Peri optikes [in Greek], id est de natura, ratione, & projectione radiorum visus, luminum, colorum atque formarum, quam vulgo perspectivam vocant, libri X.

Nuremberg: Johann Petri, 1535.

First edition, rare, and a fine copy, of the first comprehensive European treatise on optics, and the first work to contain descriptions of medieval laboratory instruments. Witelo (born ca. AD 1230) begins with the geometrical theorems required for the optical demonstrations of the remaining books. He details the essential features of optical systems, including the theory of the nature of light and its propagation, reflection by plain and curved mirrors, light, colour, perspective, the rainbow, etc. Witelo’s principal source was the Optics of Ibn al-Haytham; the present text, Witelo’s Perspectiva, is thus the first printed source for Ibn al-Haytham’s work, which was not published until 1572 (when it accompanied a reprint of Witelo’s text). “The most outstanding feature of Witelo’s method was his combination of manual and technical skill with mathematics for quantitative experiments with instruments. An excellent example of the use of this combination in the construction of an instrument is his work on the parabolic mirror, with which Alhazen’s writings as known in Latin showed no acquaintance … The problem was to construct a burning-mirror that would concentrate the sun’s rays at a single focal point … Another important example of Witelo’s method is his work on the measurement of the angles of refraction at the surfaces between air and water, air and glass, and glass and water, respectively … [Witelo gave a detailed account] of the construction of [an] instrument for measuring the angle between incident and emergent rays … Witelo used this instrument to show that not only white light, but also colours travelled in straight lines in a single uniform medium … Having given an account of the refraction of light at different surfaces, Witelo went on to discuss the properties of convex and concave lenses … A more successful application of his knowledge of refraction was his study of the rainbow … The only source of knowledge of the rainbow he acknowledged by name was Aristotle’s Meteorology, but his chapters contain much that is not in this work … In the atmosphere he held that drops of water would condense as spheres … Rays from the sun would meet the drops on the outside of the mist; and, of the rays falling on each drop, some would be reflected and some would be refracted … as by a spherical lens … The rainbow would be seen in the rays which, after going out from the sun to the mist in one cone, were reflected back to the eye of the observer on a shorter cone with the same base and axis … [Witelo tested his theory] by means of experiments with refraction through crystals and spherical vessels filled with water … [Witelo] made some admirably original observations on the more purely psychological aspects of vision. These related chiefly to direct perception and the effects of association and reasoning on vision, and such problems as illusions, visual beauty, and the perception of distance and size and of the third dimension of space” (Crombie). This work remained an important textbook for over 300 years: it had a great impact on the works of Regiomontanus, Leonardo da Vinci and Copernicus, and was the basis of Kepler’s Ad Vitellionem paralipomena of 1604. ABPC/RBH record the sale of seven complete copies at auction: Pierre Berge 2019, €10,110 (modern binding, last gathering washed and repaired); Christie’s NY 2008, $62,500 (Dunham-Green copy, 19th century binding); Sotheby’s 2002, £32,450 (De Vitry copy, later vellum-backed carta rustica); Sotheby’s NY 2001, $55,375 (binding restored, dampstaining and worming); Sotheby’s NY 1993, $16,000 (Dunham copy); Sotheby’s 1981, £1,300 (Honeyman copy, dampstained); Sotheby’s 1973, £580.

By far the most important optical treatise in Witelo’s day was Ibn al-Haytham’s Optics or De aspectibus, rendered into Latin by an unidentified translator late in the twelfth or early in the thirteenth century. Although Witelo never refers to Ibn al-Haytham by name, there can be no doubt that the latter was his chief source: Witelo normally treats the same topics in the same fashion and sometimes even in the same words; occasionally he omits or inserts a topic, and often he seeks to clarify or supplement one of Ibn al-Haytham’s points by further elaboration or an improved demonstration, but in very few respects does he escape the general framework inherited through the latter’s Optics.

“Yet other influences are evident. It is beyond dispute that Witelo used the Optica of Ptolemy, whose table of refraction he reproduces; the Catoptrica of Hero, whose principle of minimum distance he employs to explain reflection at equal angles: and the De speculis comburentibus (anonymous in the thirteenth century. but now attributed to Ibn al-Haytham), from which he drew his analysis of paraboloidal mirrors. There can be little doubt that he also was familiar with the widely circulated Optica (De visu) of Euclid, Catoptrica (De speculis) of Pseudo-euclid, De aspectibus of al-Kindī, and the physiological and psychological works of Galen, Hunayn ibn Ishāq, Ibn Sīna; and Ibn Rushd. As for Latin authors, Alexander Birkenmajer has argued that Witelo was strongly infuenced by Robert Grosseteste’s De lineis angulis et figuris and Roger Bacon’s De multiplicatione specierum. In addition, it is certain that he knew Bacon’s Opus maius and possible that he knew John Pecham’s Perspectiva communis. Witelo also relied on a number of ancient mathematical works, including those of Euclid and Apollonius, and perhaps of Eutocius, Archimedes, Theon of Alexandria, and Pappus.

“Witelo’s Perspectiva is an immense folio volume … The scope of the Perspectiva is revealed by the following outline of its contents: Book I consists of definitions, postulates, and 137 geometrical theorems, which provide the mathematical principles required for the optical demonstrations of the remaining nine books. In this book Witelo skillfully summarizes the aspects of the geometrical achievement of antiquity that are relevant to his own geometrical optics. Book II deals with the nature of radiation, the propagation of light and color in straight or refracted lines, shadows, and the problem of pinhole images, Book III is concerned with the physiology, psychology, and geometry of monocular and binocular vision by means of rectilinear radiation. Book IV treats the perception of the twenty visible intentions other than light and color, including size, shape, remoteness, corporeity, roughness, darkness, and beauty. It also deals with errors in the perception of these intentions – principally errors in judging distance, shape, and relative size. This book is thus largely psychological in tone, although it includes a number of matters that fall into the realm of traditional geometrical perspective. In book V, Witelo considers vision by reflected rays, beginning with the nature and geometrical laws of reflection and proceeding to a detailed analysis of plane mirrors. Image formation in curved mirrors occupies books VI through IX of the Perspectiva – convex spherical mirrors in book VI, convex cylindrical and conical mirrors in book VII, concave spherical mirrors in book VIII, and concave cylindrical, conical, and paraboloidal mirrors in book IX. Book X is concerned with vision by rays refracted at plane or spherical interfaces; it also includes a discussion of the rainbow and other meteorological phenomena.

“The most essential feature of any optical system might seem to be its theory of the nature of light. Witelo’s concerns were principally geometrical, however, and he formulated no systematic account of the nature of light. From scattered remarks throughout the Perspectiva (particularly its preface) one can hope at the very most to classify him within a broad tradition on this question. He writes in the preface: ‘Sensible light is the intermediary of corporeal influences’; ‘Light is a corporeal form’; and ‘Light is the first of all sensible forms.’ It is apparent from such remarks that light is regarded as the intermediary in certain natural actions – an instance of the multiplication of forms. Light is thus one particular manifestation of a more general phenomenon, the propagation of force of influence from one natural body to another. But although light is only one instance of natural action, it is the instance most accessible to the senses and most amenable to analysis; therefore it serves, for Witelo, as the paradigm for the investigation of all natural actions. Thus he writes, at the conclusion of his quantitative analysis of refraction, ‘These are the things that occur to lights and colors and universally to all forms in their diffusion through transparent bodies and in the refraction that occurs in all of them.’ And in the preface he remarks, ‘The investigation [in general, of the action of one body on another] properly proceeds by means of visible entities.’ It is evident, then, that Witelo falls very generally into the Neoplatonic tradition traceable from Plotinus through Ibn Gabirol to Grosseteste and Bacon. For Witelo, as for these predecessors, every natural body propagates its power to surrounding bodies, of which propagation of light is the principal example. Moreover, Witelo would seem to follow Grosseteste and Bacon in perceiving that optics thus becomes the fundamental science of nature.

“A second essential feature of any optical system, about which Witelo says somewhat more, is the propagation of light or visible forms. According to Witelo, light is always propagated rectilinearly unless it encounters a reflecting or refracting surface. This fact, he claims, can be verified experimentally; and he even describes the required apparatus. The same apparatus had already been described by Ibn al-Haytham, however, and there is no reason to believe that Witelo personally verified the rectilinear propagation of light by experimental means. Witelo is uninformative on the physical mechanism of propagation, but one can surmise from his use of terms like ‘multiplication’ and ‘diffusion’ that his view was not far from that of Roger Bacon. He departs from Ibn al-Haytham and Bacon and most of the ancient optical tradition on the temporal aspects of propagation, arguing that light requires no time for propagation through an extended medium. He proceeds on logical grounds, reducing to absurdity the claim that the propagation of light requires time. Witelo is unable to maintain this position, however, and later admits that ‘every light passing through a transparent body transverses it with an exceedingly swift and insensible motion. And yet the motion occurs more swiftly through more transparent bodies than through less transparent bodies.’

“The applicability of geometry to optical problems follows from the principle of rectilinear propagation: light proceeding along straight lines, subject only to the rules of reflection and refraction, clearly is amenable to geometrical analysis. Witelo draws a careful distinction, however, between the one-dimensional lines employed in a geometrical analysis of optical phenomena and actual rays (or radial lines) of light. The latter are real physical lines traversed by the smallest visible light, and ‘in the least light that can be supposed, there is width . . . Therefore in a radial line alone which light is diffused, there is some width.’ Nevertheless, ‘in the middle of that [radial line] is an imaginary mathematical line, parallel to which are all the other mathematical lines in that natural line.’ And since the mathematical lines always fall within the natural radial lines, the former adequately represent the actual path of light, and it is proper to employ them in optical demonstrations.

“It was still a matter of debate in the thirteenth century whether rays issue only from the visible object or whether, in addition, there is an emission from the observer’s eye that assists in the act of sight. Witelo follows Ibn al-Haytham (and departs from Grosseteste, Bacon, and Pecham) in acknowledging no emission of visual rays from the eye; sight is due solely to the forms of light and color issuing in all direction from every point (or small part) of the visible object and entering the observer’s eye to produce visual sensations.

“Witelo also follows Ibn al-Haytham (and the entire ancient and medieval optical tradition) in declaring that the sensitive organ of the eye is the glacial humor (or crystalline lens), which occupies the central position. Sight occurs, therefore, when the forms of light and color are arranged on the surface of the crystalline lens in the same order as the points of the visible object from which they issued: on the surface of the crystalline lens there is a ‘union of the visible forms and the soul’s organ,’ which constitutes the act of sight. But how is it possible for light to be arranged on the surface of the lens exactly as on the surface of the object, since light issues in all directions from every point of the object? Witelo supplies precisely the same answer as Ibn al-Haytham, Bacon, and Pecham: only unrefracted light is strong enough to be efficacious in sight, and there is but one unrefracted ray issuing from each point of the visible object – the ray proceeding toward the center of curvature of the humors and tunics of the eye. The collection of all such unrefracted rays maintains its configuration between the visible object and the glacial humor and consequently forms, on the surface of the latter, an exact image (albeit reduced in size) of the visible object. Yet the act of sight is not completed in the glacial humor; the forms it receives pass through to the optic nerve and thence to the anterior part of the brain, where the nerves from the two eyes intersect to form the ‘common nerve,’ the residence of the visual power or ultimum sentiens, where a final judgement is made.

“The geometrical structure that Witelo builds upon the conception of rays and mathematical lines naturally encompasses problems of geometrical perspective and image formation by reflection and refraction, but it also extends to the anatomy of the eye and the act of sight. He describes the eye in traditional terms, as a composite of three humors – glacial or crystalline, vitreous, and albugineous (aqueous) – and four tunics – uvea, cornea, conjunctiva or consolidativa, and aranea or retina. Geometrical considerations predominate in Witelo’s descriptions of these tunics and humors: all are spherical in form; all tunics and humors anterior to the glacial humor must have concentric surfaces, so that a ray perpendicular to one is perpendicular to the rest and passes through all of them without refraction; and the glacial and vitreous humors have precisely the necessary shapes and relative densities to refract the rays converging toward the center of the eye before they actually intersect, and to conduct them through the vitreous humor and optic nerve without alteration or inversion.

“Books V-IX of the perspectiva are devoted to the science of catoptrics. The foundation of this science is the law of reflection, which Witelo drives from the principle of minimum distance: since nature does nothing in vain, it ‘always acts along the shortest lines.’ Following Hero of Alexandria, Witelo demonstrates that the shortest lines connecting two points and a reflecting surface are those that make equal angles with the surface. He also argues that the plane formed by the incident and reflected rays is perpendicular to the surface of reflection (or, in the case of curved mirrors, its tangent), and that an object seen by reflection appears to be located where the backward extension of the ray incident on the eye intersects the perpendicular dropped from the visible object to the reflecting surface.

“Employing these three rules and the principles of geometry, Witelo proceeds to solve a series of very abstruse problems in reflection, drawn primarily (but not entirely) from Ptolemy an Ibn al-Hay-tham. This is the most substantial section of the Perspectiva, occupying much of books V-IX and some 200 pages in the printed editions. Witelo deals skillfully with such problems as inversion and reversal of images, determination of precise size and location of images formed by concave and convex mirrors of various shapes, and computation of the number of images of a given object visible in a concave spherical mirror. Not until the seventeenth century was his catoptrics excelled in the West.



Folio (313 x 205 mm), ff. [iv], 298 (the last blank), title printed in red and black and with a large woodcut optical vignette, full-page woodcut arms, and numerous woodcut diagrams in the text. Contemporary blind-stamped calf (minor restoration to joints, edges and head and tail of spine). A fine, clean and crisp copy.

Item #5136

Price: $120,000.00

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