Leonardo da Vinci, the Florentine artist, scientist, and inventor, was born at Vinci in Tuscany, the natural son of a notary, and died near Amboise, France. At his death he left a sizable collection of notebooks that were subsequently scattered in the various libraries of Europe. From 1881 on, many of these notebooks have been published. They consist of notes and jottings on various topics: mechanics, physics, anatomy, physiology, literature, and philosophy. They contain, moreover, plans and designs for machines that frequently have suggested Leonardo's "precursive genius." There are machines of war and of peace, flying machines based on the flight of birds, a parachute, a helicopter, tools and gadgets of all kinds. Leonardo's notebooks are also full of methodological notations on the procedures of scientific inquiry and philosophical considerations about the processes of nature. Undoubtedly many of the arguments that he discussed were taken from the philosophical literature of the time, especially from the writings of the Ockhamists; however, a coherent and complete philosophical scheme cannot be found in the notes, whose chronological order is extremely uncertain. Pierre Duhem held that Leonardo was mainly inspired by the doctrines of Nicholas of Cusa, but recent studies tend to emphasize his dependence on Marsilio Ficino. Leonardo lived in Florence for the first thirty years of his life and subsequently returned there many times.
Leonardo's Treatise on Painting (published 1651) reveals the artist and the scientist united in one personality. Painting, which he placed above all other arts, aims at representing the work of nature to the senses. Thus it extends to the surfaces, the colors, and the forms of natural objects, which science studies in their intrinsic forms. The beauty that painting seeks in things is the proportion of the things themselves, and proportion is also the object of the scientific consideration of nature. According to Leonardo, understanding nature means understanding the proportion that is found not only in numbers but also in sounds, weights, times, spaces, and any natural power whatever. Both art and science have the same object, the harmonious order of nature, which art represents to the senses and science expresses in its laws.
Leonardo held that the two pillars on which science stands are experience and mathematical calculation. As an "unlettered man" (as he called himself) he had contempt for those who, instead of learning from experience, claimed to learn from books (the commentators and followers of Aristotle). He contrasted his work as an inventor with their work of "trumpeting and reciting the work of others." "Wisdom is the daughter of experience," he said. Experience never deceives, and those who lament its deceitfulness should lament their own ignorance because they demand from experience what is beyond its limits. The judgment of experience can be mistaken; and the only way to avoid error is to subject every judgment to mathematical calculation and to use mathematics unrestrictedly to understand and demonstrate the reasons for the things that experience manifests. Mathematics is therefore, according to Leonardo, the basis of all certitude, since without recourse to mathematics it is impossible to put an end to the verbal disagreements of what he called the sophistic sciences—that is, the philosophical disputes about nature.
The privilege accorded to mathematics was most certainly a legacy from Platonism. Leonardo took from Plato's Timaeus and Ficino's commentary on it the doctrine that the elements of natural bodies are geometric forms; thus the efficacy of mathematics as an instrument of investigation was justified for him by the fact that nature itself is written in mathematical characters and that only those who know the language of mathematics can decipher it. This is the major contribution that ancient Platonism made to the formation of modern science. Nicolas Copernicus and Galileo Galilei shared this obviously metaphysical doctrine that, however, strongly contributed to launching science from its origins to its mathematical organization. It helped bring scientific consideration from the domain of quality (of natures or essences) to that of quantity by permitting consideration of the natural object as measurable; that is, in the extremes, by reducing the objectivity of nature to its measurability.
However, if the order of nature is a mathematical order, then it is a necessary order; and this necessity is, according to Leonardo, the only true "miracle" of nature: "O wondrous and awesome necessity! With your law you constrain all effects to result from their causes by the shortest path, and according to the highest and irrevocable law every natural action obeys you with the briefest operation." The phrases "by the shortest path" and "with the briefest operation" refer to another feature of the necessary order of nature: its simplicity. Nature follows the shortest or simplest path in its operations. It does not like useless loitering, and this also reveals the mathematical character of its structures. Necessity and simplicity of nature exclude the presence of arbitrary or miraculous forces, as well as the efficacy of magic and of those forces to which it appeals.
Guided by these criteria, Leonardo could arrive at and formulate important theorems and principles of statics and dynamics. The theorem of the composition of forces, the principle of inertia, and the principle of action and reaction are the most notable of these formulations, which, of course, he did not state in the precise form that they received later from René Descartes and Isaac Newton. Nevertheless, they demonstrate his genius for moving from the limited work of the inventor to the generalizations of the scientist.
Leonardo's manuscripts have been published with photographic reproductions by Charles Ravaisson-Mollien, 6 vols. (Paris, 1881–1891). They have also been published in Codex Atlanticus, edited by G. Piumati (Milan, 1894–1904) and I manoscritti e i disegni di Leonardo da Vinci, published by the Reale Commissione Vinciana (Rome, 1923–1930). The best collection of selections is J. P. Richter, The Literary Work of Leonardo da Vinci, 2 vols. (London, 1883; 2nd ed., 1939). Leonardo da Vinci on Painting: A Lost Book, edited and translated from the Codex Vaticanus Urbinas, No. 1270, and from the Codex Leicester by Carlo Pedretti (Berkeley: University of California Press, 1964), includes a preface by Kenneth Clark and some material never published before.
Works on Leonardo include the following: Pierre Duhem, Études sur Leonardo da Vinci, 3 vols. (Paris, 1906–1913); E. Solmi, Leonardo (Florence, 1900); C. Luporini, La mente di Leonardo (Florence: Sansoni, 1953); Eugenio Garin, Medioevo e Rinascimento (Bari: Laterza, 1954), pp. 311ff., and Cultura filosofica del Rinascimento italiano (Florence: Sansoni, 1961), pp. 388ff.; I. B. Hart, The World of Leonardo da Vinci (London: Macdonald, 1961); James Beck, Leonardo's Rules of Painting: An Unconventional Approach to Modern Art (New York: Viking Press, 1979); and Boris Kouznetsov, "The Rationalism of Leonardo Da Vinci and the Dawn of Classical Science," Diogenes (69 [1970]: 1–11).
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