LEONARDO DA VINCI--EARLY YEARS
Santa Maria della Fiori (Duomo), Florence, Italy. Photo credit: Steve Husarik
LEONARDO SELF-PORTRAIT [35]
http://www.artchive.com/artchive/l/leonardo/leonardo_self-portrait.jpg
INTRODUCTION: One of the great minds of the Renaissance, Leonardo Da
Vinci (1452-1519) overcame the social prejudices of being born an illegitimate
child and also of being gay in a society that forbade it. He defied the
prejudices of his day against conducting human anatomy studies (confessing
on his deathbed to having dissected the bodies of over thirty men, women and
children) and became one of the greatest medical illustrators in history. His
exceptional intellectual capacity, creativity and enthusiasm for learning
enabled him to invent the parachute, the underwater diving lung and the
military tank. He is best remembered, however, for producing two of the most
famous icons in the history of painting: Mona Lisa and The Last Supper.
MONA LISA [36]
http://www.ibiblio.org/wm/paint/auth/vinci/joconde/joconde.jpg
TIMELINE: EARLY YEARS
1452 born in Anchiano, Italy, two kilometers outside Vinci
1467 he enters the workshop of Verocchio
1472 contributes a small angel to the Baptism of Christ-- The Annunciation.
1476 in court, accused of sexual relations with a male model
1481 St. Jerome, unfinished---begins, but never completes Adoration of Wise
Men---major Tuscan artists are called to Rome including Ghirlandaio,
Signorelli, Perugino etc. but not Leonardo.
Only about twenty Leonardo Da Vinci paintings survive, yet those that remain
are outstanding examples of their types. For this reason, Leonardo is
considered one of the greatest painters of all time.
VINCI/ANCHIANO, ITALY [37]
http://static.panoramio.com/photos/original/6682052.jpg
Born in (Anchiano (near Vinci, Italy), about forty miles from Florence,
Leonardo was the illegitimate son of a notary named Sir Piero of Florence and
a peasant lady named Caterina of Vinci. The problem of his illegitimacy would
haunt him later in life when he tried to gain his legal inheritance. Ser Piero had
numerous children and Leonardo's brothers were especially keen to keep all
of the money from the estate to themselves. His brothers gave him a difficult
time over his inheritance when their father died.
Leonardo's early home in Anchiano still stands perched on a hill. As a child,
he played in a rocky grotto just below the window of his house. Folklore says
that this is the same rocky grotto he painted again and again at the bottom of
his paintings.
MADONNA OF THE ROCKS, 1ST VERSION (1483-85) [38]
http://www.romankrznaric.com/Gardening/virginoftherockslouvre2.jpg
Leonardo once wrote, "He who knows all things, can do all things. One has
but to know and there will be wings." Untangling this double negative
sentence into understandable English, it says "if you know everything, you can
do everything." Leonardo is only partially correct, because it is not possible to
know everything. Leonardo didn't know about wing-lift, about nylon, plastic,
aluminum and structural steel that aeronautical engineers know about today.
Those things came from the body of knowledge collected over the centuries
since he lived in the Renaissance. Thus, he was unable to invent the hangglider or airplane—projects that interested him greatly—but which are
dependent on modern knowledge of wing lift and light-weight materials.
SELF PORTRAIT [35] (see above)
A single person cannot expect to know everything. His red chalk self-portrait
done at the end of his life betrays his skeptical expression: at this point, even
HE must have realized he couldn't know everything.
As a teenager, Leonardo’s parents got him placed in the studio of
Verrocchio—an important sculptor in Florence. Without the legal standing of a
legitimate son, and with no hope for an upper class education, his parents
wanted him at least to gain a trade. The teen-aged Leonardo is said to have
modeled for one of Verrocchio's pieces of sculpture, entitled David.
YOUNG LEONARDO AS DAVID, VERROCCHIO [39]
http://www.kfki.hu/~arthp/html/v/verocchi/sculptur/y_david.html
Verrocchio gave Leonardo an assignment to do part of one of his paintings
called the Baptism of Christ. When he saw the difference between his own
work on the panel and that of the teenager, he is said to have given up
painting. One can tell the difference between their work by comparing two
angels in the painting: Leonardo's angel adopts a twisted theatrical pose, has
a sweet smile on her face and has a strong sense of chiaroscuro in the facial
highlights. Verrocchio’s angel has a stupid expression on her face that betrays
his lack of theatrical understanding. (The vegetable growth and distant
landscape, also by Leonardo, are exotic and mysterious.)
BAPTISM OF CHRIST, ANGEL [40] CLOSEUP
http://www.kfki.hu/~arthp/html/l/leonardo/01/1angel.html
OVERVIEW
http://www.aiwaz.net/uploads/gallery/baptism-of-christ-4638-mid.jpg
Another difference between Verrocchio and his student is the subtle use of
color. Leonardo painted the gown of the angel first in a single opaque color
brown. Then covered it with a single transparent color of blue or green, called
local color technique. He repeated application of these glazes in different hues
until he reached the desired level of depth and gloss. In ordinary hands, local
color technique—not unlike creating a piece of stained glass—the effect is
prosaic, but Leonardo carried it to a new level of interest by varying the layers
to create shifting effects of color.
SIDEBAR: CROSS SECTIONS OF LEONARDO PAINTINGS
Leonardo paintings grab hold of you when you see them in a museum. There is a reason for
this. Leonardo has a secret method for laying down paint. Typically, he began his painting on
either a wood panel or on canvas, which he then covered with gesso (plaster). He then drew
his design onto the gesso surface in a very pale brown color, putting the half tones in first. For
this reason his unfinished paintings (and there are many of them) look like studies in
monochrome brown.
If he continued, Leonardo then built up the highlights using opaque paint (with thick pigment
particles that reflect light). Typically, the opaque paint areas are located in the highlights of a
person’s face, or the tops of mountains in the distance in his paintings. In the shadows, he
used transparent glazes (with finely ground pigment particles) that, if one could tear them off
the painting, would look like pieces of stained glass.
Unlike previous painters, Leonardo darkens his glazes using a variety of colors. As the
paintings dry over the centuries, the various under layers become more apparent and multiple
colors emerge in the shadows. These paintings literally get better with age—like fine wine.
In order to fully appreciate a Leonardo painting, therefore, you have to see it in person; the
physics of light demand it. Reproductions show only the opaque qualities—whereas his
paintings have both transparent (glazes) and opaque qualities. When you view a Leonardo
painting, two things are at work: light is being reflected from the bright opaque surfaces, but it
is also being absorbed into the shadows. The light goes into the glaze, is processed in the
layers, and is then reflected back to the viewer's eye. Because of the many overlapping layers,
these paintings resonate in front of you.
ST. JEROME [41]
http://www.kfki.hu/~arthp/html/l/leonardo/01/8jerome.html
One of the unfinished paintings from Leonardo’s early period is St. Jerome.
Notice the perfect outline of St. Jerome's right arm—suggesting anatomical
precision even though there is nothing shown within the outline. It has the
photographic appearance of a real arm because Leonardo knew anatomy so
well. He would later pursue the study of anatomy extensively in order to
improve both his understanding of science and his ability to represent the
human body.
ADORATION OF MAGI [42]
http://www.gfmer.ch/Art_for_Health/Images/Italian_Renaissance/Leonardo_Adoration_Magi.jpg
Another early painting by Leonardo is titled the Adoration of the Magi (Three
Wise Men Approach Mary). Having solved the problem of the design, and laid
it out in brown outlines, Leonardo did not color the painting. He thus left still
another unfinished work. There are approximately sixty figures in the complex
design. The standing figure on the lower right—who looks toward the picture
frame—is said to be Leonardo himself. Note the use of single point
perspective in the study for the staircase.
ADORATION OF MAGI, STAIRCASE [43]
http://www.loc.gov/today/pr/images/davinci_drawing.jpg
Leonardo was doing well in Florence until one day a legal complaint was filed
against him. A black box was placed in the downtown area of Florence into
which anonymous accusers could place notes. In essence, one could accuse
anyone of anything at any time and the defendant had to prove his innocence.
Someone put a note in the box accusing Leonardo of sodomy. This was an
awkward and dangerous accusation at the time, because brutal medieval
justice was practiced around Europe. A second note was placed into the box a
month later actually linking Leonardo with one of the models at Verrocchio's
studio—one Jacopo del Saltarello. Leonardo was held for several days at
court, during which time his father disowned him. Through the help of his
uncle Francesco (who knew members of the influential Italian Medici family),
and because the cowardly accuser didn't show up in court, the charges were
dismissed.
Although professionally well established as an artist a few years later,
Leonardo was NOT invited to decorate the walls of the Sistine Chapel in
Rome as were all the other notable painters in Florence. It may be pure
coincidence, but one can't help but wonder about this curious oversight on the
part of church officials and the fact of Leonardo's illegitimacy, his being
brought up on a morals charge just a few years before and his alleged lack of
identity with the church.
MADONNA OF THE ROCKS, 1ST VERSION
MADONNA OF THE ROCKS,
(1483-85)
2ND VERSION (1506-08)
[44] http://www.romankrznaric.com/Gardening/virginoftherockslouvre2.jpg [45] http://www.ibiblio.org/wm/paint/auth/vinci/rocks.jpg
In 1483 Leonardo received a commission to do the Madonna of the Rocks.
Notice how the eye of the viewer is drawn to the angel on the right, who is
pointing to St. John on the left. Down below is the rocky grotto allegedly from
Leonardo's home in Anchiano. Leonardo completed a second version of the
same painting twenty years later, and the two versions survive today: one is in
the Louvre, the other is in the National Gallery, London. It is instructive to
compare them to see the differences between his early and late styles.
LEONARDO DA VINCI--MIDDLE YEARS
Sforza castle, Milan Italy Photo credit: Steve Husarik
TIMELINE: MIDDLE YEARS
1483—joins the court of the Duke of Milan; meets Luca Pacioli; Salai joins
him at age 10; begins Treatise on Painting; Madonna of Rocks, 1st
version; Adoration of the Magi, Lady with the Ermine
1495—Last Supper.
1499—Duke is captured and imprisoned by political enemies; Leonardo
leaves Milan with Brother Luca Pacioli and Salai.
Leonardo sent out a letter—a kind of resume—in which he listed his
numerous qualifications as an engineer, an architect, a painter, and designer.
He concluded the letter with a statement about his abilities as a painter,
saying that he could "do anything as well as any man, be he who he may."
Evidently, he sent the letter to the Duke of Milan, at the Sforza palace.
The Duke of Milan hired him not as a painter, not as an engineer, not as an
inventor, nor as a sculptor. He hired Leonardo as a court entertainer, musician
and theatrical designer. Leonardo appeared at court with a hollowed out cow's
skull with strings stretched across it, on which he played musical ditties for the
courtiers. Leonardo was very skillful in his relations with others and became a
very popular person at court. Eventually he was paid a sum equal to about
$45,000 per year in today's currency.
INVENTIONS—DRAWINGS [46]
http://www.cise.ufl.edu/~davis/Poetry/images/Leonardo_da_Vinci_helicopter_and_lifting_wing.jpg
Leonardo's appearance at the Sforza palace marked the beginning of a
twenty-year period of artistic and scientific creativity. He invented all kinds of
things, automatic bell ringers, tanks, fortresses and even whistles. He
invented an early version of the piano, the parachute, the underwater diving
lung and even tried to invent the airplane. In the 1960s he was discovered to
have invented the modern bicycle.
LAST SUPPER (1495-98) [47]
http://metalab.unc.edu/wm/paint/auth/vinci/lastsupp.jpg
He painted one of his most famous commissions, the Last Supper, during this
period. Notice how its single point perspective is arranged so that all lines
converge on a point lying just above Christ's head. The lines are adjusted in
the painting so that they extend out into the actual chapel where it is housed
and create a tromp l'oeil extension into the walls. This painting was the only
thing left standing in Milan, Italy after the American bombing of World War II.
Sandbags were piled up on either side of it and somehow it miraculously
escaped damage.
While painting the Last Supper, Leonardo was asked why he often came to
look at the painting, but did not paint. As the folklore goes, one of the priests
had complained that they needed him to finish the painting so they could get
into their refectory (kitchen). Leonardo explained to him that "I can't figure out
what the face of Judas should look like. What would a person look like who
betrays his own benefactor?" To which the priest replied, "Well, please put
something in there and get it done." And so, Leonardo supposedly painted the
priest’s face as Judas.
In 1499, Leonardo did an elaborate design with an extended knotted vine on
the ceiling of the Sala delle Asse at the Sforza palace. He took vine stem
motifs and threaded thousands of them all over the ceiling. It is interesting that
this ceiling fresco achievement predated Michelangelo's painting of the Sistine
Chapel Ceiling by more than a decade.
ANATOMY
Leonardo confessed on his deathbed to having dissected the bodies of over
thirty men, women and children. This was a very dangerous practice during
the early Renaissance because Christians, awaiting the Resurrection, did not
believe in cremation. They felt one should not defile the Christian body after
death. Thus, anatomy was a forbidden science.
ANATOMY DRAWINGS [48]
http://www.kfki.hu/~arthp/html/l/leonardo/10anatom/
Leonardo's anatomy drawings were considered classics in the history of American
medicine science until the 1920s. The stories about how he got hold of some of his
body parts are indeed strange. One time he obtained an arm and a head after a
hanging, and another time a foot. Some of the parts came from unclaimed bodies at the
hospital. He dissected a head and trunk in Milan, an old man in Florence, a human
fetus, another elderly man, and a leg. He was also a spectator at other dissections and
probably learned superficial aspects of subject in Verrocchio's studio. Eventually he
identified the "origins" and "insertions" of muscles, illustrated the mechanical and to
some extent the biological functions of the body. He was the first to site the spinal cord
as the center of life and he was the first person ever to get the fetus correctly positioned
inside the womb. He said that the smell of these bodies was horrific; but, what he
learned from the study more than justified the noxious aroma.
Leonardo’s drawings of the skeletal structure illustrate the musculature without flaw, but
when it comes to soft tissue anatomy, his observations and assertions are generally
incorrect and reflect the limitations of anatomical science of his time. He did not, for
example, discover the circulation of the blood, even though he did elaborate drawings of
the circulatory system and of the internal organs.
Leonardo was one of the greatest medical illustrators of all time. After his death, his
sketches were collected together into books by his assistant, Melzi. After Melzi died,
however, the notes were cut out of books and sold off as souvenirs.
SIDEBAR: MIRROR WRITING
Leonardo's notes are written in mirror writing and the only way to read them—even if you
understand Italian—is to hold a mirror up to them. He wrote left-hand and backwards. Some
people say that was to hide his work that might have been considered heretical by ignorant
people. This explanation doesn't fully satisfy, however, because one only need look at the
illustrations to understand that Leonardo was obviously engaged in what would be called
"black magic" at the time. The reason for his mirror writing has yet to be explained.
St. Anne, St. John and the Christ child, alternate version. School of Leonardo, Budapest Art Museum,
Hungary.
THE SECRET OF MONA LISA'S SMILE
Knowledge is constantly changing and there are new developments in all
fields of the arts. The following paper was read by this author at the National
Association for Humanities Education meeting in Cincinnati, Ohio, 1996.
Please note that it is directed to an audience of teachers and professors and
is therefore written in an elevated, literary style. You should experience this
form of discourse at least once in your undergraduate academic career in
order to understand how scholars approach their subjects and how they
communicate with other professionals in their fields. For those of you who are
writing about Leonardo on the test, this paper will also give you some
additional ideas for your essay. Others may just want to GLANCE THROUGH
AND DETERMINE THE NAME OF THE GEOMETRICAL SHAPE THAT
BECAME LEONARDO’S OBSESSION IN HIS LATER WORKS.
One of the signs of an artistic masterpiece is that it can be interpreted in a
variety of ways, and this is a useful coincidence for those who wish to find
common ties between seemingly unrelated fields such as painting and
mathematics.
MONA LISA [36]
http://www.ibiblio.org/wm/paint/auth/vinci/joconde/joconde.jpg
Madonna Lisa, or as it is popularly known, Mona Lisa, it is the subject of endless
research and has probably received more interpretation than any other European
painting. About twenty years ago, the background was located in northern Italy. It was
the old Roman bridge in Lecco that has an identifiable set of arches (including one
squeezed together). Lecco is a resort area located about an hours' train ride north of
Milan. Leonardo would have visited there by way of horseback or possibly by boat (a
river leads all the way from Milan to Lecco). It must have been very fashionable to paint
his wealthy client in front of (then popular) Ancient Roman ruins. You can see the bridge
just above Mona Lisa's left shoulder (right side of painting as we look at her). Compare
it with the modern photo.
Photo credit: Stephen Husarik
Much narrative has developed about La Gioconda herself, about the enigma of her
expression, and how Leonardo had musicians playing during the sittings in order to
achieve a special effect in her smile (Vasari 194). The painting has generated numerous
commentaries seeking to explain its stylistic or regional characteristics (McMullen,
Brown), and the smile itself has stirred interest in fields as diverse as medicine (Adour)
and computer graphics (Schwartz). Few authors, however, have attempted to relate the
geometry of Leonardo's painting with Mona Lisa's smile. Can there be an ideal form that
Leonardo projected onto his painting, transcending both the individuality of the sitter and
regional characteristics of her portrait, that would help explain Mona Lisa's smile?
In order to answer this question, one may quote Leonardo's own words: "Let no man
who is no mathematician examine the elements of my works" (Clark 47; Goldscheider
10; Richter I, 112). This double negative sentence written on the back of a Leonardo
drawing [Windsor 19118] expresses his position quite well—that a full appreciation of
his work depends upon an understanding of the mathematical principles underlying it.
As Umberto Cisotti states, ". . . it is difficult if not impossible to separate the results he
arrived at in mathematics from those he achieved in other fields. The line of
demarcation becomes cloudy in the concrete reality of a Leonardo who was a
mathematical physicist, mathematical painter, and mathematical architect" (Cisotti 201).
As a designer, Leonardo's mathematical attitude is perhaps nowhere better illustrated
than in the ceiling fresco he produced for the Sala delle Asse at the Sforza Castle, Milan
(Annoni 312, not illustrated).
SALLE DELLA ASSE
Photo credit: Stephen Husarik
This astonishing fresco depicts numerous vine branches and braided ropes growing into
a complex geometrical pattern. According to Annoni, Leonardo never erred in the
design, and did not falsify the principal motifs as they spread across the ceiling. Since
Leonardo found obvious delight in making geometrical designs out of decorative motifs,
perhaps we should look for parallels in his paintings in order to help explain Mona
Lisa and her smile.
In the early 1480s, important Tuscan artists, including Ghirlandaio, Signorelli, and
Perugino, had been called to Rome to decorate the Vatican—but not Leonardo. He left
Florence to accept a position at the Sforza court in Milan. This move had great
consequence, since Leonardo was about to embark upon what would be a twenty-year
investigation and synthesis of science, mathematics and art. At the Court of Ludovico il
Moro, he was surrounded by distinguished figures in the arts and sciences.
MAN INSCRIBED IN CIRCLE AND SQUARE (ca.1496) [49]
http://classes.design.ucla.edu/Winter09/9-1/blog/b/wp-content/uploads/2009/01/j-102-0013_vitruvian_man_5001.jpg
In 1497, Leonardo was asked by Luca Pacioli, the father of modern accounting, to do
designs for a book on Euclidian geometry entitled De divina proportione. Leonardo's
interest in the formal subject of mathematics was undoubtedly increased through their
friendship. He devoted much space to geometry in his manuscripts, and even dedicated
a hundred pages to the study of Euclid'sElements, "something that was almost certainly
conditioned by the mere presence of Pacioli and by Leonardo's commitment to
illustrate De divina proportione " (Marinoni 69). Leonardo jotted down the following
remarks in his notebooks: "Get the Friar di Brera to show you the book [by Jordanus] De
Ponderibus"; "Get the master of arithmetic to show you how to square a triangle"; "Get
Mr. [Cardano] Fazio to show you about proportionality"; Try to get Vitelone['s treatise],
which is in the library of Pavia, and treats of mathematics"; "Get master Luca [Pacioli] to
show you how to multiply roots" (Richter II, 359-361).
Because Leonardo read numerous treatises on geometry, collaborated with Pacioli
on De divina proportione, and delighted in making decorative geometrical designs, it
seems appropriate to look for an ideal form in his paintings having some basis in
geometry. This form is found in a single motif called the parabola. Euclid discussed the
parabola and other conic sections in his bookConics [now lost], and it was Appolonius
who gave these figures their names (Waerden 589). Parabolas are one of the basic
shapes that result from slicing or cutting a cone at different angles: they include the
parabola, hyperbola and ellipse. All of them are present in Leonardo's paintings, but the
parabola has exceptional importance because it ultimately became the principal motif
for his later paintings. Its derivation is shown in Figure 1.
FIGURE OF CONE [50]
Unlike other conic sections, parabolas can be easily inscribed upon any natural shape.
In a painting, they fit the sensuous contours of human flesh and the rolling hills of
natural landscapes. It is even possible to think of them three-dimensionally so that a
rotated parabola [paraboloid] can represent a solid object, such as a mountaintop in a
distant landscape. Leonardo was not the first or last to use parabolas as an element of
design: perhaps the most famous parabola is inscribed over the arms of the ancient
Greek statue by Myron, The Discus Thrower.
DISCUS THROWER [51]
http://www.mlahanas.de/Greeks/Arts/Misc/Discobolos2.jpg
Only the most conventional of geometrical patterns can be superimposed over
Leonardo's early paintings produced back in Florence [such as Annunciation, St.
Jerome and Genevra De Benci], but his Milanese designs take on a new geometrical
coherence. One of Leonardo's first paintings from Milan is the Portrait of the Lady with
the Ermine [1483]. It is a pivotal work because the main motif of the painting, the
inclination of the lady, is parabolic--as are the other curves in the painting such as the
body of the animal and the necklace worn by the sitter. These characteristics are not
immediately recognizable unless one draws the curves over the figure as shown in
Figure 2. This done, the elegance and unity of the design reveals itself.
LADY WITH ERMINE (1483) [52]
http://www.wisdomportal.com/Stanford/LadyWithErmine-1.jpg
FIGURE 2--ERMINE CONTOURS [53]
In 1499, after about twenty years of support, Leonardo's longtime patron, Ludovico de
Moro, was overtaken by political enemies and his regime fell. Leonardo left Milan and
was traveling in the company of Luca Pacioli. By this time, he had amassed a
considerable body of notes on the subjects of geometry and optics, and had even
invented type of compass that could draw parabolas (Clark and Pedretti 1:375r-a). It
was also during this period [ca. 1495-1497] that Leonardo completed the Sala delle
Asse, which unfolds its decorative motifs in an exhaustive sequence. The trend begun
earlier in his paintings-to superimpose basic geometrical shapes over the contours of
natural objects--became much more pronounced, and parabolas began to saturate his
designs.
Back in Florence in 1503, he gained a commission to paint what would become his last
formal portrait, among other subsequently completed works, the Mona Lisa. While there
is some debate over the identity of the sitter (Zllner 115), the painting itself became one
of Leonardo's few clearly attributable works, since he had it with him during his final
days in France.
MADONNA WITH THE YARNWINDER [54]
http://www.mystudios.com/art/italian/davinci/davinci-yarnwinder-1501.html
MADONNA WITH THE YARNWINDER [55]
[collection of Duke of Buccleuch, Scotland, original image available only in Goldscheider
book]
A significant parallel work from this period, Madonna with the Yarnwinder [ca. 1501], is
illustrated in Figure 3. This small painting is earmarked with the characteristics of
Leonardo's mature style--a design replete with motifs derived from conic sections. As
the chief motif for the design, the parabola is combined with itself to make various
groups. The strata of rocks upon which the child sits is a succession of parabolas. The
right arm of the child, his right leg and hip, various folds of the Virgin's gown, and the
outline of her head are all parabolic contours. The hand of the Madonna is of special
interest since it is placed in the air in such a way that a parabola can be inscribed
beneath it and rotated: the hand is literally resting upon the arc of an implied paraboloid.
This characteristic hand gesture occurs in other Leonardo paintings too, such as
the Madonna of the Rocks. Leonardo's preoccupation with mathematics and geometry
became so obsessive in 1504 that Fra Pietro da Novellara observed "mathematical
experiments have distracted him so much from painting that he cannot lift the brush to
paint" (Turner 43).
(1483-85) MADONNA OF THE ROCKS 1ST VERSION [44-45]
http://www.romankrznaric.com/Gardening/virginoftherockslouvre2.jpg
FIGURE 3--MADONNA HAND OVER PARABOLOID [56]
Including sketches and preliminary drawings, it took about ten years for Leonardo to
complete his major work, Virgin and Child with St. Anne [1499-1510]. The use of
parabolas is so obsessive here that perhaps this work should be thought of as the
culminating work in this vein. Sequences of parabolas are systematically developed
throughout the painting: the arms and legs of St. Anne and the Virgin, the shapes of the
rocky strata beneath them, the winding road to the right of the figure group, and the
unrelenting sequences of the mountaintops in the rocky landscape all contribute to the
sequence. Even the eyes and mouth of St. Anne are inscribed upon parabolic arcs as
shown in Figure 4. The parabola has here become the principal motif of the design both
in detail and overall pattern, giving the painting a unique decorative quality.
VIRGIN, ST. ANNE AND CHILD [57]
http://www.abcgallery.com/L/leonardo/leonardo3.html
FIGURE 4 VIRGIN ST. ANNE AND CHILD, DIAGRAM [58]
Heinrich Wölfflin points out, in his Art of the Italian Renaissance, that "the inclination of
the Virgin forms the main motif of the painting" (Classic Art 41). Without explaining
himself, Wölfflin seems to understand the basic geometrical unity in this painting even
though he mentions neither conic sections nor parabolas. Although thematically
prominent, the parabola formed by the Virgin is not the most conspicuous in the
painting, nor is it the largest. Consider that a curved line is formed by the division of the
painting into a brown foreground and blue background which suggests, by implication,
the segment of a large parabola whose vertex lies somewhere off to the right of the
picture frame. This classic painting is "open," to use terminology developed by Wölfflin
(Principles 15).
Examination of other paintings by celebrated Renaissance artists reveals that parabolic
sequences do not appear in their works. Take, for example, a well-known Raphael
painting, Madonna with the Goldfinch (Tansey 74, not illustrated). It has a Madonna, a
rocky landscape, plants, scenery, in fact everything one might expect in a religious
painting of this period, but it has no sequences. This statement is not intended to
suggest that parabolic curves themselves are excluded from Renaissance paintings. In
fact, other paintings by Raphael, and later, the paintings of Parmigianino, are full of
anecdotal parabolas: however, neither of these artists develop the motif into elaborate
sequences. Parabolic sequences became the unique stylistic feature of Leonardo's
paintings.
[There is an earlier painting of the Virgin St. Anne and Child located in the Budapest Art
Museum shown in LEONARDO'S MIDDLE YEARS. It is not a mature work as
evidenced by the absence of sequences of parabolas. There is even a likelihood that
the painting was not completed by Leonardo at all, but merely supervised by him.]
ST. JOHN THE BAPTIST [59]
http://www.abcgallery.com/L/leonardo/leonardo11.html
One of Leonardo's last works, St. John the Baptist [Goldscheider 55, not illustrated], is a
true curiosity. Although the painting of St. John is clearly organized around parabolic
geometry, his skewed eyes betray the fact that Leonardo has here represented a real
person, not an ideal one. Only in the smile can one find ideal form. As Wallace writes,
"Certainly in this curving, smiling pose, Leonardo expresses the quintessence of the
eternal mystery which is so much a part of his work.... It is not difficult to imagine that,
when the old man died, his eyes were fixed on that upraised finger and that enigmatic
smile" (Wallace 179). The upraised finger and the smile are, of course, both inscribed
upon parabolic arcs.
MONA LISA [60] (see above)
Let us now return to the Mona Lisa. The painting was produced at a time when
Leonardo's geometrical style was beginning to crystallize. While it does not contain an
exhaustive sequence of parabolas, it is nevertheless replete with conic shapes aimed at
producing a geometrical unity. The mountainscape immediately behind La Gioconda is
a succession of parabolas, as are the contours of her shoulders; the folds of her sleeves
are hyperbolic. In fact, the identity of the sitter is slightly obscured because her features
have been adjusted to fit geometrical shapes, Mona Lisarepresents an ideal in paintings
precisely because there is a balance between the individuality of the sitter and a
prevailing geometrical pattern. Like the Virgin and Child with St. Anne painting,Mona
Lisa appears to be just one in series of paintings directed at geometrical coherence,
where every detail of the painting--no matter how small--is geometrically related to the
overall pattern. This structural aspect of a painting is at least as important as its
thematic or photographic content, and provides a new context for viewing Leonardo's
work.
MONA LISA DIAGRAM [61] PHOTO CLIP ATTACHMENT
What does the geometrical context tell us about the secret of the Mona Lisa's enigmatic
smile? As shown in Figure 5, her smile--like the smile of almost all later Leonardo
Madonnas and angels--gains its unique character because it is inscribed upon a
parabolic arc. The tradition of Mona Lisa's so-called enigmatic smile, referred to in many
Leonardo biographies, can now be explained, at least in part, by Leonardo's interest in
and application of the parabolic geometrical form.
WORKS CITED
Adour, Kedor K. "Mona Lisa Syndrome: Solving the Enigma of the Gioconda Smile." Ann Otol Rhinol Larygnol 98, 1989.
Annoni, Ambrogio. "Leonardo as Decorator." Leonardo Da Vinci. New York: Reynal and Company, 1956.
Brown, David Alan. "Leonardo and the Idealized Portrait in Milan." Arte Lombarda 67, 1983.
Cisotti, Umberto. "The Mathematics of Leonardo." Leonardo Da Vinci. New York: Reynal and Company, 1956.
Clark, Kenneth and Carlo Pedretti. The Drawings of Leonardo da Vinci in the Collection of Her Majesty The Queen at Windsor Castle. 2nd
ed. 3 vols. London: Phaedon, 1968.
Goldscheider, Ludwig. Leonardo Da Vinci. London: Phaidon Press, 1959.
Marinoni, Augusto. "The Writer: Leonardo's Literary Legacy." The Unknown Leonardo. Ed, Ladislao Reti. New York: McGraw-Hill, 1974.
McMullen, Roy. Mona Lisa: The Picture and the Myth. Boston: Houghton Mifflin, 1975.
Pedretti, Carlo. The Codex Atlanticus of Leonardo Da Vinci: A Catalog of Its Restored Sheets. 2 vols. New York: Johnson Reprint Corp.,
1978.
Richter, Jean Paul. The Literary Works of Leonardo Da Vinci, ED. Jean Paul Richter and Irma A. Richter. 2 vols. London: Oxford University
Press, 1939. 2 vols.
Schwartz, Lillian F. "Morphing the Three Faces of Mona: The Decision-making Steps Leonardo used to create his Mona Lisa." Computers
and Graphics. 19:4, 1975.
Tansey, Richard G. and Fred S. Kleiner. Gardner's Art Through the Ages. New York: Harcourt Brace College Publishers, 1996.
Turner, A. Richard. Inventing Leonardo. New York: Alfred Knopf, 1993.
Vasari, Giorgio. Lives of the Artists, Biographies of the Most Eminent Artists, Painters and Sculptors of Italy. Ed. Betty Burroughs. New York:
Simon and Schuster, 1946.
Waerden, B. L. van der. "Euclid," Encyclopedia Britannia: Micropaedia. 15th ed. 1997.
Wallace, Robert. The World of Leonardo. New York: Time-life Books, 1966.
Wolfflin, Heinrich. Art of the Italian Renaissance. New York: Schocken Books. Trans. and Reprint of Classic Art. 1963.
---. Principles of Art History, Trans. M. D. Hottinger. New York: Dover Publications Inc., 1963.
Zollner, Frank, "Leonard's Portrait of Mona Lisa del Giocondo." Gazette des beaux-arts. March, 1993.
Acknowledgement: I would like to thank Dr. Myron Rigsby [chair, Math-Science Division, Westark College] for reviewing mathematical
terminology used in this paper.