THE ROMAN WORLD 147 



because after Galen we find no great name in anatomy until we 

 come to Vesalius, some 1400 years later. 



LATE ROMAN MATHEMATICAL SCIENCE. - - Two periods may be 

 distinguished in ancient mathematical science, the first beginning 

 with Pythagoras and ending with Hero. To these four to five 

 centuries belong all the original works in geometry, astronomy, 

 mechanics, and music. The period closes with the extension of 

 the pax Romana over the Orient. The second extends to the 

 sixth century, when Hellenism is proscribed by the new religion, 

 the genius of invention is extinct, and men merely study the older 

 works, commenting and coordinating. Astronomy gradually 

 reverts to astrology, the mathematical geography well begun 

 under Eratosthenes and Ptolemy becomes superficial and descrip- 

 tive, with Strabo and even with Posidonius. 



Whatever the eminence of the Romans in the practical arts of 

 war, politics and engineering, their interest in abstract science 

 was almost nil. On the other hand, commercial arithmetic, 

 which had been studiously neglected by Greek mathematicians, 

 now had the place of honor. The Roman numerals, clumsy as 

 they seem to us, were superior to the Greek, and a useful sy3tem 

 of finger-reckoning was developed, supplementing the skilful use 

 of the abacus. If no abacus was at hand, the corresponding lines 

 were quickly traced on sand or dust, small stones or calculi - 

 whence our words calculation and calculus, - - serving as counters 

 A complete Roman abacus - - of which no example has come down 

 to us seems to have had eight long and eight short grooves. Of 

 the former, one held five counters or buttons, each of the others 

 four, each of the short grooves one, these last counting as five 

 units each. The grooves with six counters served for computa- 

 tions with fractions. Geometry - - but of Hero rather than of 

 Euclid was valued for its utility in surveying and architecture. 

 Preparation for the engineering art included mathematics, optics, 

 astronomy, history, and law. There were also teachers of me- 

 chanics and architecture. (See Vitruvius, above.) 



CAPELLA. Early in the fifth century Martianus Capella wrote 

 a compendium of grammar, dialectics, rhetoric, geometry, arith- 



