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Los codices de Madrid


Leonardo da Vinci’s drawing of a windlass to be used for hoisting heavy loads.

The recent discovery of two large manuscripts of Leonardo da Vinci, containing drawings and notes long thought to be lost, has opened up a new, exciting chapter on the work and thought of Leonardo, the Universal Man.

por Anna Maria Brizio

The new manuscripts form part of the extraordinary collection of notes and drawings into which Leonardo poured a lifetime of research, experiment and reflection on art and "natural philosophy" (science), on mechanics, geometry, anatomy, hydraulics, the motion of air and the mechanics of flight.

The two notebooks have added no less than 700 pages to the former total of 6,000 pages of Leonardo manuscripts. The Madrid Codices are rich in new information which now helps to clarify issues which have long been discussed by Leonardo scholars and left unsolved because of insufficirnt or fragmentary evidence.

Together, the new notebooks cover the fifteen-year period between 1491 and 1505 when Leonardo was at the peak of his creative activity. However, the two manuscripts differ from each other in subject-matter: Codex Madrid I presents an exceptionally uniform range of material and deals principally with mechanics, whereas Madrid II covers a wide variety of subjects, most of which have some connexion with art.

For example, Madrid II contains subtle notes relating to painting and deals with colour and colour effects. Extracts from some of these notes in fact appear in Leonardo's Treatise on Painting (compiled after his death). An entire section of the Codex is devoted to plans for casting the Great Horse of Milan, the equestrian statue of Francesco Sforza which Leonardo worked on for many years but which was never actually cast (see page 37). The Codex also includes a series of architectural sketches of fortifications.

When we are dealing with Leonardo, however, any distinction between artistic and non-artistic drawings is meaningless and indeed unjustified for he conceived of no such distinction in his work. His artistic and scientific activities always sprang from a single source, so that the conclusions reached in an artistic venture affected the development of a scientific project and vice versa.

Furthermore, Leonardo's drawings are always a living language endowed with extraordinary creative force and possessing the same clarity and elegance, whatever their subjectmatter. The airy red chalk drawings of mountains in the Madrid folios are modern in their luminous and impressionistic depiction of landscape. It is interesting to note that they were in fact executed as part of a series of maps of the Arno river valley.

Again, the drawings of machines in Madrid I are so lucid and compelling that they suggest not only the surface appearance of the objects but also the dynamic force which makes them work. We get the same impression from Leonardo's anatomical drawings.

Of all the Leonardo notebooks which have come down to us, Madrid I is one of the most systematic (if such a word can ever properly be applied to Leonardo), perhaps because it is almost entirely devoted to a single subject mechanics. In appearance too it is one of the most orderly, and many of its pages give the impression of being a definitive copy. On many pages the drawings are so neatly and carefully sketched and shaded, and the accompanying texts so impeccably laid out, that one wonders whether he was actually preparing them for publication.

publication. The earliest and latest dates mentioned in Codex Madrid I are 1493 and 1497. However, I am personally inclined to place the work as a whole nearer to the earlier of the two dates, because of the numerous parallels with other Leonardo manuscripts from the early 1490s.

This was the crucial period of Leonardo's work in Lombardy, when he was applying himself with growing determination and success to both the theoretical and practical aspects of mechanics. His theoretical work centred on the definition of the "powers" (Leonardo uses the word "potenzie") which move the universe: weight, force, motion and impact. His practical work consisted in the application of these principles to the construction of mechanical devices.

Leonardo set forth his ideas on the link between theory and practice in two famous maxims: "The book about the science of machines precedes the book of applications"; and "Mechanics is the paradise of the science of mathematics, because through it one reaches the fruit of mathematics."

The most spectacular section of Leonardo's Madrid I manuscript is the part devoted to a detailed analysis and depiction of machinery, or more precisely, the components of various machines. This manuscript constitutes a kind of handbook of mechanics and gained immediate fame for the beauty and elegance of its drawings.

Ladislao Reti was the first Leonardo scholar to examine the Madrid notebooks at first hand. He spent years of passionate study on them, and drew special attention to the large number of Innovations and ingenious solutions to mechanical engineering questions found in Codex I. Many of these are based on principles and techniques which are astonishingly in advance of his time foreshadowing developments made many decades or even centuries later.

From amongst the mass of observations on mechanical engineering contained in Madrid I, Reti underlines two themes which, he says, are worthy of exceptional interest because of their originality and the extensive treatment given them by Leonardo, namely, the motion of projectiles and the motion of the pendulum.

Leonardo divides motion into "natural motion" and "accidental motion", and analyzes their characteristics and the laws which govern them. Natural motion, in Leonardo's sense of the term, is dependent on the force of gravity: "All weights desire to fall towards the centre of the earth by the shortest possible path", writes Leonardo in his typical style in which he often personified things and events In Nature.

"Accidental motion", on the other hand, is caused by a force (Leonardo uses the word potenzia, or "power"), which opposes the object's "desire" to get as near to the centre of the world as possible. And "accidental" motion will be violent, says Leonardo. On the recto side of folio 147 of Madrid I, Leonardo analyzes the laws and behaviour of natural and accidental motion.

"We shall propose as example", he writes, " a round weight suspended from a cord, and let this weight be a (above, letters reversed). And it shall be lifted as high as the point of suspension of the cord. This point will be f ... I affirm thus, that if you let this weight fall, all the motion made from a to n will be called natural, because it moves in order to approximate itself as near to the centre of the world as possible. After reaching the desired site, that is, n, another motion takes place, which we will call accidental, because it goes against its desire."

Leonardo next asserts that "Such accidental motion will always be less than the natural..." and "Consequently, natural motion, the more it approaches its end (from "a" to "n" as in the diagram) increases its velocity. Accidental motion (from "n" to "m") does the contrary."

In the same passage, Leonardo also analyzes the motion of a projectile launched in the air: "But if such motions are made towards the sky, as stones thrown in an arc, then the motion made by accident will be greater than the one we call natural..." and (in its return towards the ground after it has reached the zenith of Its upwards motion) "the stone will cease to follow in the air the shape of the arc it began, but, due to the great desire to go back down, it describes a line of much greater curvature and shorter than when it went upwards."

Almost a century later Galileo still believed that the line traced by the motion of projectiles in the air was a perfect parabola. With his sharp eye, Leonardo had "seen", both literally and metaphorically, the real trajectory of projectiles and correctly depicted the curve in his drawings.

Leonardo had also correctly observed the motion of the pendulum. He had seen that when a pendulum swings, the arc of its upwards motion is shorter than its descending arc, and that this ascending arc becomes shorter as the oscillations of the pendulum become slower. Leonardo also realized that the smaller the arc becomes, the more uniform become the pendulum's oscillations.

We know about Leonardo's research into the possible application of pendular mechanisms to drive saws, pumps, and especially mill-wheels. But did he ever think of applying the pendulum to clocks? This question has been much debated, but never fully resolved.

In many pages of the Madrid I Codex, however, Ladislao Reti found a significant number of notations and drawings by Leonardo which he carefully analyzed and found to be studies for the adaptation of the pendulum to a clock escapement. Reti's arguments were sufficiently impressive to convince Silvio Bedini, one of the world's great experts on clockwork. The two scholars have written an entire chapter on the subject for the book The Unknown Leonardo amply illustrated with reproductions from Leonardo's Codex Madrid I.

Leonardo was always interested in time-keeping devices. He shows a clear knowledge and deep curiosity in the large clocks and planétariums that existed in Lombardy at that time. He was particularly interested in the clock in the tower of the Abbey of Chiaravalle near Milan, and the astronomical clock (or astrarium) by Giovanni de Dondi in the ducal library of the Visconti Castle at Pavia, and made many sketches of their highly complicated parts.

Bedini and Reti point out that certain pages of the Madrid I Codex (folio 9 recto, folio 61 verso, and above all folio 157 verso) contain conclusive evidence that Leonardo had the completely original idea of applying the pendulum to clocks, thus anticipating the research of Galileo in this domain.

On folio 9 recto, Leonardo draws a crown-wheel connected to a horizontal rod, driven by a drum with cord and weight. On folio 61 verso there are some exceptionally clear-cut drawings of two different kinds of pendular escapement, one with a horizontal tooth-wheel, the other with a vertical tooth-wheel.

Finally, on folio 157 verso there is a rapidly drawn sketch, but it depicts a complete mechanism with a counter¬ weight using a cord wound round a drum-wheel, a series of cog-wheels, a cam with sinusoidal track, and a fan escapement. All these components recur repeatedly in various folios of Codex Madrid I, but here they are apparently assembled into an ideal mechanism.

Yet nowhere in Codex Madrid I did Leonardo actually draw a complete clock with a pendulum mechanism; on folio 157 verso, for example, there is no indication as to the motor required to drive the device.

However, it is characteristic of Codex Madrid I that Leonardo generally tends to sketch the individual component parts of a mechanism, in order to gain a clearer picture of its structure and the way it works, rather than to make a final drawing of the fully assembled model. In the drawing on folio 157 verso we are fully entitled, according to Bedini and Reti, to see the first ever project for a pendulum clock almost a century before Galileo!

All kinds of other mechanisms are analyzed by Leonardo in Codex Madrid I: springs for driving time-keeping devices, mechanisms using the spring principle to obtain a constant motor drive, cog-wheels to transmit motion, and so on. Leonardo pays considerable attention to the problem of reducing friction and comes up with some ingenious solutions.

Here I should like to develop several observations by Carlo Zammattio, who has pointed out how absorbed Leonardo was In water-courses when he was in Lombardy. Leonardo was interested in water and the uses it could be put to, such as providing power for machines, driving a mill-wheel, etc.

A particularly compelling example of the way Leonardo proceeds to a universal rule from his observation of a specific phenomenon is provided by his method of working out the "powers" (i.e. the motor force) of a series of jets of water pouring from apertures of the same size but at various different heights in a receptacle which is kept full of water at the same level. Now, Leonardo is aware that the force behind the individual jets remains identical.

This is how he explains the phenomenon: each particle of water, once it falls free from the aperture, responds exclusively to its own weight and acquires an impetus which produces a corresponding force of impact if It meets something in its path. But in the original receptacle, the water particles are subject not only to their own weight, but also to the weight of all the water that lies above them.

So when the jets of water emerge from their apertures at varying heights and fall towards the same horizontal surface below them, the force of their impact is bound to remain constant, because their "power" is a sum of the weight of the column of water that pressed down on them in the receptacle and the velocity acquired during their downward trajectory once released from it. Hence the more the one increases, the less the other becomes, and vice versa.

Zammattio points out that the method and conclusions in this analysis by Leonardo correspond to the theorem enunciated in 1738 by Daniel Bernoulli, in other words, the fundamental equation of hydrodynamics. Such were the formidable results which Leonardo was capable of drawing from minute observation.

A number of other comments remain to be made in connexion with Leonardo's Madrid II Codex. There is, for example, a passage which immediately became famous because of its obvious reference to Leonardo's mural for the Palazzo Vecchio in Florence, The Battle of Anghiari, which was ruined before completion:

"Friday the 6th of June, 1505, at the stroke of the thirteenth hour I began to paint in the Palace. As I lowered the brush, the weather changed for the worse and the bell started to toll, calling the men to the court. The cartoon was torn, water poured down and the vessel of water that was being carried broke. Suddenly the weather became even worse and it rained very heavily till nightfall. And the day turned to night."

Some persons have considered this passage as a solemn record of the day on which Leonardo began to paint The Battle of Anghiari; this interpretation does not seem to me to have a solid basis. This is a typical reference to an exceptional meteorological occurrence. These always fascinated Leonardo, and as well as arousing his scientific curiosity about their natural causes, stimulated the fantastic, apocalyptic side of his imagination.

A long list of Leonardo's books comes next, containing 116 titles. It is the longest list of book holdings that Leonardo has recorded in any of his manuscripts, and therefore constitutes a precious source of information about the authors which he drew on.

There is also a shorter and more cursory list of fifty books. The titles are not recorded and the books are simply grouped according to their shape and size. This list almost certainly refers to autograph manuscripts by Leonardo himself.

There are also some superb coloured maps of the Arno valley and the plain of Pisa, drawn up as part of Leonardo's research into a plan to divert the course of the Arno in order to cut Pisa off from the sea at a time when the Pisans were at war with Florence. These maps can be dated to the summer of 1503. Also there are the red chalk sketches of mountains which we have already referred to.

A side of Leonardo's activities which was completely unknown until the discovery of the Madrid II Codex is revealed in the repeated references around November and December 1504 to Leonardo's work on the harbour and citadel of Piombino. The Codex contains many drawings dealing with problems of architecture and fortifications.

Once again the insatiable student of nature that Leonardo was could not resist the proximity of the sea, and in the Madrid II manuscript we find notes on currents, winds and navigation. There are also drawings of sailing ships in the different positions they adopt according to the changing direction of the wind. Often these drawings are no more than a few rapid strokes but they are always strikingly evocative.

Then come drawings and notes on the flight of birds, descriptions dealing with aspects of painting, comments on geometry, proportion, and so on. The quantity of material is breathtaking.

However, Codex Madrid II is not a single manuscript. It actually contains two separate manuscripts. The folios numbered 141 to 157 verso make up a separate section entirely devoted to the casting of the "Great Horse of Milan" for the monument to Francesco Sforza. This monument was never cast. Leonardo protracted his research into it for so long that the duke eventually used the bronze which he had allocated for the horse to smelt some cannons instead. Nonetheless, the detailed studies which Leonardo made for the project and which he records in these pages are packed with bold and ingenious solutions.

Taken together, the two Madrid Codices cover a long period of time, from 1491, a date which can be found in the part devoted to the casting of the Great Horse, to 1505, the date of the projected Battle of Anghiari mural. This period stands at the very centre of Leonardo's creative span, covering his experience at Milan and Florence, his activities as "engineer general" to Cesare Borgia, and (as we now know from Codex Madrid II) his service as an engineer to other local despots, such as the Duke of Piombino.

Above all, the Madrid notebooks were rediscovered at a time when Leonardo studies were directed more at the contents of da Vinci's manuscripts than his paintings and other works of art proper. The immense range of subject matter found in the notebooks, especially the scientific and engineering studies, has come to light at a time when the world is increasingly interested in science and technology and their history.

The forthcoming publication of the facsimile edition of the Madrid Codices, reproducing the beauty and elegance of the originals, will place a unique fund of new knowledge at the disposal of scholars and the general public everywhere.

Anna Maria Brizio

President of the Ente Raccolta Vlnclana (the famous Centre for the collection of Leonardo da Vinci's works) at Vinci, where Leonardo was born. Anna Maria Brizio is a member of the Commissions Vinciana (Committee of Vinci studies) and the Higher Council of Fine Arts of Italy's Llncel National Academy. Professor of art history at the University of Milan, she is the author of many important studies on Leonardo da Vinci.