problems of flight. He kept working out the proportions of wing span to
the weight of the load. Indeed, he had already started designs for a
flying machine. He had chosen a room which was the highest in one of the
towers of the castle and which had access to a roof. Leonardo’s plans
for a flying machine were a secret, and, with the exception of an
assistant, no one knew about them. He made sure that he could not be
seen by the workmen on the dome of the cathedral and proceeded to block
off his room with beams which he planned to use as supports for his
model.
He had thought at first that any attempted flight should take place over
water in order to cushion a possible crash—but as his plans progressed
he designed a parachute. It was a pyramid-shaped “tent of linen”
twenty-four feet broad and twenty-four feet high, and it is believed to
have been successfully tried out from a tower especially constructed for
that purpose.
Since Leonardo was no longer working for Ludovico, he lived more simply
than ever. He made regular lists of his expenses down to the last penny.
His habits were frugal although he always kept himself neat. His meals
were spare; he drank a little wine at meals and never ate meat. To his
pupils and apprentices, he recommended regular habits such as not
sleeping during midday, eating only when hungry and chewing well,
exercising moderately, and sleeping well covered.
Yet, even though Leonardo lived cheaply, he was now greatly in need of
money. Swallowing his pride, he wrote to Ludovico, placing himself at
the duke’s service once again. His absence from court, he said, had been
necessary so that he could earn a living. In this and other ways,
Leonardo attempted to heal the break between them.
It turned out that Ludovico was glad to have Leonardo back. Perhaps
mindful of the fame that the model of the equestrian monument had
brought the house of Sforza, he now commissioned Leonardo to paint a
picture. The Dominican monastery of Santa Maria delle Grazie was the
nearest church to the Sforza castle and a favorite retreat of Ludovico.
Here he used to walk in the quiet garden while the white-robed monks
silently went about their chores. In gratitude for the peace he found
there, Ludovico had had the refectory rebuilt and on the back wall, a
crucifixion scene had been painted by Montorfano, a Lombard. But the
front wall was given to Leonardo. On this Leonardo decided to paint a
picture of the Last Supper—the painting that has since become one of the
best known in the world.
8
_The French_
The noonday sun was baking the deserted streets of Milan as Leonardo
hurried across the drawbridge of the castle. The guard dozing in the
entrance arch started to his feet, but when he saw who it was he sat
down again, muttering about a madman. Taking the shortest way, Leonardo
arrived at the monastery gate and pulled on the bellcord. When the gate
opened Leonardo brushed past the startled monk and made directly for the
scaffolding in the refectory. He looked at his almost completed painting
for a moment, took a brush and mixed a color swiftly on the large
palette. Then he climbed the scaffolding and very quickly applied three
or four strokes. With this he sighed and smiled. Then, just as abruptly,
he put away his brushes and, without a backward glance, he left, making
his way back to the castle in the hot sun.
For three years, Leonardo had been working this way on the “Last
Supper.”
Sometimes he would work from dawn to dusk forgetting to eat; other
times, he would stay away for days and then run back just to add a
touch. Once he arrived and, with his arms folded across his chest, he
stood in front of it for two hours just studying what he had done.
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?”
“Excellency, the figure of Judas must be of incomparable evil. Every day
I search for this face in the criminal quarter, and every day I fail to
find the evil that I am looking for. If I cannot find this man, however,
I can use the head of the prior—it would do admirably, but I have
hesitated for fear of hurting his feelings.”
Ludovico slapped his knees and roared with laughter. There were no more
complaints.
Finally, in 1498, the scaffolding was removed from the painting and
Leonardo’s masterpiece was revealed. The twelve apostles grouped at the
table are shown each responding in his own way to the words of Christ,
“One of you shall betray me.” Again hundreds flocked to see this latest
marvel of Leonardo’s. Its striking influence was felt by generations of
painters. Even now, more than four hundred and fifty years later, the
world still comes to stand before the genius of Leonardo da Vinci in the
refectory of Santa Maria delle Grazie.
The clouds of war were gathering again over Italy. In April of 1498,
Charles VIII of France died and his successor was Louis of Orleans, who
became Louis XII. The new King of France laid claim to the Dukedom of
Milan, and Ludovico again tried to form an alliance against him. But the
years of juggling enemy against enemy and friend against friend were now
coming to an end. No one trusted Il Moro any more, and suddenly he
realized that he was to be alone in this new fight. After nearly twenty
years of power sustained by powerful alliances, Ludovico was forced to
turn to his own people of Lombardy. Frantically he tried to correct the
injustices of years. The people had been cruelly taxed to support the
extravagances of the Sforza court, and, in addition, they had been badly
treated by petty government officials. Ludovico now sought to repay the
past miseries of his people and to rally them to his support. In such a
spirit he remembered his court painter, Leonardo da Vinci, and gave him
a vineyard and considerable piece of land not far from the Porta
Vercellina.
Now, for the first time in his life, Leonardo knew financial security.
With the income from the vineyard, and in the peace of his estate, he
was left free to follow his own researches. He took no notice that his
“peace” was surrounded by the threat of war. Indeed, he remained aloof
from politics and court intrigues as much as was possible for a man
living in the midst of such chaotic times.
Leonardo now had the opportunity to follow up an early interest—the
study of plants. He made many beautiful drawings; no plant was too small
to catch his eye. His notes on botany began to grow. With his genius for
observation and analysis of nature, Leonardo made some extraordinary
discoveries of botanical laws entirely unknown before his time. He wrote
of the phenomenon of _heliotropism_, or the movement of plants toward or
away from the sunlight. In addition, he described the phenomenon known
as _geotropism_, or the growth of plants according to gravitational law,
as for example, roots growing downward and shoots growing upward. He
also defined the laws of phyllotaxis, which describe the system or order
of leaf arrangement on a plant’s stem. That is, leaves are arranged
spirally around a stem so that the third leaf above grows out over the
third leaf below on one type of plant; or, on another type, the two
third leaves are over the two third leaves below. The same natural laws
apply to the branches of plants as well; they occur so that every leaf
and branch can receive sufficient air and light. Amazingly enough, these
laws, which Leonardo described so completely, were not rediscovered
until almost two centuries later!
Leonardo went even further in his botanical studies. He experimented
with gourds, planting them in various aqueous solutions; this
anticipated modern methods of growing plants in chemicals. He also
tested the actions of arsenic and mercury poisons in plants. He
reproduced the shape and form of leaves by pressing them on paper coated
with lampblack, a method that was not used again until the nineteenth
century. Carefully noted, too, in his writings was the rising of sap
from the roots to the branches by capillary action; this, too, was not
rediscovered until much later—in the eighteenth century. Leonardo also
extracted oils and essences from flowers and studied the influences of
altitude on the development of vegetation. Indeed Leonardo’s very
approaches to a systematic classification of plants were the forerunners
of modern methods of classifying.
In the seclusion of his own home, as he continued his studies of
geometry with Pacioli, Leonardo again turned to his observations of the
heavens. On the roof of his house he had set up a small observatory for
watching the sky at night. Often he looked at the stars through a
pinhole in a sheet of paper. Leonardo did this to stop the “twinkling”
of the stars which he recognized as an optical illusion. Moreover, by
looking at the stars in this manner, he noticed that some were larger
than others, and imagined to himself how our own earth might look from
them. Would we not be but another “star” in a vast collection of stars?
And if that were true—how could the earth be the center of the universe?
By the same imaginary reasoning, he speculated on how we must look to
someone on the moon. Realizing that the moonlight on earth faintly
illuminates the dark side of the earth, he reasoned that then there must
be an “earthlight” doing the same on the moon. Thus he was the first to
explain the dim reflected light on the dark side of the moon. Moreover,
Leonardo is known to have looked at the moon through a convex lens, and
perhaps even a form of telescope. Indeed, he had built telescopic-type
tubes with lenses in them and had written directions for their use. It
seems certain that at about this time Leonardo became convinced of the
heliocentric theory, the theory that states the sun is the center of our
universe. On a sheet of mathematical notes Leonardo wrote in large
letters, “the sun does not move.”
During this time he continued to seek out books on astronomy. Leonardo
was familiar with Aristotle’s _Meteorology_, Archimedes’ _On the Center
of Gravity_, and with _Problems in Aristotle’s Books of the Sky and the
World_, a work by Albert of Saxony. This last book Leonardo had to read
with the help of a Latin dictionary, because his Latin was not good. He
had already read Plutarch, who had defined the moon as a solid. Plutarch
had written further that the “spots” on the moon were the result of
shadows cast by irregularities on its surface. This theory, that was
apparently abandoned during the Middle Ages, supported the conclusions
that Leonardo had reached by his own observations. But he still
struggled against a mistaken idea of his own. For a long while he
maintained that there were seas and waters upon the moon which accounted
for the sunlight being reflected so brilliantly.
Meanwhile, in July of 1499, the French army had reached Lombardy.
Ludovico was now in a state of desperation. He tried to appeal to the
people of Milan, explaining that their heavy taxes had been due to the
constant threats from abroad. But, however hard he tried to arouse their
sense of loyalty to him, the public of Milan turned a deaf ear. They had
not forgotten how Ludovico had allied himself with Charles VIII—a
foreign king! Ludovico now had to put his trust in his army commander,
Galeazzo da Sanseverino, despite warnings that this was a man of
doubtful loyalty. Moreover, to make matters worse, Louis XII had
succeeded in forming an alliance against Ludovico; and, among his allies
was a powerful cardinal, son of Pope Alexander VI—the notorious Cesare
Borgia.
From a note on a page of designs for supplying and heating a bath we
know that Leonardo continued his quiet life, only vaguely disturbed by
the political upheaval taking place around him. His note reads, “On the
first day of August 1499 I wrote here of movement and weight.” He had
made many experiments and calculations concerning the movement and
weight of objects. He had drawn, for example, the flight of an arrow to
describe motion through air and although he wrote no specific formula,
he marked the three stages of its trajectory—the initial push, the
slowing and the steeper downward path as the arrow’s momentum was
overcome by the resistance of the air. He also defined the law of
movement on an inclined plane and he arrived at the root principle of
Newton’s law of gravitation when he wrote, “every weight tends to fall
toward the center by the shortest way.”
A diagram of this period is probably the first scientific graph.
Leonardo had experimented with two balls dropped from a height. First he
dropped them together and then one after the other. In attempting to
solve the mathematical problems presented by these falling bodies he
drew a graph of vertical and horizontal lines. The times it took for the
balls to fall were marked on the horizontal lines and the distances on
the vertical lines—thus, he could trace their relationship.
But this peaceful time of productive work was running out for Leonardo.
Ludovico’s commander, Galeazzo, had yielded the fortress of Alessandria
to the French at the first battle. Ludovico himself had sent his sons
and his treasure to his brother, Cardinal Ascanio, in Germany. When he
saw that his cause was lost, he turned the Sforza castle over to
Bernardino da Corte, a trusted commander, making certain that it was
fully supplied with arms and food. Then in sorrow, Ludovico Sforza, Duke
of Milan, left his city for the last time as ruler of Lombardy. The
gates of Milan were opened to the French in October of 1499, and
Bernardino da Corte surrendered the Sforza castle.
French soldiers now occupied Milan as conquerors and the people of the
city were in a state of confusion. Those who could made their peace with
the French; but others, who had been supporters of Ludovico, fled to
avoid arrest. Leonardo, who would be suspect to the French, packed up
his few possessions—although he did manage to retain his estate—and
left, together with Pacioli and an apprentice, for Mantua.
[Illustration: _Leonardo had to flee Milan._]
9
_Cesare Borgia_
Leonardo, Pacioli, and Salai, the apprentice, arrived in Mantua in
February of the year 1500. They were given refuge in the castle of
Isabella d’Este, who was the sister of Beatrice, and the wife of
Francesco Gonzaga, governor of Mantua. Isabella was one of the eminent
women of her time and attracted to her court the intellectual life of
Italy. In Leonardo she recognized the man of genius; indeed, she treated
him as an equal, putting her castle at his disposal. She persuaded him
to paint her portrait and Leonardo commenced a preparatory drawing.
In the evenings at the castle there were discussions and music and here
Leonardo again met his pupil and companion on the trip from Florence so
many years ago—Atalante Migliorotti who had left Milan in 1490 to assume
the post of court musician to Isabella.
Although Leonardo had found a haven of peace in the political storm that
raged about the city state of Mantua, he and Pacioli took to the road
again for reasons unknown. Isabella d’Este, who still wanted Leonardo at
her court, sent many a letter and messenger in the following years to
bring Leonardo back—first to finish the portrait and then, when that
failed, to sell to her any picture that Leonardo wished to send.
Strangely enough, however, Leonardo seems to have turned his back upon
the one sympathetic person he had met in a world of indifference.
The first, warm breezes of spring were blowing over the lagoons of
Venice when Leonardo and Pacioli stepped ashore on the Piazzetta, or
Little Square of San Marco. But the beauty of this jewel-like city
rising from the sea was momentarily ignored by the two travelers for an
angry, frightened crowd had gathered about the Doge’s palace on the
Piazzetta.
The people of Venice were fearful because their fleet had just suffered
a crushing defeat by the Turks. This meant that their power at sea, once
supreme, was now no more. Year by year, moreover, their possessions in
the east had been slowly whittled away, and now the city itself was
threatened by invasion. At this same time, the Venetian ambassador,
Manenti, hoping to make peace with the Turks, had been rudely rejected
by them. Panic soon swept the city and rumors of the bloodthirsty
infidel passed from person to person like the rush of an ugly wind.
Barricades were put up and windows were barred. In this charged
atmosphere, Leonardo and Pacioli sought out their lodgings.
Soon after Leonardo’s arrival here—either because his reputation had
preceded him or, more likely, because of Fra Luca Pacioli’s
recommendations—he became directly involved with the defenses of Venice.
Immediately he was sent on an inspection trip of the city’s existing
defenses, especially those inland from where an invasion would probably
come. When he had seen them, he recommended a system of defenses along
the Isonzo river near the present border of Yugoslavia, using the river
itself to the disadvantage of the enemy. He also made suggestions for
the improvement of forts, and even drew up plans for a completely new
type—a circular fort. This consisted of a central, circular fort
surrounded by two belts of fortresses each separated by a moat. In the
outside moat were four semicircular outposts. Communication was by
underground galleries. The total absence of superstructure and
projecting balconies was a new idea for the times. Another new defense
idea was to station in the moat itself a low, thick tower almost
completely submerged, defended by a thin opening near the waterline. It
was reached from the main fort by an underground passage and the
gunsmoke was removed by vents. According to Leonardo no enemy could
conceal himself in any part of the defenses and not be seen from such an
outpost.
Leonardo’s most unusual scheme for defending Venice, however, was his
idea of approaching an enemy fleet under the water and then putting
holes in the hulls of their ships. Actually, the idea of diving was not
a new one. Aristotle had written of diving and diving bells, and
certainly the stories of pearl fishers in the Orient were well known in
the Renaissance. But Leonardo designed a diver’s suit closely resembling
those used today. This consisted of a complete suit of leather with
helmet and eyepieces; it was made airtight by spirals of steel at the
joints. He then added a bladder for holding air which fastened inside
the suit at the diver’s chest. It is possible that Leonardo also
invented an air chamber that could be used by the diver while under
water—but he was very secretive about this invention for fear of how men
might abuse such a discovery. He wrote, “... and this I do not publish
or divulge, on account of the evil nature of man, who would practice
assassinations at the bottom of the seas....”