Among Leonardo’s other maritime devices were designs for boats that could dredge canals, harbors, and lagoons. What was the result of all these plans? We do not know. Whether any one of them was used against the Turks is a mystery.

At any rate, Leonardo and Pacioli left Venice that same spring and arrived in Florence in April of 1500. One of the purposes of Leonardo’s journey was to visit his father who was now living on Via Ghibellina with his fourth wife. Leonardo was now forty-eight. Still tall and straight with the strength of his youth, his face prematurely aged and his hair thinning back from his high forehead, Leonardo was more than ever an outstanding looking man. He still scorned fashionable clothes and dressed according to his own comfort which made him even more noticeable among the crowd. His deep-set eyes with their direct and penetrating glance, framed by his full, reddish beard, never missed a thing, although he now wore spectacles at his work.

Now that he was back in Florence, Leonardo needed lodgings and a job. He had banked his small savings, and he did not want to touch that. His father’s house with the five children of his present wife plus the sons from his previous marriages was too full to accommodate Leonardo. Moreover, the relationship between Piero and Leonardo was polite but distant, as Piero preferred the children of his later marriages.

Luckily, the place to live and the commission Leonardo needed presented themselves at the same time. The Church of the Annunciation of the Servite Order of Monks needed an altarpiece, and, as Leonardo’s fame was great, they offered him and his apprentice quarters in the monastery. Here, in the solitude of a monastic cell, Leonardo was able to return to his own researches. His long association with Fra Luca Pacioli continued as they worked together on Pacioli’s edition of Euclid’s Elements. At the same time, with his absorption in geometry, Leonardo commenced his studies of the transformation of solids; that is, changing the shape of something to another shape without diminishing or increasing its substance.

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.

In his travels through the countryside, Leonardo could not help but notice how primitive the mills were. Feeling how strongly the wind blew in from the sea, he designed a windmill with a roof that turned with the sails. For the mechanism inside he devised a band brake—a semicircle of wood into which the large cogwheel of the mill was forced. This mill resembles the “Dutch” mills of the Netherlands and was among the first of its type to be brought into existence.

In the fall Leonardo was at Imola. There he created another of his beautifully rendered maps. He drew this with the help of a magnetic compass of his own invention. It consisted of a board with an arc on it and a compass needle, and was probably the first magnetic needle on a horizontal axis. This time the map was of the city itself, the walls, the castle and the principal buildings all touched with color and the river winding through the fields. Drawn in the shape of a circle, it resembles a view through a telescope from directly above. In Imola, too, he met NiccolÒ Machiavelli, the famous historian and political scientist, who was an emissary from the Signoria, the Council which now governed Florence. These two men became friends and, later, collaborators in Leonardo’s scheme to make the Arno river navigable to the sea.

At this time Cesare Borgia, having achieved great success in his military campaigns and confident of his conquests, decided to return to Rome. With the disbanding of Borgia’s headquarters at Imola, Leonardo’s duties were finished. Together with his new friend NiccolÒ Machiavelli and two other Florentines, he left Imola and the service of Cesare Borgia to return to Florence.

In January of 1503, a mathematician named Giovanni Battista Danti attempted a flight in a machine that he had designed. This flight was part of the entertainment at a wedding reception in Perugia. Danti climbed into his apparatus on top of the tower of St. Mary of the Virgin. It was pushed off into the air, hovered a few seconds, then began slowly drifting toward the ground. But suddenly, one of its wings hit a building projection and it crashed. Danti was carried away with a broken leg.

The news of the event traveled quickly to Florence.