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Rh obtained the support of his friend the Marquis del Monte, and through his aid and that of his friends succeeded in securing the post against the rivalry of the man who had defeated him for the Bologna professorship. He was appointed for four years certain at a salary three times as great as he had received at Pisa, roughly £40 a year. Besides this increase, the greater number of students at Padua meant a much larger income from pupils. For their benefit he wrote a great number of treatises (some of which have been lost, as they were for a long time only in manuscript), treating of such diverse subjects as fortifications, the geometry of the sphere, and mechanics, that is to say, the lever, the pulley, and the screw, including that of Archimedes for raising water. In this was the first development of the principle that what is gained in power is lost in speed, the foundation of equilibrium conditions. In his first summer at Padua Galileo and two friends went to sleep in a cool or perhaps poisonous draught from a cavern, with fatal effects soon afterwards, except in Galileo's case, though his previously strong constitution did not save him from acute chronic disorder.

Some three years later he invented the geometrical and military compass, known to us as the sector, for mechanically solving a great many problems, and this with other similar inventions met with such practical success that he started a workshop in his house and employed a staff of mechanics to make them under his personal supervision. Some of the ideas were plagiarised by Simon Mayer (or Marius) under cover of another man's name, but Galileo had no difficulty in proving priority.

The four years of the appointment had stretched to six years, as was contemplated by the conditions, and Galileo carried on for a seventh year without raising any