Perspectiva in qua, quæ ab aliis fuse traduntur, succincte, neruose & ita pertractantur, ut omnium intellectui facile pateant … Edited by Johann Combach. [Bound with:] Specula mathematica: in qua, de specierum multiplicatione, earundemque in inferioribus virtute agitur: liber, omnium scientiarum studiosis apprime utilis … Edited by Johann Combach.

Frankfurt: Wolfgang Richter for Anton Humm, 1614.

First editions of these two rare works on optics by the ‘Doctor Mirabilis’ Roger Bacon (1214/1220-1292) – ‘perspectiva’ for Bacon had a different meaning from today’s ‘perspective’. Bacon’s “skill in mathematics, experimental science and mechanical inventions was so remarkable for his time that … he acquired the reputation … of being a magician” (Ferguson, Bibliotheca Chemica I, p. 65). It is appropriate that the Perspectiva and Specula mathematica are here bound together, not only because they have the same publisher and date, but because the subjects treated in the two works are complementary. The Perspectiva deals with the physiology of the eye and the geometrical optics of reflection and refraction, while the Specula mathematica presents Bacon’s theory of the propagation of light. Remarkably, the latter work anticipates the inverse square law, normally ascribed to Newton four centuries after Bacon. “[Bacon’s] major claim to fame in science is that he is the first Latin Western thinker to comprehend and write on most of the ancient sources of optics. In brief, he initiates the tradition of Optics/Perspectiva in the Latin world. This tradition would be formulated as teaching texts by his contemporaries Pecham and Witelo. Bacon’s optics was also read and commented on in 14th century Italy, especially by Lorenzo Ghiberti. It was known to and used by Leonardo Da Vinci. And it was part of the tradition of learning that led to Kepler and Descartes. In his Perspectiva and De scientia experimentali, Bacon outlines a sketch for a scientific method, one that takes optics as the model for an experimental science. In fact, he succeeded in his endeavor in that perspectiva was added to the four traditional university subjects of the quadrivium: arithmetic, geometry, astronomy, music” (Stanford Encyclopedia of Philosophy). Part I (‘Distinctio I’) of the Perspectiva deals with the anatomy of the eye and the optic nerve. Bacon realised that seeing involved not just the eye but the brain, and following Avicenna he divides the brain into ‘cells’. In Part II Bacon recounts a whole range of optical phenomena – long sight, near sight, errors of vision, clarity of vision, on the moon, on our perceptions of magnitude, and so on, all drawing on a wide variety of earlier sources, and on experimentation. Part III deals with reflection and refraction, discussing the geometry of the former in various sorts of mirrors, showing a good understanding of focal point and focal plane. The Perspectiva concludes with Bacon’s treatise De speculis comburentibus, a commentary on the last proposition of Euclid’s De speculis by means of an analysis of burning mirrors and the passage of light through small apertures. The Specula mathematica contains a long discussion of the usefulness of mathematics, “the door and key to all knowledge” (p. 2), but most importantly includes his treatise De specierum multiplicatione, which “is acknowledged by him as the key to his Optics” (ibid.). It is in this work that Bacon discusses radiation. As Lindberg puts it, “This is a complete physical and mathematical analysis of the radiation of force – and, thus, of natural causation.” The Perspectiva and Specula mathematica formed parts V and IV, respectively, of Bacon’s six-part Opus majus, composed in 1266-67 but not published in its entirety until 1733. But both were soon disseminated as separate works, and they served as important textbooks throughout the 14th to 16th centuries. The reason for their late publication is unknown.

“Nobody contributed more to the development of the science of perspectiva in the West than Roger Bacon. On the methodological issues that separated Robert Grosseteste (c. 1158-1253) and Albert the Great (c. 1200-1280), Bacon dismissed Albert’s opinion nearly as enthusiastically as he praised Grosseteste’s. Although Bacon did not study under Grosseteste, and may never even have met him, he did have access to Grosseteste’s library, left to the Franciscan convent in Oxford, and was clearly inspired by his example. However, Bacon was also powerfully moved by sources that had been unavailable to Grosseteste, principally the optical works of Ptolemy and Alhacen, where the promise of geometrical optics had been much more completely fulfilled.

“Thus Bacon, even more than Grosseteste, became an apostle of the application of mathematical method as the gate and key to all subjects, claiming, for example, that ‘no science can be grasped without this science [mathematics], and … nobody can perceive his ignorance in other sciences unless he is excellently informed in this one. Nor can things of this world be known, nor can man grasp the uses of body and things, unless he is imbued with the mighty works of this science’ … Following Alhacen’s lead, [Bacon] applied geometrical analysis to optical phenomena wherever promising and possible, given the conceptual framework and the mathematical techniques available to him, thereby pushing the mathematization of light and vision as far as it would go before the seventeenth century …

“Several examples will serve as illustrations. First, the magnitude of Bacon’s commitment to a mathematical analysis is superficially apparent from a glance at his Perspectiva, which contains fifty-one geometrical diagrams, or his On the Multiplication of Species, which contains thirty-nine, all fully integrated into the argument of their respective treatises. Second, Bacon’s works reveal a complete mastery of the geometry of reflection and image-formation in plane, convex, and concave mirrors” (Lindberg & Tachau, pp. 501-502).

“Bacon fully understood and successfully communicated the basic geometrical principles governing reflection in plane, concave, and convex mirrors; the equality of the angles of incidence and reflection; location of the images of objects seen by reflection at the intersection of the rectilinear extension of the visual ray issuing from the eye (or the reflected luminous ray entering the eye, since Bacon could conceptualize the problem either way) and the perpendicular drawn from the visible point to the reflecting surface (the cathetus). He also dealt successfully with questions of the magnification and diminution and the inversion and reversal of images; and his analysis of image formation in convex spherical mirrors implicitly embodied the concepts of focal point and focal plane … Bacon’s geometrical analysis of the phenomena of refraction was equally successful. He revealed no interest in the quantitative problem of discovering an algebraic or trigonometrical law of refraction. Ptolemy had already made a serious attempt in that direction and Bacon was undoubtedly familiar with it. Bacon aimed only to establish the geometrical (and thus qualitative) principles governing refraction at interfaces of various shapes separating media of different densities. He understood that radiation is refracted when passing from one medium to another in such a way as to fall closer to the perpendicular in the denser medium; he knew also that the image of an object seen by refracted rays is situated at the intersection of the rectilinear extension of the visual ray emerging from the eye (or the luminous ray entering the eye) and the perpendicular drawn from the visible point to the refracting interface; and he understood that the degree of refraction depended on the relative transparencies (we would say ‘optical densities’) of the two media. To display these principles, he offered a successful geometrical analysis of ten cases of refraction at plane and spherical interfaces, each illustrated with a geometrical diagram.

“There is a temptation for those of us who have received a modern education in the physical sciences to regard the successful geometrical analysis of reflection and refraction as obvious and inevitable. We must remind ourselves, therefore, that taking a geometrical approach to problems of the propagation of light seems self-evidently efficacious to us only because of our membership in, or encounter with, the tradition of geometrical optics on which Bacon was (in the Latin world) one of the founding fathers. There was nothing obviously efficacious about the geometrical mode of analysis until he and others made it obvious” (Lindberg (1996), pp. xlv-xlvi). 

“We can see the depth of Bacon’s commitment to the mathematization of optical phenomena in a third example – Bacon’s remarkable supposition (following Alhacen) that the visual apparatus and the very act of vision will submit to geometrical analysis. According to Bacon, all of the tunics and humors of the eye (cornea, crystalline lens, aqueous and vitreous humors, and retina) are defined or enclosed by spherical surfaces, the centers of which are situated on a straight line running from the center of the pupil at the front to the opening into the optic nerve at the back. He believed, as Alhacen had taught, that only rays incident on the eye perpendicularly, which enter it without refraction, are capable of stimulating the eye’s visual capabilities. These perpendicular rays form a cone or pyramid extending from the visual object as base toward an apex (which the rays never actually achieve) at the center of the observer’s eye. The rays that make up this visual cone pass without refraction through the cornea and front surface of the crystalline lens (which are concentric, so that a ray perpendicular to the one will be perpendicular to the other). At the rear surface of the crystalline lens, they are refracted in such a way as to be projected through the opening of the optic nerve, which conducts them to its point of union with the other optic nerve (our optic chiasma). There the completion of vision occurs, as the species from the two eyes join to form a single image. That image, in turn, continues to multiply itself into the three chambers of the brain that house the five inner senses defined in Avicenna’s On the Soul. Although Bacon’s theory contains much more detail, a striking feature of his quest to understand the act of vision is his willingness (following Al-kindi, Grosseteste, and especially Alhacen) to extend mathematical analysis to something so apparently unmathematical as human anatomy” (Lindberg & Tachau, pp. 502-503).

The Perspectiva also contains Bacon’s treatise De speculis comburentibus (p. 168 et seq.). “The problem was the classic one of explaining how radiation from a spherical body such as the sun, passing through a small triangular or rectangular aperture, can produce a circular image … In the long run his analysis does not succeed, as Kepler was to make clear, but it was thorough, intelligent, influential, and (above all) geometrical; it taught Bacon’s successors that the solution to the problem was to be sought in a geometrical analysis of the modes of radiation” (Lindberg (1996), pp. xlix-l).

“Bacon’s treatise De multiplicatione specierum[contained in the Specula mathematica], his major later work on physics, written before 1267, is closely related to the study of light, vision, and perception in the Perspectiva. Bacon takes Grosseteste’s physics of light, a development of Al-Kindi’s universal radiation of force, out of its metaphysical background and develops a universal doctrine of physical causation … What Bacon achieves is a comprehensive theory of physical force divorced from psychological, moral, and religious interpretation … The use of ‘species’ in this account … is ‘the force or power by which any object acts on its surroundings’ … As Bacon himself notes, ‘species [force, power] is the first effect of an agent … the agent sends forth a species into the matter of the recipient, so that, through the species first produced, it can bring forth out of the potentiality of matter [of the recipient] the complete effect that it intends. This is a universal theory of natural causation as the background for his philosophy of vision and perception. Most importantly, species is a univocal product of the agent. The first immediate effect of any natural action is definite, specific, and uniform. This production is not the imparting or imposition of an external form. The effect of the species is to bring forth the form out of the active potency of the recipient matter’ (Lindberg (1983), pp. 6-7).

Bacon “outlined a quantitative theory of any propagation along straight lines, and so arrived at the inverse square law, at least implicitly, since he attributed the weakening of the action with distance to the decrease in the cone (solid angle) under which the acted-on body is seen by the agent [Specula, Distinctio III, Caput II]. Bacon calls multiplicatio secundum figuras the law of dependence on distance of an action that radiates in all directions along straight lines, and he adds that the lines along which it radiates terminate in the concave surface of a sphere [ibid., II, III]” (Russo, p. 377). Bacon applied his general theory of the propagation of species to optics: species – in this case light and colour – emanate in every direction from every point of the surface of a visible object and do this continuously; the path is represented by straight lines or rays.

The Specula mathematica also deals, as its title suggests, “with mathematics and the applications of mathematics. Bacon presents reasons for a reduction of logic to mathematics (a kind of reversal of modern logicism) and sees mathematics as the key to an understanding of nature. Clearly, he is proclaiming the ‘usefulness’ of mathematics for knowledge; he is not doing mathematical theory. And the branch of mathematics that is important here is geometry. Following his abbreviation of the De multiplicatione specierum in part four of the Great Work, which shows how mathematics might be applied to physics, he deals with the application of astronomy/astrology to human affairs, the uses of mathematics in religious rites as in chronology, music, symbolism, calendar reform, and geographical knowledge, and a resume of astrology … Bacon was very interested in the applications of astronomy/astrology to human events … Although committed to freedom of the will, Bacon held to a deterministic notion of causation in nature based on the Introductorium Maius in Astronomiam of the Islamic authority on Astrology, Albumassar, on the De radiis of al-Kindi, and on the Centiloquium by Pseudo-Ptolemy (Ahmed Ibn Yusuf). And since he held to a doctrine of universal radiation in nature, he had to account for the influence of the heavens on the human body and hence indirectly on the human mind. Much of the polemic in his later works consists of a justification of this interest in an astrologically necessitated universe in the face of traditional theological objections. These works play a big role as background for his natural philosophy in De multiplicatione specierum” (Stanford Encyclopedia of Philosophy).

“Bacon was a transitional figure of great importance, who played a critical role in the transmission of Greek and Islamic learning to medieval Europe. It was he, more than any other, who introduced Latin Christendom to the mathematical optics of Euclid, Ptolemy, Alkindi, and Alhacen; who synthesized their works, clarifying and exhibiting their methodological achievement; and who, consequently, stood at the head of the European tradition in geometrical optics” (Lindberg (1997), p. 273).

Two works bound in one volume, 4to (200 x 155mm), pp. [viii], 207, with four leaves of plates of woodcut diagrams printed on recto and verso between pp. 160 & 161, numerous woodcut diagrams in text (last two pages misnumbered 204 & 189 as usual, gathering c misbound but complete); pp. [viii], 83, woodcut diagrams in text (light browning and foxing in both works). Contemporary blind-ruled vellum with later black lettering-piece on spine (a bit soiled).

Item #5811

Price: $7,500.00