The arithmetical textbook of Diophantus, which is extant, is remarkable as being the first to contain a complete exposition of algebra and the use of algebraic symbols and methods. Euclid solved quadratic equations geometrically and Hero solved them algebraically, although without using symbols. But in Diophantus's arithmetic quadratics are solved by the use of algebraic symbols. After several centuries, when the Euclidean geometry was in the ascendant, and many problems which were suited to arithmetical and algebraic methods of analysis were solved by geometrical and trigonometrical means, Diophantus succeeded in renewing interest in arithmetic and mathematics generally. Political changes and other intellectual interests soon after the time of Diophantus turned men's thoughts in other directions and no great scientists were afterward developed by the Greeks. While the physicists were making their discoveries, medical men were studying anatomy, biology, and materia medica. Medical science in the time of Diophantus had a status, with a theory and practice, closely resembling those of to-day. Hippocrates of Cos (460 B. C.), was the greatest leader of Greek medical science. He cast superstition aside and based his researches and practice upon the same principles of inductive philosophy that had proved so valuable in other sciences. He established hospitals for the nursing of the sick, and had attendants note the symptoms and the histories of the cases. In this way a number of casebooks were made. He wrote a work on Public Health. His operations in trepanning were more heroic than would be undertaken by good surgeons to-day. These are described in his book on Injuries of the Head. Many of his works are extant and furnish very interesting and valuable pictures of the state of medical science in Greece. During the several centuries in which the Greeks placed science and all the leading departments of knowledge upon firm bases, stripped of the sentimental and traditional trappings which had come down from remote times, changes of a political nature were causing the immigration of foreign peoples to Greece. The importance of preserving racial purity was not recognized. The result was that the original Greeks, who were of the long-headed type, were forced to give way to the hordes of inferior peoples coming in from Asia. These new, round-headed people were not original thinkers, and were unable to advance science and the arts as the Greeks had done. They were, to a large extent, even unable to appreciate the wonderful treasures of knowledge bestowed upon them by the cultured people they had displaced. The Egyptians and Babylonians advanced knowledge for practical purposes and when these were served they showed no desire to explore further. But the analytical mind of the Greek called for knowledge of basic laws and first principles. CHAPTER VII THE ROMAN AND MIDDLE AGES