Now that Leonardo had a steady income and the relief from meeting painting commissions by fixed dates, he was free to explore his other favorite avenues of knowledge. It seemed that his ever-active mind could never stop roaming over the whole field of scientific knowledge. He continued with his early interests—the nature and movement of air, astronomy and geometry. He was also still concerned with movement and weight, for he set down in his notes, “The thing which moves will be so much the more difficult to stop as it is of greater weight.” This is a hint at a principle formulated by Isaac Newton almost two hundred years later in his First Law of Motion—the law concerning inertia. For example, the motion of an arrow shot into the air maintains itself in flight so long as the influence of the initial force is maintained in it. [Illustration: _Da Vinci’s cone-headed mitre valve for use in a hydraulic pump._] On a note dated April 28, 1509 he wrote, “Having for a long time sought to square the angle of two curved sides ... I have solved the proposition at ten o’clock on the evening of Sunday.” As always, Leonardo was deeply involved in the study of mathematics. Too deep perhaps to recognize the new rumblings of war. Louis XII, still pursuing his campaign in northern Italy, had again arrived in Milan amid the salutes of the French artillery. Following his personal banner of a gold porcupine on a white field, he had come back prepared to do battle with the Venetians whose power, as it diminished in the east, was extending westward into Italy. Alarmed at this Venetian expansion, the French King had allied himself with Pope Julius II and the powers of Europe to form the League of Cambrai to push back this threat. Charles d’Amboise, the French Viceroy, had already taken to the field and at the castle of Cassano, overlooking the Adda river near Milan, he awaited the arrival of his king. By the end of May, Leonardo was in the saddle once more. Surrounded by the best knights of France and the nobles of Milan, he personally accompanied the French King as military engineer to the meeting with the Viceroy of Milan at Cassano. During the next three months, through the battles and defeat of the Venetians at Aquadello where sixteen thousand dead were left on the field, and the siege of Caravaggio and the capture of Peschiera, Leonardo served as military consultant and map maker. More than ever his eye was attracted to the possibilities of utilizing the many rivers they crossed both for warfare and commerce. He envisioned making the Adda river navigable from Milan to Lake Como. During this time, he devised not only a revolving bridge but even one of two layers in a single span—the upper level for pedestrians and the lower one for vehicles.