Leonardo da Vinci, Pathfinder of Science

by Henry S. Gillette

Now, in 1498, the painting was nearing completion and the only faces still left blank were those of Christ and Judas. Leonardo had drawn hundreds of sketches, taking his models wherever he found them—once he sketched a man just for his hands. Now that his name had become well known he always had an audience while he worked. His pupils, the monks, visiting nobility, church officials, and frequently Ludovico himself watched him as he painted the “Last Supper.”

But Leonardo, as usual, was involved in many different tasks. He was supervising the installation of a hydraulic pump over seventy feet high beside a stream which would use the power of the stream itself to pump water into the castle. Mindful, too, of the uncertainty of court patronage, he was designing commercial machinery, hoping thereby to secure an income outside the court. Among the most notable of these were an olive press, an automatic file-cutter, a hydraulic saw, and a needle sharpener. This latter was a forerunner of modern sharpeners with their mass-production methods. With it, Leonardo dreamt of sharpening four hundred needles at a time, or forty thousand an hour so that in twelve hours one person could sharpen four hundred and eighty thousand needles! The needles were arranged successively on a moving belt of leather and brought against a rotating grindstone. This grindstone was set in such a way that the needles were sharpened into curvilinear points rather than the usual triangular points.

In his travels to Vigevano and other parts of the countryside around Milan, Leonardo had studied flour mills. He had talked with the workmen, asked the prices of grain, and noted the time that it took to do the milling. Then he made calculations on ways to cut down the time, and, in fact, redesigned the entire mill. He mounted twelve cylindrical millstones in rows of four on one side of a canal and another twelve on the other side. In the canal were hydraulic wheels or paddlewheels. Each wheel was attached to a rod that ran underneath four millstones. Geared to the one rod were four grinding levers to the stones above. In this way it was possible to have twenty-four millstones operating at the same time.

But most fascinating to Leonardo now was the construction of his flying machine. His first models involved the principle of an air-screw mounted on a platform on which a man stood. But where would the necessary power come from to lift his machine from the ground? At first he thought of operating his air-screw by means of a steel spring coiled around a drum, but this he apparently abandoned. Later, however, Leonardo did design another model on this principle which has been called the forerunner of the modern helicopter. It was to be operated by four men standing on a platform. Each man would hold a bar which wound a spring-driven mechanism, much as in a modern clockworks. The air-screw was a broad blade spiraling about a vertical shaft—the ancestor of the modern propeller.

The model that Leonardo wanted to construct now, however, was of a different principle. Instead of an air-screw he substituted a pair of wings fashioned after those of the birds. There was still a platform on which the flyer stood and two springs were still the essential “motor” to raise and lower the wings. But as Leonardo worked on his apparatus he began to realize that it would be too much at the mercy of a sudden gust of wind or a violent updraft. It was necessary to return to his study of the air and its currents.

With all of this activity in mechanical devices Leonardo had reawakened his interest in mathematics. During this time he was introduced to a man at Ludovico’s court who became his friend and collaborator. He was a Franciscan monk named Fra Luca Pacioli who had been appointed a professor of mathematics by Ludovico. He, too, came from Florence, and in 1496, when he met Leonardo, he was forty-six years old and the author of Summa di Arithmetica, the first printed scientific work of his time. Pacioli was now at work on a book of geometry to be entitled De Divina Proportione and he enlisted Leonardo’s aid in drawing the plates for his book. As Leonardo had already made a study of human proportions, the association with Pacioli was of benefit to them both. Among Leonardo’s best known drawings of human proportion is a beautifully rendered figure-study of a standing man with his arms at his sides and then outstretched, his legs together and then apart, inscribed within a square and a circle. It was made to illustrate a passage from Vitruvius on the proportions of a human figure and demonstrated, among other things, “the span of a man’s outstretched arms is equal to his height.”

Moreover, Leonardo found with Pacioli confirmation of many of his own observations and experiments and in turn Pacioli gave to Leonardo a confidence in his own methods. Pacioli also helped Leonardo with his arithmetic, a subject that Leonardo had neglected in his impatience to study geometry. The association also helped to free him further from the cobwebs of medieval beliefs. For Pacioli, the friendship with Leonardo was a revelation. Although Pacioli was a learned mathematician, Leonardo demonstrated to him that the application of his science encompassed all sciences—even art—for Leonardo later wrote, “Let no one read me who is not a mathematician....”

Legend relates that Leonardo became so absorbed in his studies that the prior of the monastery complained to Ludovico that the “Last Supper,” although nearly completed, still lacked the faces of Christ and Judas. Ludovico summoned Leonardo to court and laid the complaint before him. Leonardo, however, was quick to reply.

“The good prior is an esteemed man, your Grace, but he is a monk and not a painter. Little does he know that I spend at least two hours a day on my painting.”

“But Master, he says he never sees you there, so how do you explain these two hours a day?”