In his preoccupation with geometry, Leonardo had apparently done little about the commission which the Servite monks had given him. He finally yielded to their complaints, however, and commenced to draw the preliminary study for the subject, which was “St. Anne with the Virgin and Child.” Again his knowledge of geometry is most apparent in the finely constructed composition, every gesture of which is as plotted as a geometric exercise. In April of 1501, the drawing was finished; it caused an immediate sensation throughout Florence. For two days the public was allowed to pass in front of it.

But now a change was taking place in Leonardo. He was no longer content with simply painting. His highly original researches for pictures had slowly grown to the point where the research was more important than painting. In a sense the scientist had taken the brush from the artist. In two letters from Isabella d’Este’s emissary in Florence we learn, “He is entirely wrapped up in geometry and has no patience for painting.” This excerpt from a letter dated April 8, 1501, was followed six days later by another which said in part, “In brief, his mathematical experiments have made painting so distasteful to him that he cannot even bear to take up a brush.”

A few months after the completion of the St. Anne drawing, Leonardo received a letter signed by Cesare Borgia, Duke of Valentinois. Leonardo frowned and thought back to his last days in Milan. When King Louis XII of France had entered the city, he had summoned the painter of the “Last Supper” to an audience. The king had been generous in his praise and had tried to persuade Leonardo to remain. At that same audience had also been Cesare Borgia, an ally of the French. Leonardo remembered the man now—the dark hair and eyes, the black, arched eyebrows, and the face marked by some old disease. He was a powerful-chested, thin-hipped man who had originally been made a cardinal by his father, Pope Alexander VI. But the attractions of secular power soon persuaded him to abandon this title. With the enthusiastic help of his father, Borgia had fought, murdered, and deceived his way to a formidable position of authority in these last years. Leonardo, in the seclusion of the monastery, had lately heard that Borgia’s army had even been at the gates of Florence.

The letter addressed to Leonardo was an offer to assume the post of Architect and Military Engineer to His Excellency, Cesare Borgia. He thought of Ludovico Sforza—defeated and captured at the battle of Novara just a year ago as he attempted to regain his dukedom. Now the duke was a prisoner at Loches in Touraine; Leonardo had written of him, “The duke lost his State, his personal possessions and his liberty, and none of his enterprises have been completed.” And Leonardo also thought of his equestrian monument still standing in the castle being used for target practice by the French archers. Like the duke, nothing of his own had been completed either. Perhaps this Borgia offer was an opportunity. Leonardo decided to accept it.

In May of 1502, after having presented himself to Cesare Borgia in Rome, Leonardo began his hectic travels through Tuscany and Umbria. He was to inspect the fortresses and cities of Cesare’s new conquests there, and to make whatever recommendations he felt necessary for their improvements. Arriving in Piombino, he at once set down a project for draining the marshes and reclaiming the land. Also, while he was here, he spent hours by the sea watching the waves curl in from the Adriatic and studying the crash of water over the beaches. Moving on to Arrezzo, he drew up the first in a series of remarkable maps for the army of Vitellozzo which, with the backing of Cesare Borgia, was marching against Florence. These maps are bird’s-eye views of Tuscany and Umbria, and somewhat resemble modern aerial photographs. Drawn from Leonardo’s own observations, the green mountains stand, according to their height, in relief, with the roads winding over them and down through the valleys. The streams and their tributaries are in blue and even the villages and cities are drawn with great exactitude. Indeed Leonardo had learned his lessons from old Toscanelli well, and he was one of the first to bring the art of cartography to such perfection.

In July and August Leonardo was in Urbino and Pesaro, and by the 8th of August he had reached Rimini. Here he strengthened the fortifications and then rode quickly on to Cesena. Between Cesena, capital of the Romagna, and Porto Cesanatico, he spent from the middle of August to September planning a canal between the two, redesigning government buildings, and drawing up a new quarter to be built for the city of Cesena. At this time he constructed an instrument for telling him the speed of water currents in a stream. It told him whether the flow was swifter at the surface or at the bottom or on one side or the other of the stream’s bed.

In the meantime, Florence, alarmed at the growing power of Cesare Borgia, appealed to Charles d’Amboise, Regent of Milan for France, to come to her aid. Charles responded in the absence of the French King and helped to protect Florence. The enemies of Cesare took advantage of this to form an alliance, and soon Cesare was being forced back from his newly won possessions. Cesare himself then hastened to Milan, and there he suddenly came face to face again with Louis, the King of France, who was on his way to Naples. Borgia, who could exert great charm and influence when he wished, persuaded the king that, all rumors to the contrary, he, Cesare, was fighting the enemies of France. Again he won over the French, which greatly strengthened his position. Then, from Pavia, he issued a decree placing every facility possible at Leonardo’s disposal. In addition, he instructed all officials to help Leonardo in every matter, referring to him as “our highly esteemed court architect.”

While Leonardo was in Porto Cesanatico, a delegation from Bayzid II, Sultan of Turkey, paid a visit to Cesare Borgia. Among other things the delegation was looking for an engineer to build a bridge between Constantinople and Pera to replace a temporary wooden structure. Leonardo designed for them a single-arched bridge with double ramps at either end (looking very much like a present-day “thruway” entrance). He provided that it should be approximately twelve hundred feet long, eighty feet wide, and one hundred and forty feet above the water.

Da Vinci’s proposed bridge from Constantinople (Istanbul) to Pera. Looking very much like a modern “thruway” entrance, it was to have double ramps on both sides.