The first steps towards this end were taken when Galileo went to Florence in the Easter recess of 1610 to show his telescopic discoveries to Cosmo II., especially the stars which bore the name of the reigning house. We afterwards find Galileo entering eagerly into the negotiations which followed. In the letter to Vinta before mentioned, of May 7th, 1610, he presses for a decision, for, he says, observing that day after day goes by, he was determined to set a definite purpose before him in the ordering of the life that may be left to him, and to devote all his powers to perfect the fruits of his previous efforts and studies, from which he might look for some fame. He then mentions the conditions on which he at present serves the republic, perhaps in order that they might be guided by it at Florence; but what he lays most stress on is that it is of the utmost moment to him that leisure should be assured him for the completion of his labours, by his being freed from the obligation to give public lectures; but it will always confer on him the highest honour to give lectures to his sovereign, to whom also he will dedicate all his writings. The same letter is also of the highest interest as giving us an insight into the scientific projects he was then cherishing. He communicates to the Tuscan secretary of state the works the completion of which lies so near his heart. He says:— “The works which I have to finish are chiefly two books _de systemate, seu constitutione universi_, a vast project full of philosophy, astronomy, and geometry; three books _de motu locali_, an entirely new science, for no other inquirer, ancient or modern, has discovered any of the wonderful phenomena which I show to be present in natural and induced motion; I may therefore with perfect justice call it a new science discovered by me from its first principles; three books on mechanics, two relating to the demonstration of the principles and fundamental propositions, one containing the problems; although others have treated of the same subject, what has been hitherto written upon it is neither as to extent nor in other respects a fourth part of what I am writing. I have also various smaller works in view on matters connected with nature, such as _de sono et voce_, _de visu et coloribus_, _de maris æstu_, _de compositione continui_, _de animalium motibus_, and others. I am also thinking of writing some books for the soldier, not only to cultivate his mind, but to teach him by select instruction all those things connected with mathematics which it would be an advantage to him to know, as, for instance, castrametation, military tactics, fortification, sieges, surveying, estimate of distances, artillery, the use of various instruments, etc.”[59]