolution round the sun*; Jupiter, much farther distant, took twelve 

 years, and Saturn thirty. 



The system of Ptolemy eventually triumphed over that of Aristarchus, 

 and at the close of the fifth century the great Boethius (Fig. 57), the favourite 

 minister of Theodoric the Great, who loved and patronised literature and 



