Leonardo Studies II: Continuity and Discovery in Optics and Astronomy

Introduction

i. Definitions of Optics

The modern term, optics, closely resembles the Greek optike. However, that is about as far as the resemblance goes. In Antiquity optics was chiefly a study of sight: today it is primarily concerned with the physics of light. In Euclid's time optics was chiefly subjective: today it ranks among the most objective and quantitative of the physical sciences. In today's terms Euclid's work would be classified as psychological optics which is but one of a spectrum of contemporary branches ranging from geometrical, physical/physiological, and meteorological to what might be termed metaphysical optics.

The present study will focus on a single chapter in the complex story of how and why the scope of optics has changed so fundamentally in the twenty-four centuries since Euclid. We shall examine in detail Leonardo da Vinci's writings on optics and suggest where he stands in relation to his seventeenth century successors Kepler, Huygens and Newton.

ii. Images

In the story of how optics developed and changed, Kepler's Ad Vitellionem Paralipomena (1604) marks an obvious milestone. Here Kepler made a basic distinction between two kinds of images: one which would be seen in the air but not measured (imago); the other which could be focussed on walls and other surfaces and be measured (pictura). The imago of sight was subjective: the pictura of light was objective. The study of vision now posed itself as an obstacle to objective science. Kepler's successors followed his advice to concentrate on the pictura and within two generations Huygens and Newton had formulated laws of optics strictly in terms of the science of light. Kepler's distinction between imago and pictura thus played a critical role in shifting the definition of optics from a study of vision to a science of light. What then were the factors that made Kepler's distinctions possible?

In Antiquity the distinction would simply have been unthinkable. Plato, for instance, in his Timaeus speaks about the images of vision and the images of dreams indiscriminately.^[2] For him the eidola of nature and the eidola of the mind are interchangeable. He makes no distinction between a physical eye and the mind's eye. Lucretious' attitude is the same.^[3] The ambivalent treatment of images, whereby mental and physical images are interchangeable, continues in the late Antique writings of Ptolemy and throughout the Arabic tradition. Alhazen appears to come close to making a distinction ^[4] but does not. Nor do his successors in the Latin West: Witelo, John Pecham or Piagio Pelacani da Parma. For these thinkers optics is primarily an intellectual pursuit, is given a certain flair by geometrical diagrams, but remains ultimately a philosophical topic with metaphysical overtones. Experiments one might perform provide interesting themes for discussion. But there is little concern with actually carrying them out.

Leonardo works fully within this tradition. There is evidence that he consulted Witelo's optical compendium.^[5] We know that he copied out the beginning of Pecham's Perspectiva communis.^[6] Yet, where his predecessors had been content to discuss possibilities, Leonardo appears to have made experiments. In volume one, we showed how Leonardo's experimental approach led him to find perspectival laws the existence of which his predecessors and even his elder contemporaries had denied. In the realm of optics he did not actually discover fundamental laws.

His experimental approach was, nonetheless, of enormous significance: it brought to what had traditionally been a domain of mental speculation, a new criterion of physical demonstration. Thereby he set the stage for precisely that distinction between physical and mental image made famous by Kepler. In short, we would claim that Leonardo's work on optics and astronomy provides a basic context for Kepler's treatise on optical astronomy (astronomia pars optica). So dramatic a claim, one might expect, would long since have been thoroughly examined in the secondary literature. In fact it has not.

iii.Survey of Secondary Literature

As noted earlier, (vol. 1, p. ) Leonardo's scientific work was certainly known in the sixteenth and seventeenth centuries. In the eighteenth century Robert Smith mentioned Leonardo's contributions to binocular vision in his Complete System of Opticks (1737).^[7] Venturi (1797) basing his comments on a direct study of the notebooks, claimed that it had been Leonardo and not Maestlin or Kepler who had discovered that the moon's light was caused by reflection from the earth. According to Venturi, Leonardo had also discovered that the twinkling of the stars was actually an illusion originating in the human eye. Venturi went on to note that Leonardo had described the camera obscura and had compared its function with the eye long before Porta or Kepler. Venturi also held that Leonardo had explored the possibility of a telescope.

In the Philosophical Transactions (1838) Wheatstone published a significant essay "On some remarkable and hitherto unobserved Phenomena of Binocular Vision." Wheatstone had observed that when an "object is placed near the eyes that to view it the optic axes must converge: under these conditions," a different projection is seen by each eye. This led him to conclude that it was impossible for artists to give a faithful representation of any near solid object.... When the painting and the object are seen with both eyes, in the case of painting, two similar objects are projected on the retina, in the case of solid object the pictures are dissimilar. Wheatstone searched for precedents and found only the comments in the Treatise of Painting (cf. Smith, 1737 above) and he therefore praised Leonardo as a pioneer in the study of binocular vision.

Even so Leonardo's fame was still far from being universal. When Emil Wilde set out to discuss all writers on optics from the thirteenth to the seventeenth centuries in his standard Geschichte der Optic (1838) he included A. Thylesius and B. Telesius but omitted Leonardo altogether. Libri in his Histoire des sciences mathematiques en Italie (1840) included some fifty pages on Leonardo's science in general, but only a single page to optics. Here Libri based his remarks primarily on Venturi, but also added two discoveries to Leonardo's name: capillary action and diffraction.

Gilberto Govi (1872) had more to say on this theme. He noted Leonardo's work on the camera obscura and his treatment of the eye as an instrument. According to Govi, Leonardo had anticipated Maurolycus with respect to the shape of images on passing through an aperture, and also Bouguer with respect to comparison of different intensities of light. Govi acknowledged the significance of Leonardo's work with concave and convex mirrors. He denied, however, that Leonardo had invented the telescope. In Leonardo's notes on coloured shadows, Govi found an anticipation of von Guericks, Buffon and Scherffer.

Brun (1879) touched on Leonardo's optics, crediting him with invention of the camera obscura and anatomical dissection of the eye. Guardasoni (1880) mentioned Leonardo's interest in stereoscopic vision without citing any specific texts. At the same time he queried whether Leonardo had ever been read by his successors. Raab's Leonardo da Vinci als Naturforscher (1880) appeared that same year. According to Raab the Ancients had explained vision in terms of an extromission process with rays emanating from the eyes and Leonardo had corrected this erroneous view by demonstrating the reverse. To do this, claimed Raab, Leonardo had used a camera obscura. Moreover, to convince his students, he had used a model eye. In Raab's opinion Leonardo had anticipated Kepler by a century.

In 1881 Ravaisson-Mollien published the Manuscript A of the Institut de France. Within a decade he had edited Leonardo's most important notebooks on light and vision (Manuscripts C, D and F) complete with transcription and French translation. Meanwhile, Ludwig (1882) had published the Treatise of Painting with a German translation and Richter his Literary Works of Leonardo da Vinci (1883). Under such headings as "Six Books on Light and Shade" and "Theory of Colours" Richter made a first attempt at organizing Leonardo's optical notes.

Leonardo had claimed that stars seen through a small aperture appear smaller than those seen with a naked eye. He had also held that two flames positioned close to one another, would appear joined together if seen from afar with a naked eye, whereas they would be distinguished as two separate flames if viewed through a small aperture. These claims convinced Theodor v. Frimmel (1892), himself myopic, that Leonardo must also have been myopic. Venturi (1797) and Raab (1880) had credited Leonardo with the invention of the camera obscura. Nonetheless, Muntz (1898) devoted an entire article to the theme and this served, in turn, as starting point for Elsasser (1900) who turned to how the eye functioned. Elsasser claimed that Leonardo had not been aware of the inverted position of retinal images and had instead believed that images in the eye were inverted twice. Nor, according to Elsasser, had Leonardo been aware that the eye functions as a camera obscura. Indeed, he claimed that Leonardo's anatomical ideas of the eye were effectively identical with those of Alhazen. Elsasser was thus led to conclude, that even if Leonardo had described two experiments later repeated by Scheiner, he had not brought about any dramatic advance in the theory of vision.

In this period the other major notebooks containing optical work were being published. Piumati edited and transcribed the Codex Atlanticus (1894-1904) and in the meantime, with Sabachnikoff, produced an edition with accompanying French translation of the Windsor Anatomical Folies A and B (1898-1901). At the same time Rouvèyre was also publishing facsimiles of the Windsor collection (1901). A decade later, Vangenstein, Fonahn and Hopstock began producing a more thorough edition (1911-1916) complete with English and German translation. The optical material in the Codex Arundel (1923-1930) and the Forster Codices (1930-1936) was only published later.

Meanwhile, Colombo (1903) a teacher of optics at Bologna, had studied the existing literature and set out to determine precisely what contribution Leonardo had made in this field. Colombo's point-form conclusions provided a succinct account of the state of scholarship at the time:

Leonardo da Vinci not only knew the principle of the camera obscura but also described the optical instrument that goes under this name (excluding the lens). He recognized that the same principle of the camera obscura should apply to the eye. As a logical consequence he admitted the crossing, within the eye, of luminous rays coming from the objects seen and thus the re-inversion of their images. He observed the movement of the rainbow under the stimulus of light and understood the reason through experiment. He observed that the retina was dazzled through the excess of light and understood the disastrous consequences for the eye of staring at the sun. He noted some phenomena that are characterized by asthenopia, (and) remarked on the existence of the near point of distinct vision and the impossibility of simultaneously seeing nearby and far [things] distinctly. He described retinal adaptation, the persistence of retinal images, [and] consecutive images. He noted that the field of indirect monocular vision exceeded the right angle along the horizontal meridian. He described the phenomenon of the fosteni of pressure. Meanwhile, Baratta (1903) in an appendix to a book on Leonardo's science, published an important discovery: a passage on CA 203ra had been copied directly the Pecham's Perspective communis. This established that Leonardo had first hand knowledge of the most popular mediaeval textbook on optics.

Edmondo Solmi's Nuovi studi sulla filosofia naturale di Leonardo da Vinci (1905) was the first major study of Leonardo's optical writings. Solmi took it for granted that Leonardo had diligently studied earlier authors and that Leonardo was in the mainstream of Western science and philosophy. Solmi divided his study into three parts. The first section dealt with experimental method and had a brief chapter on the role of observation. The second section on astronomy discussed why the apparent rise of the sun, stars and planets was different at the horizon than when seen directly above; why objects in the mist appear larger; what shape is assumed by a light source after passing through an aperture of a different shape; that the twinkling of the stars was an optical illusion, which idea Leonardo probably adopted from Cecco d'Ascoli or via Ristoro d'Arezzo; questions of moonlight and spots on the moon; Leonardo's conviction that the stars have no independent light and his awareness that if the light from individual stars could somehow be combined, this would produce far more light than the moon.

Solmi devoted the third part of his study specifically to Leonardo's theory of vision, beginning with his idea that not only light but also sound, odour, magnetism and even thought are all propagated by wave motion. Solmi went on to show that although Leonardo considered both extromission and intromission theories of vision he clearly favoured the latter. Basic to Leonardo's optics, claimed Solmi, was the concept that every point in the air carries with it infinite images of the things opposite. To test this concept, Solmi claimed, Leonardo had made experiments with the play of light on objects of different colours, with camera obscuras and various mirrors placed in different positions.

Solmi then examined Leonardo's concepts of light: his notion that it is a spiritual force (virtu spirituale) and not material; that light is propagated rectilinearly and spherically; that this spherical propagation is well illustrated through the analogy of a stone thrown into water that produces waves, an analogy that applies equally to sound. Finally he examined Leonardo's studies of mirrors to show that the angle of incidence equals the angle of refraction.

In a second chapter Solmi considered Leonardo's writings on the structure and function of the eye: how he compared the eye with a camera obscura; how he rejected the traditional notion that vision occurs at a point, appealing to both experience and experiments to confirm this and to arrive at the idea that images are formed on the surface of the retina; how and why he conceived of images as "all in all and all in every part"; how he concluded that the visual image was twice inverted within the eye and why he believed that the visual power was located at the extremity of the visual nerves.

In his third chapter "On Sensations and Visual Perception" Solmi considered Leonardo's work on after-images, the effects of pushing the eyeball with a finger; his experiments to determine how pupil size affects the perception of light and shade, optical illusions, binocular vision and its consequences for artists wishing to draw in relief. In his final chapter Solmi examined Leonardo's concepts of colour, his notion that the amount of colour varies with light, his definition of the simple colours, his concept that a mixture of colours could produce infinite variety, his ideas on the rainbow, on the effects of background on both the apparent intensity and size of coloured objects in the foreground and how the apparent size of some lights increase with distance.

Solmi's book was a major contribution towards an understanding of Leonardo's theories of vision and light. It was the first survey to indicate the scope of Leonardo's optical researches. At the same time it made clear that these studies were not to be understood in isolation, that Leonardo's questions and concepts were both a development from earlier authors such as Aristotle and Witelo and a preview of the later work of persons such as Huygens and Helmholtz. To understand Leonardo one thus had to study the entire optical tradition.

Perrod (1907) wrote an article on Leonardo's studies of dioptrics of the eye, which was essentially a collection of quotations from the notebooks to explain how the eye functioned, how it could be likened to a camera obscura, what were the limits of visual acuity, how retinal images persisted and about spectacles. Perrod pointed out that Leonardo had concentrated on healthy vision and had avoided almost entirely the pathology of vision. According to Perrod, he had done little or nothing by way of actual dissection of the eye, and the resulting gaps in his anatomical knowledge had led to inevitable errors. Nonetheless, Perrod acknowledged the profundity of Leonardo's experiments and claimed that his methods were essentially those codified by Helmholtz, Claude Bernard and others.

In 1910, Otto Werner under the supervision of Wiedemann, published a doctoral dissertation at Erlangen, which remains the best overall survey of Leonardo's theories of vision and light to date. The dissertation set out to understand Leonardo's physics and opened with a brief outline of his life followed by a list of sources that Leonardo may have used. Werner provided an outline of earlier theories of vision and turned then to consider Leonardo's concepts; his definitions of the visual species, how these were propagated, how they intersected without interference, his conviction that light did not move instantaneously, his concept of the visual pyramid, its strength and its function.

Werner proceeded to consider Leonardo's ideas on the eye and the visual process. Using a series of diagrams, mainly from the Manuscript D and the Codex Atlanticus, Werner traced in details how Leonardo kept modifying his ideas of the double inversion of images within the eye. This reliance on Leonardo's diagrams marked an important step. For Werner was the first scholar to realize intuitively that the diagrams in Leonardo's notes were not simply illustrations of claims made in the text, but actually functioned as independent visual statements. Werner believed that Leonardo's theory of vision owed much to the Arabic tradition, but had also been modified as a result of his own experiments with the camera obscura. Werner went on to consider Leonardo's work on other optical problems: binocular and stereoscopic vision, optical illusions, his experiments to demonstrate the rectilinear propagation of light. These, claimed Werner, derived mainly from Alkindi and Alhazen. (Werner's supervisor Wiedemann was an expert an Arabic optics and science.) In the case of the camera obscura and images projected through irregular apertures Werner claimed to find precedents in Kamal ad Din al-Farissi and Levi ben Gerson.

Werner next examined Leonardo's statements on reflection in mirrors of various shapes, and proceeded to discuss his notes on dioptrics: his refraction experiments using both glass spheres filled with water and half spheres of crystal. Werner concluded the section with Leonardo's comments on spectacles and rainbows. In the remainder of his thesis, Werner considered briefly Leonardo's acoustics, - the laws of which, as he pointed out, Leonardo himself had compared to optics - and finally heat and magnetism. In spirit Werner's thesis furthered Solmi's approach. Both authors assumed that Leonardo's problems were only to be understood in light of the Western-Latin and Arabic - tradition. In retrospect, however, Werner's search for sources appears somewhat over zealous.

A period of lesser contributions ensued. That same year there appeared also a book by Seidlitz on Leonardo (1910), with a chapter on light and shade, but this scarcely got beyond basic definitions. Feldhaus (1914) produced a short paper on Leonardo's diving and other spectacles. An article by Angelucci (1919) entitled "La maniera in pittura e le legge ottiche di luci e colori" offered less precise analysis than its title promised. Vetri (1926) returned to the theme of binocular vision and stereoscopy. Marcolongo (1929) provided a likely reconstruction of Leonardo's instrument to deal with Alhazen's problem. Moller (1930) published the Weimar sheet (our fig. ) and that same year, Nicodemi (1930) wrote briefly on Leonardo's light. McMurrich (1939) entered upon the problem of the ocular nervous system. In the Corriere della Sera appeared an article which cited Leonardo's perspectival drawing of an armillary sphere (cf. vol. 1, fig. 272) as proof that he had invented the telescope.

The great exhibition in Milan in 1939 led to the construction of 275 models of Leonardo's inventions, plus a two-volume work with chapters on individual aspects of his studies. Among these was an essay on optics by Argientieri, which remains the most enthusiastic assessment of Leonardo's contributions to this field. Argientieri saw in Leonardo's description of the wave motion of light not only a precedent but even a possible source for Huygen's theories. The Ancients, believed Argientieri, had maintained that light was propagated instantaneously and, according to him, Leonardo first recognized the finite speed of light a century and a half before Roemer (1676). Leonardo, claimed Argientieri, had given a clear explanation of the intromission theory of vision. Moreover, Argientieri suggested, he may well have been aware of the Doppler-Fizeau principle. Leonardo, in his discussion of the propagation of rays cites Aristotle to claim that Nature always acts in the shortest way possible. Argientieri forgot Aristotle and saw in Leonardo's claim an early statement of Fermat's law.

Argientieri did acknowledge that Leonardo had been aware of earlier authors, that he was, for instance interested in Alhazen's problem and stimulated by Witelo's refraction studies. But Argientieri's prime concern was to prove Leonardo's modernity: how the fifteenth century genius had discovered properties of colours by mixing light three centuries before Fernel; the laws of photometry long before Bouguer and Rumford; how he experimented with diffraction before Grimaldi; how he invented a projector and even the telescope.

Argientieri pointed out that Leonardo had made model eyes and claimed that his notion about images being twice inverted in the eye had nothing to do with psychological prejudices. It was, according to Argientieri, a result of trying to account for the role of the crystalline lens. Leonardo had also experimented with pupil size, had explored the limits of the visual field and, if he made a few wrong conclusions, Argientieri noted, Leonardo nonetheless anticipated later experiments by Czermak and Scheiner concerning visual perception and anticipated Kepler and Wheatstone in their study of stereoscopy. If Argientieri's study was too generous in its assessment of Leonardo's originality, it nevertheless marked a valuable contribution. Its 104 illustrations, most of them photographs taken directly from the notebooks, provided an important visual survey of Leonardo's optical researches.

The most controversial element in Argientieri's article was his reconstruction of what he believed to have been Leonardo's telescope described on Ms.F 27v at the Institut de France. In July of the same year (1939), Vasco Ronchi, then director of the National Institute of Optics, wrote a three page typescript essay in which he rejected outright the possibility that Leonardo had invented such a telescope. By way of a reply, Argientieri immediately published a 37 page paper explaining a full detail his assumptions and method in arriving at the reconstruction.

Meanwhile the Milan exhibition was attracting interest abroad. In Britain the ophthalmologist Walter Gasson (1939) was prompted to write an article on Leonardo's optical contributions in which he mentioned themes such as binocular vision, rectilinear propagation of light, the twinkling of stars, optical illusions and the laws of perspective. Gasson claimed that Leonardo appeared not to have been acquainted with Euclid's Optics. Gasson believed that Leonardo had been aware of the possibility of telescopes, but found no clear evidence of his ever having constructed one.

The following year the models from the Milan exhibition travelled to the United States where they inspired further interest. Ingalls (1940), in an enthusiastic Scientific American article reported how he believed he had been the first to guess that Leonardo was acquainted with telescopes until, on consulting Nicodemi, he learned of Argientieri's work. Maestro (1941) mentioned another optical invention of Leonardo: the diploscope. The following year, Boring (1942) brought Leonardo's work on binocular stereoscopic vision to the attention of psychologists, describing it as "Leonardo's paradox."

At the instigation of Elmer Belt, Nino Ferrero (1951) produced "an original new translation" of the Manuscript D, but with the exception of fol. 9v, he omitted the diagrams. Ferrero offered no analysis, only a note to indicate that Leonardo had discussed optics elsewhere in his writings, and a bibliographical survey listing the studies of Angelucci, Argientieri, Elsasser, McMurrich, Perrod and Venturi. O'Malley and Saunder's (1952) publication served to render more accessible some of the pertinent anatomical drawings but did not significantly advance understanding of Leonardo's optics. Pirenne (1952) in an important article established that linear perspective corresponded with optical reality.

Hofstetter and Graham (1953) claimed that Leonardo had invented contact lenses. Sergescu (1953) returned to Leonardo's instrument for dealing with Alhazen's problem. Abetti (1953), made general claims that Leonardo's optical work was based primarily on Witelo who had, in turn, drawn upon "the rudimentary theories of the Arabic scientist Alhazen." According to Abetti, Leonardo had made accurate studies of shadows, had explored the camera obscura, was interested in the principles underlying the telescope but there was no evidence that he ever constructed one. Senaldi (1953) mentioned Leonardo's anatomical studies of the eye.

Zubov (1954) in an important article in Russian, identified several passages with striking parallels between Leonardo and his mediaeval predecessors Alhazen and Witelo. At the same time, Zubov noted differences in Leonardo's approach: where Witelo had been content with a general statement, Leonardo had turned to experiments. Where Witelo had been satisfied with certain isolated examples, Leonardo had insisted on every possible combination, claimed Zubov. Indeed, he concluded, Leonardo's studies could be seen as a concrete version of Witelo's abstract themes.

Brizio (1954) showed that there were clear connections between some optical notes in the Codex Atlanticus, the Folio B at Windsor and the Manuscripts A and C at the Institut de France. Ronchi (1954) believed that Leonardo's philosophical doubts had ultimately led him to mistrust the sense of sight. Ronchi claimed that Leonardo had learned about the camera obscura and various other optical phenomena from Alhazen and Witelo, but that he had never actually experimented with the camera obscura. Ronchi was, moreover, of the opinion that Leonardo had probably been slightly myopic. As evidence he cited a passage in the Treatise of Painting in which Leonardo claimed that the white hat of a woman dressed in black would appear larger than it actually was. Ronchi turned to what he considered to be Leonardo's entirely confused notions of how bodies produce rays that are propagated spherically. Ronchi was, moreover, convinced that there was no serious evidence that Leonardo had ever constructed a telescope.

Keele (1955) assessed Leonardo's work on vision from a medical standpoint, acknowledging his debt to earlier authors but adding that the experiment described in Manuscript K marked "one of the earliest examples of the technique of imbedding tissue for section-cutting." Leonardo's belief in the double inversion of images in the eye was, claimed Keele, based on observation and experiments. According to Keele, Leonardo had also experimented with the camera obscura, had made models of the eye, and had examined the effect of adjustments in the pupil's size. Keele went on to suggest that Leonardo had worn glasses for presbyopia and that this would explain why Leonardo discussed presbyopia while making no mention of myopia. Keele noted that Leonardo had also studied the optic nerves, had arrived at a masterful diagram of the optic chiasma, explored eye movements and stereoscopic vision.

Garin (1956), found in Ronchi's assessment of Leonardo's optics a "most serious and balanced contribution," but felt, nonetheless, that Ronchi had overemphasized Leonardo's intromission theories. Garin pointed out that the notebooks also evidenced extromission theories. Garin saw certain similarities between Leonardo and Bacon; was of the opinion that Leonardo must have known Alhazen and Witelo either second-hand or through a compendium; disagreed with Abetti's judgment that Alhazen was rudimentary. In conclusion, Garin called for a more detailed comparison between Leonardo's notes and to his optical treatises.

Giovannini (1957) offered another summary of Leonardo's optical work, alluding to his anatomical researches, his experiments with the camera obscura, his study of binocular vision, the principles of photometry and the laws of contrast. In Giovannini's opinion Leonardo was far ahead of his time. Keele (1961) returned to develop themes raised in his earlier article. He examined the development of Leonardo's concepts of the optic chiasma and the cranial nerves, analysed the Weiman sheet and emphasized the significance of his injecting the cerebral ventricals with wax. Thereby, Leonardo had revealed a cerebral central mechanism of vision. That same year, Garin (1961) broached afresh the problem of Leonardo's sources, challenging the approach of Duhem and Solmi who had assumed Leonardo could read. Garin believed that Leonardo was illiterate (omo sanza lettere) and that he had acquired his knowledge either second-hand through compendia or even third-hand through conversations with learned friends and patrons. By modern standards, claimed Garin, Leonardo's scientific achievements had been "very modest." In support of this opinion he cited Ronchi's negative conclusions.

A study by Pedretti (1962) of a manuscript, (H 227 Inf.) in the Ambrosiana provided important evidence concerning lost chapters from Leonardo's book on light and shade. The manuscript, compiled by Father Antonio Gallo (1639-1640) appears to have marked a first anthology of Leonardo's notes. Pedretti's study ended with a useful concordance between the manuscript and the notebooks. A general article on Nature and vision in Leonardo's work by Bottari (1963) may simply be mentioned in passing.

Brizio (1963) basically accepted Ronchi's negative assessment of Leonardo's optical work. She questioned, however, whether Leonardo was best understood through comparison with modern concepts. Her alternative was to compare him with earlier authors such as Witelo on the question of reflection in convex and concave mirrors. The close parallels she found between Leonardo and Witelo led Brizio to challenge Ronchi and Garin's claim that Leonardo had been unaware of the mediaeval optical tradition.

A doctoral dissertation by Strong (1967), supervised by Pedretti, marked the most detailed study to date of Leonardo's optical researches. Strong centred his work around the Manuscript D, which he translated into English before reassembling its contents and assessing its significance for the chronology of the other manuscripts. Strong compared statements in the Manuscript D with analogous comments in other notebooks. In a chapter on Leonardo's method Strong emphasized how his ideas had evolved with time. After 1505, claimed Strong, Leonardo became increasingly interested in determining the causes of things and establishing the mathematical certitude of phenomena, a trend which Strong attributed to Pacioli's influence. Strong then turned to assess the position of the Manuscript D in the late mediaeval optical tradition. He characterized the change from thirteenth to fourteenth century optics as a shift from metaphysical to physical interests. Strong noted some problems of definitions of terms and how Leonardo had alternatively considered both intromission and extromission theories of vision. In reply to Garin's claim that Leonardo had acquired his knowledge primarily from discussions and vernacular texts, Strong insisted that the evidence is overwhelming that Leonardo sought out and confronted directly classical and Mediaeval treatises pertinent to his interests in the libraries of Florence, Milan, Pavia, Urbino and Rome.

Strong proceeded to mention some of the texts most likely to have influenced Leonardo: the anonymous Della prospettiva, Euclid's Optics, Giorgio Valla's De fugiendis et expetendis rebus, the anonymous De visione stellarum, Alhazen and Witelo's optical writings, Roger Bacon's Opus Maius, which offered direct comparisons with Leonardo's ideas, and John Pecham's Perspectiva communis. Study of this mediaeval tradition revealed the Leonardo had not been the inventor of the camera obscura nor the first to discuss eye movements. In a final chapter, Strong considered the impact of Leonardo's optics in his art; how his optical studies of the mobile eye could account for Leonardo's interests in anamorphosis, and that these studies on the mobile eye had, in any case, aimed to eliminate Alberti's "recalcitrant space" and his principle of the immobile eye. Strong went on to claim that Leonardo's modelling techniques were an attempt "to exploit the mobile eye and its contact with the form to intensify the visual experience." Strong saw the forma serpentina of the Leda as an illustration of this.

Lindberg (1975), in an otherwise important book on the history of visual theories came to a very negative assessment of the "man without letters," which began with a brief summary of Leonardo's opinions on radiant pyramids and intromission/extromission theories. The standard interpretation claimed that Leonardo's approach to vision was mechanistic. Lindberg rejected this interpretation, claiming that it resulted from a misunderstanding of Leonardo's analogy between the spherical diffusion of light and the circles produced by stones thrown into water.

In Lindberg's estimation Leonardo's anatomical work was "exceedingly primitive" but had, nonetheless, led to two contributions: study of the variable diameter of the pupil and the analogy between eye and camera obscura. Lindberg believed that if Leonardo owed a "very substantial debt to the past," his writings confirmed that he had no understanding at all of the central issue of traditional optics - the problem of a multiplicity of rays from every point in the visual field influencing all parts of the eye. According to this view Leonardo is thoroughly confused concerning the entire mediaeval tradition and his writings reveal that "the problem of sight was not to be solved through a fresh start by an ingenious empiricist working in an intellectual vacuum."

Borsellino and Maltese (1976) analysed Leonardo's experiments in the Manuscript D using a needle viewed through a pin-hole in a piece of paper and concluded that Leonardo had thereby discovered "some curious deceptions of the senses," but had not arrived at the modern explanation.

In his important Richter Commentary, Pedretti (1977) drew attention to new manuscripts, hitherto untranslated passages on light, shade and vision as well as providing a host of suggestions concerning the chronology of individual notes. Kemp (1977), cf. 1981) felt that scholars had not appreciated sufficiently the traditional roots of Leonardo's ideas and set out to show that Leonardo's optical studies "centre on essentially mediaeval themes." As examples he cited the concept of the visual pyramid and the idea that vision is "all in all and all in every part." Ackerman (1978) also analysed this idea in an article which surveyed Leonardo's optics in relation to the mediaeval tradition and mentioned some consequences of his optics on painting. While introducing little that had not been discussed previously, Ackerman provided a useful survey for non-specialists. An article by Ehrich (1979) provided a useful summary of literature concerning Leonardo's supposed invention of contact lenses and provided an experimental reconstruction of the same.

The new edition of the Windsor Corpus by Keele and Pedretti (1979-1981) has provided a valuable new transcription, a first complete English translation of the anatomical notes, and has radically altered our picture of the chronology of these notes. Keele (1983), who describes knowing "how to see" as Leonardo's gateway to science, provides a lucid survey of his studies on optics and vision. Keele emphasizes links between vision and perspective in Leonardo's approach, outlines his definitions of light and shade; his concepts of the pyramidal nature of light and connections with the four powers of Nature, especially percussion; his experiments with the camera obscura, how light spreads in circular waves and how all the powers involve movement. In the second part of the chapter Keele examines Leonardo's writings on the physiology of the eye, the optic chiasma, the ventricles, their location, their link with the soul; Leonardo's theories of extramission and intramission, the experiments he carried out concerning these theories, his concepts of the pupil, cornea, optic nerve and imprensiva.

The above survey, in which we have deliberately limited ourselves to the most important articles and books on Leonardo's optics, reveals that a great deal has been written on the subject. It also confirms that much remains to be done. Most of the contributions have been piecemeal, concentrating on whether Leonardo invented or mentioned this or that. How often he mentioned a problem: whether it occurred merely in passing or whether it was a recurrent theme in his notebooks has usually been overlooked. And notwithstanding the admirable contributions of Werner and Strong, there exists as yet no comprehensive study of Leonardo's optical researches. This will be an aim of the present study.

iv. The Problem of Sources

On the question of Leonardo's literacy, whether he stood fully within the optical tradition or whether he did not, there are two radically opposed schools of interpretation. One, championed by figures such as Santillana, Sarton, Garin and Lindberg believes that Leonardo was truly a man without letters8 (omo sanza lettere) and that the great wealth of classical and mediaeval learning was literally a closed book for him. According to this school his awareness of the optical tradition was at best incidental and gained second-hand through vernacular compendia and by word of mouth with learned friends. It bears noting that no member of this school has read the complete works of Leonardo carefully.

A second school has insisted that Leonardo's optical - and other - studies cannot be understood without a detailed knowledge of classical and mediaeval sources. The champions of this approach have tended to be specialists on Leonardo: Solmi, Werner, Brizio, Keele, Pedretti, Strong and Kemp9 to mention only some. Considering that Leonardo had a personal library of at least 116 books10, many of them in Latin, there is, in our opinion, little doubt that he must have been aware of the optical tradition and in the course of this work we shall present evidence to establish this viewpoint.

Indeed, at one point in the research it seemed a reasonable ideal to read through all the major optical sources such as Euclid, Ptolemy, Alkindi, Alhazen, Witelo and Pecham in an attempt to solve these debates once and for all. On reflection however it became clear that this attempt really involved two quite independent questions: first, whether Leonardo was aware of a problem in the tradition and secondly, what was the particular source of his knowledge of that problem. The first of these questions can be answered assuming one knows sufficiently the whole of Leonardo and the whole of the optical tradition. The second question often cannot be answered.

The second question concerning direct sources remains difficult. Euclid's Optics was available in various mediaeval manuscript. Witelo had also included almost all its propositions in the fourth book of his great optical compendium to which, incidentally, Leonardo refers at least five times. A number of the propositions in Euclid's Optics recur in Bacon, Pecham, Biagio Pelacani da Parma, the anonymous author of Della prospettiva and even in Alberti's Della pittura.

A serious search for sources would therefore require confronting each of Leonardo's phrases with each of these authors and then with all their manuscript variants. For this reason we have limited ourselves to pointing out parallels between the tradition and Leonardo's work. It remains for a future student, possibly with the aid of a computer, to establish whether one can identify specific manuscripts from which he copied verbatim. For the present only Pecham's Optics and Alberti's Elementa picturae (cf. below p. ) are known.

v. Scope of the Present Study

Nonetheless, the general question of Leonardo's relation to the optical tradition will be one of the basic themes of our study, which will open with an introductory chapter on how the meaning of optics gradually shifted from sight to light, how the qualitative concerns that dominated Euclid's Optics were gradually replaced by a quest for quantitative analysis. In short we shall outline the tradition that prepared the way for Kepler's distinction between subjective and objective images, between the imago and the pictura. Within this context we shall examine in detail Leonardo's optical researches and contributions.

In the first volume of our studies it was shown that the whole of Leonardo's science sprang from a combination of his perspectival studies with his concept of the four powers. This second volume offers a case study of the general proposition explored in the first. There we were concerned with the whole of his science. Here we are concerned only with his optics. There we were concerned with all four powers: percussion, force, impetus and movement. Here we are concerned chiefly with percussion, since this power underlies the whole of his physics of light and shade. The link between percussion and optics, we shall find, is an Ancient one: it can be traced back at least to Aristotle, and we shall follow its development through Ptolemy, Alhazen and Pecham, examining how Leonardo inherits it and transforms it.

We shall turn then to Leonardo's definitions of basic optical concepts such as point, line, rectilinear propagation, pyramid and pyramidal diffusion, again note precedents, and go on to examine the physical and metaphysical roots of Leonardo's concept that images are "all in all and all in every part."

With this understanding of the historical context of Leonardo's ideas we shall, in part two, enter into the details of his physics on light and shade. Following a list of basic definitions and distinctions we shall reconstruct the contents of his proposed seven "books" - chapters in our terms - on light and shade, plus a further book on the movement of shadows. This will reveal various aspects of his systematic approach. Parallel with these demonstrations in the open air, there are a number of others involving the use of a camera obscura. That Leonardo was familiar with the camera obscura. That Leonardo was familiar with the camera obscura is well known: that he devotes over two hundred and thirty figures to this problem has never before been suspected. Among these diagrams will be found further evidence of his systematic experimental approach, which ultimately served to confront metaphysical speculation with the realities of physical demonstration.

Part three will focus on Leonardo's studies of the eye and vision. By way of introduction his notes on the eye as the noblest of the senses and as window of the soul will be cited. His demonstrations concerning the anatomy and physiology of individual parts of the eye such as eyelids, cornea and optic nerves will then lead to his theories of the visual process: his opinions on extromission versus intromission theories; his study of the idea that images converge to a point; his demonstrations to refute this, his interest in both single and double inversion of images in the eye and his experiments in which he substitutes a camera obscura for the pupil and a glass sphere filled with water for the crystalline lens.

Leonardo is also very interested in the conditions under which the eye is deceived. It will be shown that the situations which he considers have numerous parallels with Euclid's Optics, a difference being that were Euclid remains abstract and geometrical, Leonardo provides concrete examples from everyday experience. This interest in subjective visual appearances leads him, in turn, to explore optimal and minimal conditions for vision, including the role of the central ray, the visual field, distance, size, light as well as monocular and binocular vision.

Part four will open with Leonardo's demonstrations and comparative studies of pupils in animals and humans and lead to consideration of a connection that he saw between pupil size and apparent size, a connection that reveals why optics and astronomy are so closely linked in his mind and indeed why he felt that his studies of the eye were ultimately a prelude for his studies of the heavens. Leonardo was preoccupied with the optical part of astronomy as was Kepler a century later. To support this claim the structure of the Manuscript D will be reconsidered. An analysis of the Manuscript F will reveal another treatise of 21 consecutive pages on this theme. A further series of notes from the Manuscript F and the Codex Arundel will serve in the reconstruction of Leonardo's projected Fourth Book: On the Earth and Its Waters which reveals why he became so fascinated with reflections of the sun in water. If the surface of the water is completely smooth, the reflection is small. When there are waves, each of these waves functions as an individual mirror and reflects the sun, such that the whole surface becomes aglow with reflected light. Leonardo takes this principle and proceeds to ask what would happen if one looked at the ocean from a position high above the earth. He imagines that the entire ocean would reflect the sun's light. His imagination now takes over. If a planet were entirely covered with oceans, he reasons, then the whole planet would reflect light. Once a month the full moon reflects light over its entire surface. Ergo the moon must be covered with oceans.

Very much aware that there are competing explanations for the full moon Leonardo sets out to explore their viability: one is that the whole surface of the moon is like a convex mirror. He therefore studies the nature of images in convex mirrors and in the end demonstrates why the mirror hypothesis cannot explain why we see the full moon. And having accounted for this Leonardo turns finally to eclipses. Thus the whole of his study of optics as it is on earth is ultimately in order to understand astronomy as it is in heaven.

In the appendices will be collected Leonardo's notes on optical instruments such as spectacles, his much debated telescope, lens grinding instruments, his work on mirrors plane, convex and concave and finally on meteorology celestial - haloes - and terrestial - rainbows. The challenge of presenting this material in a comprehensible form has led to a threefold approach. First, there is a problem of understanding Leonardo in his own terms. This requires that we imagine ourselves in his world, (what the Germans call sitz im Leben and some term horizontal history), that we enter into his way of thinking and re-construct his arguments, as he himself might have done had there been more time, or if he had a good secretary. This approach is the main focus of this study.

A second approach is useful in order to establish the validity of his claims using a positivistic standard (verticle history). Ideally, such an approach would include an experimental reconstruction of all his demonstrations and claims: a task for a future project. Inherent in this approach, however, is the temptation of a holier than thou attitude, as if history could be reduced to the question: how many marks would Leonardo get on a modern physics test? To understand an individual also requires insight into why a person stops asking questions; to discern how a man with a critical mind can accept a wrong answer as the correct solution; to perceive how a way of explanation can become so convincing that it remains a close system. In becoming sensitive to why a Leonardo is often blind by our own standards, we become aware that even the most modern among us today is, in turn, equally blind when judged by standards of tomorrow. Hence blind alleys of the past may prompt new avenues for the future. But these are questions of philosophy.

Although an historian of ideas may point to such questions his main task lies elsewhere. In creating an intellectual biography of Leonardo it is not enough to end with an elegant list of the man's knowledge and opinions. Insight is required into why Leonardo wrote the notebooks the way he did. Here a third approach is necessary to comprehend why an individual with such coherent arguments should present them in what strikes us at first as an incoherent manner (eg. figs. ).

Such a threefold approach may be eminently logical and easy to describe in theory but in practice this does not eliminate the problem of comprehension. In Leonardo's notebooks a paragraph ostensibly devoted to one problem inevitably slides into two or three others. If, for instance, on W19150r (KP 118r, 1508-1510), he begins by speaking about the rectilinear propagation of light, he may well demonstrate this by means of a camera obscura and then, carried away by his camera obscura-eye analogy, discuss the nature of rays in the eye. Hence a paragraph that begins as physics of light ends as physiology of vision.

Leonardo's train of thought is easy to follow. The problem comes when we wish to analyse his work from a positivistic point of view and need to break things down into separate problems: physics of light, camera obscura, anatomy of the pupil, physiology of the eye, etc. For we then find ourselves with a choice of either repeating each paragraph three or four times or creating what easily becomes a labyrinth of cross-references.

There are further problems. When he feels something is important he repeats it to the point of boredom and beyond. The idea that the surface of a body participates in the colour of the surrounding objects is a case in point. There are some 75 passages on this idea alone (see below pp. ). On closer inspection it is found that these passages involve various kinds of proofs. One involves concrete objects in the open air (fig. ), another involves a camera obscura (fig. ), and a third involves a purely mathematical demonstration (fig. ). Each of these demonstrations is in turn related to others of its kind, for instance, the mathematical demonstration to show that colour participates is one of a coherent set of abstract mathematical demonstrations. In this case it is desirable to refer to a proof once under the idea it supports and a second time under the type of proof.

The result is a web of ideas which is often repetitive and which, on first encounter, prompts the question: "why didn't he...?" As we enter further into the labyrinthine logic of his mind, however, we find ourselves thinking afresh about physics of light and shade, the visual process, problems of perception and connections between optics and astronomy. The quality of some minds is measured in terms of the rightness of wrongness of their answers. There are rare minds, however, where the assessment of quality involves other criteria: where the actual answers are less important than the process of asking questions; where questions become windows into new landscapes of experience which provoke one to look afresh at oneself and the world around one with a new sense of wonder. This study is a journey into the landscapes of such a mind, replete with fields of unfinished thoughts.