by Ross King
Leonardo’s writings do, however, show an undeniable strain of anticlericalism: an opposition to some aspects of organized religion, friars in particular. He took a dubious view of the religious orders, with one of his notes reading, simply: “Pharisees—that is to say, friars.”40 He called them, in effect, self-righteous hypocrites. This hypocrisy is elaborated in one of his notes, a riddle in which he asked: who gives up labor and poverty to live in great wealth in splendid buildings, “declaring that this is the way to make themselves acceptable to God?”41 His riddle voices the anticlericalism that runs from Dante, who placed Pope Nicholas III upside-down in a pit in the eighth circle of hell, through Chaucer’s description of the Pardoner with his bag of fake relics, to the numerous complaints in the fifteenth century about indulgence hawkers and other unscrupulous clerics “who pay little attention to the spirit but a great deal to the money.”42
Beyond Vasari’s story about Vincenzo Bandello, nothing attests to any dispute between Leonardo and the friars, and so it is impossible to say whether the experience of working among the Dominicans of Santa Maria delle Grazie was responsible for any of these sentiments. Leonardo’s anticlerical views, however, had their limits, and he could regard friars with affection and, in one special case, with great admiration. A more charitable attitude toward monks appears in one of his jokes. Leonardo loved jokes and humorous stories. He owned several books of funny (and often indecent) stories, such as an edition of Poggio Bracciolini’s Facezie (Jests). He evidently planned to produce his own book of funny stories, because around the time he worked on The Last Supper he wrote out a series of fables, jokes, and riddles—funny stories and intellectual puzzles with which he diverted Lodovico’s bored courtiers.43
One of Leonardo’s best jokes concerns two monks and a traveling salesman. Priests and nuns were figures of ridicule and derision in Sacchetti’s Trecentonovelle and Boccaccio’s Decameron, which contain numerous tales about corrupt and lascivious priests. Indeed, most writers of these funny stories were unabashedly anticlerical: they depicted convents as hotbeds of vice and corruption, and monks as greedy and licentious hypocrites. However, Leonardo’s story is unusual in that it portrays monks in a more favorable and sympathetic light.
His joke is actually a very funny one. Two Franciscan friars are journeying through Italy when they stop at an inn. Here they meet a merchant, also traveling on business. As the inn is a poor one, the food is meager: nothing appears at dinnertime but a small roast chicken. The merchant craftily points out that due to the time of the season and the rules of their order, the friars must not eat any meat—and so he greedily eats the whole chicken himself while the famished friars make do with scantier rations. They exact their revenge the following day when, leaving the inn and traveling together, one of them agrees to carry the merchant across a river on his shoulders. In midstream the friar asks his passenger if he has any money on his person. “You know I have,” replies the merchant. “How do you suppose that a merchant like me should go about otherwise?” The friar informs him that the rules of his order forbid him from carrying money—at which point he drops the merchant into the river. The story ends happily, with the merchant, smiling and blushing with shame, peaceably enduring the friars’ revenge.44
CHAPTER 11
A Sense of Proportion
Leonardo enjoyed making lists. His notebooks include many catalogs and inventories evidently made on the occasions he packed up his belongings for a trip or a move. He also composed lists of things he hoped to learn or acquire. Quite often the two lists got jumbled together, making for some strange juxtapositions. In one such list he made himself a note to get Avicenna’s work on “useful inventions” translated, before going on to itemize such artistic necessities as charcoal, chalk, pens, and wax. Then he abruptly added, “Get a skull.” The list rounds off with mustard, boots, gloves, combs, towels, and shirts. Another list combines his ambition to learn the multiplication of square roots with a reminder to pack his socks.1
If these possessions and ambitions were haphazardly itemized, Leonardo took much greater care when listing his books. He once declared that he was not “a literary man,” but in fact he was well-read and owned a well-stocked library. Lacking much in the way of a formal education, he was one of history’s great autodidacts. By the time he started moving in courtly circles in Milan, he evidently felt the need to burnish his learning. In the late 1480s he began copying out in a small notebook the longest of all his lists, a lexicon of words—some foreign, some Latin, some technical—intended to boost his vocabulary. His list is more than fifty pages long, running to some nine thousand words and allowing him to impress Lodovico’s courtiers with words the likes of “archimandrite” (leader of a group).2
Leonardo admitted that “presumptuous persons” could be justified in saying he was not a man of letters. “My subjects are to be dealt with by experience rather than by words,” he asserted in his defense.3 And yet his notebooks quote or mention an astonishing array of authors: not only ancient writers such as Plato, Pliny, Virgil, Lucretius, Livy, Quintilian, and Plutarch—among numerous others—but also the medieval Islamic mathematician Thabit ibn Qurra, the physicists Richard Swineshead and Biagio Pelacani, the Franciscan John Peckham, and Leon Battista Alberti. Once again there is a gulf between what Leonardo said and what he did. He was every bit as interested in book learning as he was in firsthand experience. However, he aspired to take nothing on the authority of others. Even the Bible was not spared his forensic scrutiny.
Leonardo eagerly hunted down copies of books he wished to purchase or read, frequently recording where they could be found or from whom they might be borrowed. “A book, treating of Milan and its churches, which is to be had at the last stationer’s on the way to Corduso,” reads one of his notes. Another book he hoped to borrow from a local doctor: “Maestro Stefano Caponi, a physician, lives at the Piscina, and has Euclid De Ponderibus.” His notebooks are peppered with these memoranda as he tracked down one volume after another. “The heirs of Maestro Giovanni Ghiringallo,” he noted, “have the works of Pelacano.” Another promising lead he follows was Vincenzio Aliprando, “who lives near the Inn of the Bear,” and who owned a book on Roman architecture. Leonardo also sourced his books from libraries: “Try to get Vitolone which is in the library at Pavia and which treats of mathematics.” On the same page he added, “A grandson of Gian Angelo’s, the painter, has a book on water which was his father’s.”4
Leonardo set about collecting books after his move to Milan, and in about 1495 he meticulously copied down the titles of forty books in his possession. This list encompassed works of a very wide variety. His library was stocked with treatises on surgery, agriculture, and warfare—such works as we might expect to find on his shelves—but also with books by ancient Roman authors such as Pliny, Livy, and Ovid. These works shared space with volumes of a more whimsical nature. Indeed, his library appears to have been divided equally between serious scientific volumes and more humorous or lighthearted offerings. One of the books he owned was Luigi Pulci’s Il Morgante maggiore, a burlesque poem (part of which was later translated by Lord Byron) about a giant who eats camels and picks his teeth with a pine tree. He also had a copy of the fanciful travel stories of Sir John Mandeville (who describes an island of sixty-foot giants and a bird that can carry an elephant in its talons) and a collection of Aesop’s fables.5 Another list made a decade later shows that by then his collection had swollen to 116 volumes, meaning he must have purchased, on average, seven or eight books each year.6
Perhaps the most fortuitous of all Leonardo’s book purchases was made around the time he received the commission for The Last Supper. At the end of 1494 or beginning of 1495 he bought a copy of Fra Luca Pacioli’s Summa de arithmetica, geometria, proportioni et proportionalità (Summary of arithmetic, geometry, proportions and proportionality). He paid 119 soldi for the work, almost double what he paid at the same time for his Malermi Bible.7 The book was hot off the press in Venice: clearly
Leonardo was not willing to waste time searching for the volume in libraries or borrowing secondhand copies from local doctors. The book did not disappoint, and within a year he had convinced Lodovico Sforza to bring the friar to Milan as yet another dazzling adornment for the court.8
The Franciscan Order had produced a number of great philosophers and scientists. Most notable was Roger Bacon, who anatomized the brain and called himself a “master of experiment.”9 Fra Luca Pacioli was the latest of these intellectual luminaries. In the eyes of many of his contemporaries, he was one of the great wonders of the world. “How many excellent qualities are in the man,” exulted one writer, “how much genius, how great a memory, what an abundance of material and profound appreciation of learning.” He was compared to Aristotle and Homer, and celebrated as “a man of the rarest pattern and almost unique... It is not possible to recount the many glories of the man’s learning.” For another admirer, Pacioli was simply “a wonder of our times.”10 History remembers him with a more unassuming moniker: the “Father of Accounting.”
Luca Pacioli was born in 1445 in the Tuscan town of Borgo San Sepolcro (today Sansepolcro), forty-five miles southeast of Florence. He was educated by Franciscans before serving an apprenticeship, first with a local merchant and then probably (though no hard evidence exists) with the most famous son of Borgo San Sepolcro, the painter and mathematician Piero della Francesca. Pacioli later described Piero as “the reigning painter of our time,”11 but the two men shared mathematics rather than painting in common. Piero had written his Trattato d’abaco, a book on “the arithmetic necessary to merchants,” at the request of a family of wealthy Borgo merchants. Pacioli, too, became a mathematics teacher to the merchant class, moving to Venice as a young man to teach the three sons of a businessman named Antonio Rompiasi.
After Rompiasi’s death in 1470, Pacioli followed a peripatetic regime, traveling around Italy and giving lessons and lectures on mathematics. In Rome he met the architect Leon Battista Alberti, and in Urbino he became tutor to Guidobaldo da Montefeltro, son and heir of the duke. In about 1477 he took his vows as a Franciscan, later returning to Borgo San Sepolcro, where he composed his treatise on mathematics, the Summa de arithmetica. When he returned to Venice to oversee its publication, an artist named Jacopo de’ Barbari captured him in a portrait. Barbari showed Pacioli’s Franciscan habit cinched at the waist with a cord (the three knots symbolize his vows of poverty, chastity, and obedience) and his head covered with a cowl. His face, however, is clearly visible: that of a middle-aged man with fleshy cheeks and a double chin. To a handsome young man who stands beside him, wearing a haughty glare, he gives a geometry lesson, complete with chalkboard, textbooks, and two models of polyhedra, one of which is made of glass, half-filled with water, and suspended in midair.
Luca Pacioli, by Jacopo de’ Barbari
One of the textbooks shown in the painting is Euclid’s Elements. The other is Pacioli’s own Summa de arithmetica. As its cumbersome name suggests, this was an encyclopedia, an exhaustive, six-hundred-page-long compendium of arithmetic, algebra, and geometry. As the introduction stated, the book offered “complete instructions in the conduct of business.” It was most famous for its exposition of the system of double-entry bookkeeping used by Venetian merchants—hence Pacioli’s reputation as the Father of Accounting, the Father of the Balance Sheet, and the Father of Profitability.12
The work’s mind-numbing disquisitions on business accounting may explain the supercilious boredom on the face of the young man by Pacioli’s side. Leonardo, on the other hand, was a great enthusiast for such mathematical treatises. By the 1490s he owned no fewer than six books entitled Libro d’abaco—handbooks of mathematical instruction and calculation. He was introduced to mathematics at his abacus school in Vinci, where, according to Vasari, he had baffled his master with questions. Later he became adamant about the importance of the subject. “Let no one read my principles who is not a mathematician,” he famously declared (less famous is the fact that the principles he was referring to were his theories of how the aortic pulmonary valve worked).13 Ironically, he himself was a poor mathematician, often making simple mistakes. In one of his notes he counted up his growing library: “25 small books, 2 larger books, 16 still larger, 6 bound in vellum, 1 book with green chamois cover.” This reckoning (with its charmingly haphazard system of classification) adds up to fifty, but Leonardo reached a different sum: “Total: 48,” he confidently declared.14
Pacioli was paid by Lodovico to give public lectures in mathematics. However, the prestige he brought to the Sforza court came not from his expertise in double-entry bookkeeping so much as from his interest in, among other things, polyhedra like the ones shown in the Barbari painting. A polyhedron (from the Greek “many faces”) is a multifaceted geometrical shape such as a tetrahedron (a pyramid), an octahedron (a diamond), or an icosahedron, which is composed of twelve pentagons and twenty hexagons, and looks like a soccer ball. Plato, Euclid, and Archimedes all described the properties of these and other polyhedra, and interest in them revived during the fifteenth century. The Florentine artist Paolo Uccello used polyhedrons in his paintings (particularly in the form of the padded, doughnut-shaped hat known as a mazzocchio) and in a design he created for a mosaic on the floor of the basilica of San Marco in Venice. Pacioli was the latest enthusiast for these kinds of geometrical acrobatics. He claimed to have made glass models of sixty polyhedra while in Urbino (though no record of them has ever been found) and he would make a set in Milan for Galeazzo Sanseverino, to whom he was probably introduced by Leonardo.
Leonardo and Pacioli quickly became friends. Later they would live together in Florence, and Pacioli probably shared space with Leonardo in the Corte dell’Arengo in Milan. Leonardo clearly believed there was much he could learn from the friar, whom he no doubt bombarded with questions. “Learn the multiplication of roots from Maestro Luca,” reads one of his notes.15
The two men had more in common than merely a love of mathematics. Like Leonardo, who amused courtiers with robotic creatures and tricks such as turning white wine into red, Pacioli appears to have become a kind of highbrow jester at the Sforza court. Soon after arriving in Milan he began work on a treatise called De viribus quantitatis (On the Powers of Numbers). It contained not only brain-twisting problems in algebra that Pacioli probably demonstrated and solved before the court, but also numerous magic tricks. Pacioli’s manuscript described such ingenious feats as:
How to Make an Egg Walk over a Table
How to Make an Egg Slide up a Lance by Itself
How to Make a Cooked Chicken Jump on a Table
How to Eat Tallow and Spit Fire
How to Make Worms Appear on Cooked Meat
The secret behind making cooked chicken jump on the table was to mix quicksilver with “a little bit of magnetic powder,” pour the contents into a sealed bottle, and then tuck the bottle inside a chicken “or other cooked thing, which must be hot, and it will jump.” He made worms appear on cooked meat by chopping up the strings of a lute “in great lengths, just like natural worms,” and then concealing them inside the meat. As the meat is roasted, the strings, “made from gut, will slowly twist and they will appear to be worms and those that see them will get sick.”16
To such entertainments did the “wonder of our times” devote himself. He may have been assisted in some of these recipes by Leonardo, who likewise enjoyed pranks and spectacles. One of Leonardo’s notes gives instructions on how to “make a fire which will set a hall in a blaze without injury.” The trick involves evaporating brandy in a sealed room, suspending powder in its fumes, and then entering the room with a lighted torch. “It is a good trick to play,” he observed. He was also known for inflating sheep intestines with a bellows so they filled the entire room, forcing his guests to crowd into a corner. “He perpetrated hundreds of follies of this kind,” reported Vasari.17
If Leonardo and Pacioli spent some of their time diverting bored courtiers with these sorts of tric
ks, they also shared loftier concerns. Soon after Pacioli arrived in Milan, the two men began collaborating on the friar’s magnum opus.
One of Leonardo’s most famous drawings was done a few years before he began work on The Last Supper. Carefully sketched in pen and ink, it shows a naked man flapping his arms and legs as if making a snow angel. He is standing inside a square that is intersected by a circle. In his neatest mirror script Leonardo explained the point of the drawing: if you open your legs far enough to reduce your height by one fourteenth and at the same time “spread and raise your arms till your middle fingers touch the level of the top of your head,” your navel will be at the center of your outspread limbs and the space between your legs will describe an equilateral triangle.18
Through this apparently bizarre postural exercise Leonardo evoked the ancient Roman architect and engineer Vitruvius, and consequently his famous drawing is known as Vitruvian Man. In The Ten Books on Architecture, composed around the time of the birth of Christ, Vitruvius described an experiment in geometry, proportion, and the human body: “For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centred at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom.” The body likewise yields a square, Vitruvius claimed, since the distance from the toes to the top of the head equals that from fingertip to fingertip if arms are outstretched.19
