by Martin Kemp
c. 1507–13, Milan, Biblioteca Ambrosiana, Codice atlantico, 307v
Leonardo believed that arithmetic and geometry “embrace all things in the universe.” Above all, the design of nature, whether static or dynamic, worked with “proportion . . . which is not only found in number and measure but also in sounds, weight, time, and positions, and every power that exists.”
In 1501, he became acquainted with a comprehensive philosophical encyclopedia by scholar Giorgio Valla (1447–1500) that began with substantial chapters on arithmetic, music, and geometry. It was from Valla that Leonardo picked up an intense interest in the relationship between areas enclosed by figures with curved and straight sides. This was related to the ancient and intractable problem of squaring the circle—that is to say being able to define a circle that was absolutely the same in area as a given square. Leonardo tested various solutions, practical and theoretical, and more than once convinced himself that he had found the answer.
Around 1514 he felt confident enough to declare that “as I have shown . . . various ways of squaring the circle. . . . I now begin the book called De ludo geometrico [On Geometrical Recreations].” This was to contain diverting exercises on the magic of number and form. The illustrated page here is characteristic of the dense patterns of equivalent areas formed by shaded and unshaded portions of intersecting circles.
At the top of the page he listed numbers that contain the aliquot of 6, such that proportional multiples of 6 rule throughout. In the big geometrical construction, he drew a circular figure that contains 6 circles surrounding a central one, each of which contains 6 units, making 42 units as a whole. He additionally constructed an isosceles triangle that divides the circumference of the larger circle into a sixth.
Although such constructions may seem to be no more than abstract “games,” Leonardo saw them as indicative of the profound wonders of the mathematics that lie behind natural design. The heart valve (see pages 172–75) is an example of geometrical areas in dynamic action in the organ that regulates our life.
95. Studies of a Fetus in the Womb and of the Placenta
c. 1515, Windsor, Royal Library, 19074v
This moving study of the “great mystery” of the fetus in the womb stands at the formal and emotional climax of a series of drawings of human reproduction. The convincing pose of the fetus, modeled with densely curved pen strokes over red and black chalk, indicates that it was studied from nature. However the womb is more synthetic.
The spherical womb, also apparent in the smaller sketches, reflects Leonardo’s desire that the gravid uterus should adopt the most perfect form, as it seems to do when a woman is in the late stages of pregnancy. In the diagrams in which he peels back the surrounding membranes and uterine wall, the fetus is seen to be encircled as if in a round seed-case.
The “cotyledonous” placenta consists of a series of separate pads on the uterine wall and the membrane surrounding the embryo of the kind he had observed in his dissection of a pregnant cow. He explained that as the uterus contracts after birth, the pads draw together and are packed as hexagonal units within a single placenta.
The demonstrations at the top right show how the fingers of each unit of the placenta interdigitate with those of the uterine wall, either as matching protrusions or as insertions into receptive cavities. The diagrammatic technique that he adopted to demonstrate the peeling back of the two membranes is wholly novel.
The other two diagrams on the page might seem to have nothing to do with the main subject. The demonstration at the middle of the right margin shows how a round ball on a slope can be eccentrically counterweighted so as not to roll. In fact, this is relevant to the rotation of the baby in the womb, given that it is not in the head-down position necessary for a standard birth. The optical diagram at the bottom left shows “why a picture seen with one eye will not demonstrate such relief as when shown with both eyes.” He was in effect saying that even his very powerful modeling of the fetus cannot equal seeing stereoscopically.
Detail of womb opening from Studies of a Fetus in the Womb and of the Placenta.
96. A Chain Ferry on the Adda at Vaprio near the Villa Melzi
c. 1511–13, Windsor, Royal Library, 12400
During his second period in Milan (1506/7–1513), Leonardo was joined by Francesco Melzi (c. 1493–1570), a young nobleman from Vaprio d’Adda. Unlike the standard workshop apprentices, Francesco was well educated and socially adept. He became Leonardo’s close companion and heir to the master’s drawings and manuscripts. He is elusive as an artist in his own right, but seems to have copied the master’s drawings skillfully. When Leonardo died in 1519, Francesco testified that Leonardo was “like an excellent father to me. . . . Everyone is grieved by the loss of such a man whose like nature no longer has it in her power to produce.”
This small drawing in pen and brown ink was made looking down from the Melzi family’s villa. We can see a ferryboat consisting of two conjoined hulls, a platform, and a small hut. Moving along the chain or rope, the boat edges across the shallow and turbulent river. A man brandishing a stick appears to be in charge of at least one cow or ox on the ferry. Even at the tiny scale of the drawing, we can see on the right the landing platform of logs and a small, three-arched bridge over a lateral channel that is still visible today. It is rare to be able to look over Leonardo’s shoulder at a view that survives, albeit with an ugly road bridge in place of the ferry. The minute vitality of his fine touch is miraculous. It is one of his most spontaneous and nonanalytical drawings.
To the left of the view portrayed with such delicate and energetic fidelity is the Naviglio Martesana canal that runs parallel to the unnavigable river below the villa. The canal was a major engineering achievement, but stopped just north of Vaprio in the face of massive rocks at Tre Corni. Leonardo worked out an unrealized scheme for a very deep lock beside the rock barrier that would permit boats to change levels from the low section of the canal at Vaprio to the much higher level north of Tre Corni.
A contemporary view of the three-arched stone bridge that appears in Leonardo’s sketch.
97. An Old Man, with Water Rushing Turbulently Past Rectangular Obstacles at Different Angles
c. 1510, Windsor, Royal Library, 12579r
The effect of this sheet—which was folded when Leonardo used it—is misleading. Originally, the old man was not glumly contemplating the enormous complexities of water in turbulent motion. He may well have been intended to be a St. Joseph, who is typically characterized as bewildered by events, not least by the pregnancy of his virgin wife.
Leonardo grappled heroically with the chaotic phenomenon of water in turbulent motion. He was fascinated with the way that water moving in spirals progressively accelerates rather than slowing down like most moving bodies. He decided that this is because the impetus is confined to a constricted space but still has to complete its designated motion.
Looking at the radical effect of an upright stake in a rapidly moving stream of water, he characteristically sensed an analogy: “observe the motion of the surface of water, which resembles the behavior of hair, which has two motions, of which one depends on the weight of the strands, the other on its line of revolving. This water makes revolving eddies, one part of which depends on the principal current, and the other depends on the incident and reflected motions.” The power of visual analogy carried him across dynamics and statics.
There is no Leonardo painting that does not feature some aspect of helical form, whether hair, drapery, the growth of plants, or the motion of water itself. The lost Leda would have been a symphony of such forms, and vortex hair plays leading roles in the Ginevra de’ Benci, the Portrait of a Man with a Sheet of Music, the Salvator Mundi, and St. John, while it plays supporting roles in The Annunciation, the Munich and Benois Madonnas, the Virgins of the Rocks, the Madonnas of the Yarnwinder, the Mona Lisa (in a gentler manner), the St. Anne cartoon, and the Louvre St. Anne (in the curls of the infants). In this as in other of his concerns, L
eonardo moved from an instinctual grasp of form and motion toward an analytical understanding that was ever more mathematical in nature.
“There is no Leonardo painting that does not feature some aspect of helical form, whether hair, drapery, the growth of plants, or the motion of water itself.”
98. Studies for a Spiral Staircase and a Pump
c. 1516, London, British Museum, Codex Arundel, 264r
On moving to the court of Francis I in 1516, Leonardo was housed grandly in the manor house of Cloux (Clos Lucé) and paid a large salary. He was accorded the status of a magus or wise man. It was reported that “King Francis, being enamored to the very highest degree of Leonardo’s supreme qualities took such pleasure in hearing him discourse that he would only on a few days in the year deprive himself of Leonardo. . . . The king said that he did not believe that a man had ever been born in the world who knew as much as Leonardo, not only of sculpture, painting, and architecture, but also that he was a very great philosopher.”
Leonardo was displayed to visiting dignitaries, and he showed them the paintings that remained with him, including the Mona Lisa and the St. Anne. He also showed the notebooks that contained his diverse range of designs and researches.
The biggest project that involved Leonardo during the three years before his death in 1509 was for a very grand palace complex at Romorantin (Romorantin-Lanthenay) in the Loire, which would in effect have constituted a kind of a new town. The grand plan embraced gracious courtyards, trim gardens with fountains and a water clock, and a network of canals for irrigation, sanitation, and boating. The palace buildings were to combine the latest Renaissance motifs with the great corner towers of French chateaux. Leonardo’s unrealized plans exercised a huge impact on the castles of the Loire.
The page here (turned sideways) is part of a larger double sheet that contains another pump design. The pump on the page shown is upside down. The double sheet involves two prominent aspects of the Romorantin scheme, namely the management of water (for function and fun) and the design of spiral staircases. The “snail staircase,” as Leonardo describes it, is presented lucidly to show a double handrail that is cunningly inset into the newel post. The two detailed sections of the central axis show how the grooves allow the user’s fingers and thumbs to slide upward and downward while ascending and descending.
99. A Deluge Wrecking a Mountain, Woods, and a Township
c. 1515–17, Windsor, Royal Library, 12380
This is one of sixteen drawings at Windsor that represent hugely violent “deluges.” Most are in somber black chalk, but this one is finished in pen and ink and wash, endowing it with a strangely formalized dynamism.
The deluge drawings somehow combine expressive fury with the scientific content of fluids in vortex motion. They could have served as illustrations for Leonardo’s Treatise on Painting, which was to include instructions on how to represent “wind, tempest at sea, deluges of water, forests on fire, rain, bolts from heaven, earthquakes, and the collapse of mountains, razing of cities.” These were not stock subjects, and he was envisaging genres of art that were yet to be invented.
The note on this drawing is oddly objective: “On rain. Show the degrees of rain falling at distances of varied darkness; and the darker part will be towards the middle of its thickness.” His word-painting of deluges contains comparably analytical passages:
Let the pent-up water go coursing around the vast lake that encloses it with eddying whirlpools, which strike against various objects and rebound into the air as muddied foam. . . . The waves that in concentric circles flee the point of impact are carried by their impetus across the path of the other circular waves moving out of step with them, and after the instant of percussion leap up into the air without breaking formation.
But the human horror of the four elements run amok is also evoked with great power:
O what fearful noises were heard throughout the dark air as it was pounded by the discharged bolts of thunder and lightning. . . . O how much weeping and wailing. O how many terrified beings hurled themselves from the rocks. . . . O how many mothers wept for the drowned children they held upon their knees, their arms raised towards heaven as they voiced their shrieking curses. . . . Others crouched forward with the breasts touching their knees and in their hugely unbearable grief gnawed bloodily at their clasped hands and devoured their fingers they had locked together.
100. St. John the Baptist
c. 1507–14, Paris, Louvre
The St. John is probably the “St. John the Baptist as a young man” seen in Amboise by Antonio de Beatis in 1517. It also appears on the Salaì list in 1525.
The image of the pointing saint is the most intense of Leonardo’s experiments in the direct communication between the subject and the viewer. It is related to a project of an Angel of the Annunciation, known through a student’s drawing corrected by the master. The angel in the drawing is announcing directly to us—a daring innovation. St. John is also announcing the coming of Christ: “After me cometh a man which is preferred before me.” The saint holds a prophetic reed cross.
Characteristic features of Leonardo’s later style are expressed in extreme form. The saint’s unavoidable gaze and enigmatic smile are irredeemably ambiguous because none of the forms are rendered with clear edges. The apparent sharpness of the saint’s right arm and pointing hand has resulted from restoration to rectify the damage described in an inventory of Charles I’s collection. The saint’s hair is the most profuse version of the vortex coiffures in which Leonardo delighted. The strongly directional light and dark background achieves the heightened sense of “relief” that he emphasized as a major goal for the painter.
The seductive androgyny of St. John is typical of the portrayal of youthful saints by Leonardo and other artists. This is true above all of St. John the Evangelist—“the disciple whom Jesus loved”—sitting next to Christ at The Last Supper (see page 66). Leonardo was aiming for a transcendent beauty that defies categorization by gender. The message of the painting is uncompromisingly spiritual. We are confronted with the mystery of a world we think we can see, but which lies beyond our understanding. St. John knows secrets that are inaccessible to us. Leonardo left “the definition of the soul . . . to the minds of friars, fathers of the people, who by inspiration possess the secrets. I let be the sacred writings, for they are the supreme truth.”
Detail of Perspective Study for the Adoration of the Kings, c. 1481–82.
LEONARDO’S LIFE
Key Dates and Works
1452
April 15
On Saturday, April 15, around 10:30 pm, Leonardo is born in Vinci out of wedlock. Leonardo’s father is Ser Piero di Antonio da Vinci (1427–1504), a notary working in Florence, and his mother is a young orphan, Caterina. The baby is publicly baptized the following day, with six prominent godparents.
1457
February 28
The five-year-old Leonardo is listed in Vinci as a dependent in the tax assessment of his grandfather, Antonio.
First Florentine Period (c. 1464/69–c. 1481/83)
c. 1469
Leonardo moves to Florence at an unknown date and enters the workshop of Andrea Verrocchio.
1472
Leonardo appears in the account book of the Compagnia di San Luca, the painters’ confraternity of Florence.
1473
August 5
He inscribes a mountainous landscape drawing: “The Day of S. Maria delle Neve [Holy Mary of the Snows] on the 5 August 1473” (Florence, Uffizi).
c. 1473–74
Around this time he paints The Annunciation (Uffizi).
c. 1475
Leonardo paints The Madonna and Child with a Vase of Flowers (Munich, Alte Pinakothek).
1476
At some point, probably about 1476, he contributes substantially to Verrocchio’s painting of The Baptism of Christ (Florence, Uffizi).
April 9 and June 7
Leonardo remains in Verrocchio’s workshop. On the
se dates he is among those twice charged with homosexual activity with a seventeen-year-old apprentice in a goldsmith’s workshop. The charges are not followed up.
1478
January 10
Commission for an altarpiece in the Chapel of San Bernardo in the Palazzo della Signoria of Florence. He receives a payment on March 16, but there is no other evidence of work on the commission.
A drawing in the Uffizi is inscribed “. . . ber 1478, I began the two Virgin Marys.” One of them may be the “Benois Madonna” (St. Petersburg, Hermitage).
Around this time the Portrait of Ginerva de’ Benci was painted.
1481
In July, Leonardo signs an interim agreement about the Adoration of the Magi for the main altar of San Donato a Scopeto on the outskirts of Florence. Between June and September, payments in money and commodities (including wine) are made for work on the altarpiece.
Before and around this time, he begins to explore aspects of technology (civil and military) and science, including anatomy.
The unfinished St. Jerome (Rome, Vatican) may date from this time.
First Milanese Period (1481/3–1499)
1481–83
Between September 1481 and April 1483, he leaves Florence for Milan.
1483
April 25
With the brothers Evangelista and Giovanni Ambrogio de [or da] Predis, Leonardo signs the contract to decorate a large altarpiece for the Confraternity of the Immaculate Conception in their chapel at the San Francesco Grande in Milan. The central painting is to portray the Madonna and Child. His contribution is to be the Virgin of the Rocks in the Louvre, which may be the “Nativity” sent by Ludovico Sforza as a wedding present to Emperor Maximillian I.
1483–90