KEPLER, Johannes.

Ad vitellionem paralipomen quibus astronomiae pars optica traditur; Potissimùm de artificiosa observatione et aestematione diametrorum deliquiorumq[ue] solis & lunae. Cum exemplis insignium eclipsium. Habes hoc libro, lector, inter alia multa nova, tractatum luculentum de modo visionis, & humorum oculi usu, contra opticos & anatomicos.

Frankfurt: Claudius Marnius & heirs of Johannes Aubrius, 1604.

First edition, an excellent copy, of the foundation work of modern optics. “Working within the perspectivist tradition of Alhazen, Roger Bacon, Witelo, John Pecham, and others, Kepler accepts that sight is possible due to rays emitted from visible objects, with these rays emitted in all directions from each point on the object’s surface. He overcomes a major shortcoming of the earlier theories by establishing a logically acceptable one-to-one correspondence between the points on the observed portion of the object and the points on the image produced on the surface of the eye’s retina; instead of rejecting all rays hitting the eye non-perpendicularly, as Alhazen had done, Kepler argues that all the rays incident on the eye from any specific point on the object will arrive at a single point on the retina after refraction in the eye’s humours. In consequence, the retina receives an unfocussed, although inverted, image of the object. Kepler also presents experimental results, examining, for instance, the range of applicability of Ptolemy’s direct proportionality between the angle of incidence and the angle of refraction; and he formulates the principle that the intensity of illumination is inversely proportional to the square of the distance from the illuminating source” (Parkinson, Breakthroughs, p. 62). “Kepler’s interest in optics arose as a direct result of his observations of the partial solar eclipse of 10 July 1600. Following instructions from Tycho Brahe, he constructed a pinhole camera; his measurements, made in the Graz marketplace, closely duplicated Brahe’s and seemed to show that the moon’s apparent diameter was considerably less than the sun’s. Kepler soon realized that the phenomenon resulted from the finite aperture of the instrument; his analysis, assisted by actual threads, led to a clearly defined concept of the light ray, the foundation of modern geometrical optics … Kepler intended at first to publish his optical analyses merely as Ad Vitellionem paralipomena, but by 1602 this ‘Appendix to Witelo’ had taken second place to the broader program of Astronomiae pars optica. The book was published in 1604 with both titles … The six astronomical chapters include not only a discussion of parallax, astronomical refraction, and his eclipse instruments but also the annual variation in the apparent size of the sun … The immediate impact of Kepler’s optical work was not great, but ultimately it changed the course of optics” (DSB). The work also contained an important advance in the theory of conic sections, introducing the ‘point at infinity’ and the ‘principle of continuity’ which unified the different types of conics (ellipse, parabola, hyperbola).

“In the summer of 1600, Kepler assembled a large wooden instrument (described at the beginning of Chapter 11 of the present work), and set it up in the Market Square in Graz to observe the solar eclipse of June 30/July1. His experience with this instrument drew his attention to certain optical matters that had been troubling astronomers. From a few notes written down at the time of the eclipse, his optical project grew to encompass metaphysical and theological speculations about the nature of light (Chapter 1), a thoroughgoing attempt to account for refraction, involving a novel treatment of conic sections (Chapter 4), a study of the anatomy and physiology of the eye (Chapter 5), a historical study of solar eclipses (Chapter 8), and many other matters relating to the light of the heavenly bodies and how it behaves. The result is one of the most important optical works ever written, which, even when it is wrong, is wrong in an interesting and fruitful way.

“The problem that Kepler had initially encountered, that initiated his optical studies, involved the way light flows through pinholes. Astronomers had been puzzled about why the Moon seemed smaller in a solar eclipse than it did at other times. Kepler figured out why. In a characteristic series of numbered sentences jotted down on a piece of paper at the time, he set out point by point the way a finite luminous object and a small but finite opening interact to form a slightly enlarged image. (An expanded version of these notes constitutes Chapter 3 of the present work.)

“At first, Kepler had it in mind to publish this important discovery in a separate small work, which he had actually written during the following month. But his exile from Styria, move to Prague, and involvement with the work of Tycho Brahe intervened. Much of his time in the next year was taken up with the orbits of Mars and the Earth.

“With the death of Brahe in October, 1601, everything changed. As his successor in the post of Imperial Mathematician, Kepler was expected to produce works that would reflect well on his patron, Rudolph II. In particular, he was to complete the work unfinished by Brahe and to produce the astronomical tables that would bear the name of Rudolph. Kepler filled sheet after sheet with computations and ruminations about the orbit of Mars, which, he believed, held the key to the deeper astronomy. But in the spring of 1602, his investigations took a surprising turn: he discovered that the orbit could not be perfectly circular, but had to be squeezed in slightly at the sides. The unexpected complications that this introduced, together with difficulties with the Brahe family regarding use of the Tychonic observations, led him to realize that the Mars book would not be finished as soon as he hoped, and that he had better find something else to fill in. His thoughts returned to the book on pin-holes.

“However, the project turned out not to be as simple as it had seemed at first. As Kepler outlined in his dedication to the Emperor, he thought he should also discuss the other main optical problem in astronomy, the refraction of light in the atmosphere. That, in turn, required an understanding of refraction itself, which demanded a study of the nature of light. And since there was some uncertainty about how the eye itself interacted with astronomical sights, it seemed that he needed to understand how the eye functions. To fill these needs, he worked his way through Witelo’s Perspectiva, itself no insignificant feat, and compared Witelo’s treatment of vision with the anatomical and physiological approaches of Jessenius and Platter. Further, his study of refraction suggested to him that curves other than circles would be required to explain it, and that led him to a study of Apollonius’s Conics, which he recast in Keplerian style. And, having gone this far, he thought he would round it out with a few chapters on ‘the light, the place, and the motion of the heavenly bodies,’ and the theory of parallax, so important for the Moon’s motion. As a result, although he confidently promised the book for Christmas of 1602, he was still hard at work on it in the summer of 1603. In May, he wrote, ‘measuring refractions: here I get stuck. Good God, what a hidden ratio! All the Conics of Apollonius had to be devoured first, a job which I have now nearly finished.’ He at last sent the finished manuscript to the Emperor in January, 1604.

“The book everywhere shows signs of the haste with which it was written. Syntax is often jumbled, words misspelled, numbers wrong, citations incorrect, and demonstrations vague. Once the book was in press, Kepler had second thoughts about many passages, for which he wrote notes, often extensive, which he advised the reader to consult first. Production was difficult owing to Kepler’s having entrusted the book to a printed in Frankfurt, perhaps hoping that, in this great center of publishing and marketing, production would be quick and efficient and sales brisk. As it turned out, the pace was far from quick, and it was not until the autumn of 1604 that the book finally appeared, with a lengthy (and incomplete) errata sheet appended.

“The resulting work is historically important in many ways, some of which, at least, have not yet been explored. Attention had been disproportionately directed to those parts of the [work] that are seen as points of departure for later scientific theories, for example, the inverted retinal image and the way lenses work … [but] the way in which Kepler’s astronomical works are related to his work in optics has received little attention. Chapter 10, in which Kepler argues, on the basis of their optical works, that the ancient optical writers were heliocentrists, is a notable example of this, as is his stated intention of building his unfinished Hipparchus on the foundation of his optics” (Donahue, pp. xi-xiii).

“Subjects treated [in the present work] are: the nature and properties of light; colour; reflection and refraction of light of stars; diminution of moon’s diameter in solar eclipses – his is a continuation of Brahe’s work; measurement of refractions; errors due to faulty instruments and incorrect sight; dimensions of sun and moon; light, positions, and motion of stars and comets; age of moon; parallaxes; eclipses; occultation of stars; twilight; phases of moon; altitude of sun and stars; anatomy of human eye and binocular vision. Occasionally philosophical discussions intrude: thus the sphere, having a centre, interior and surface, is an emplem of the Trinity, and there is a long discussion of the reasons why the human eye is placed at the side of the nose and not at the top of the head (‘because man is a social and political animal’). Kepler details an experiment undertaken to explain why the sun’s image in a camera obscura is round, although the light is admitted through a rectangular slit. Among numerous results obtained are: the speed of light is infinite; the diameter of the sun in perigee is 31’, in apogee 30’; in July 1600 the diameter of the moon was between 31’ 12” and 29’ 30”’ the height of the atmosphere is 0.0005578 of the earth’s radius, the latter being 860 ‘German miles’’ while binocular vision is perfect, a correction should be applied in the case of the astronomer who uses only one eye. There are some well printed parallactic and refraction tables (with a long list of corrigenda)” (Swinden, p. 45).

In Chapter 4, Kepler made an important advance in the theory of conics, introducing for the first time the ‘point at infinity’ and the ‘principle of continuity’, later introduced independently (apparently in ignorance of Kepler’s work) by Desargues and Poncelet. Kepler introduced points at infinity in 1604, in a context not of pure mathematics but of geometrical optics, to provide the parabola with a second focus and thus to unify the theory of the various types of conics. “Of sections of the cone, [Kepler] says, there are five species from the ‘recta linea’ or line-pair to the circle. From the line-pair we pass through an infinity of hyperbolas to the parabola, and thence through an infinity of ellipses to the circle. Related to the sections are certain remarkable points which have no name. Kepler calls them foci. The circle has one focus at the centre, an ellipse or hyperbola two foci equidistant from the centre. The parabola has one focus within it, and another, the ‘caecus focus,’ which may be imagined to be at infinity on the axis within or without the curve. The line from it to any point of the section is parallel to the axis. To carry out the analogy we must speak paradoxically, and say that the line-pair likewise has foci, which in this case coalesce as in the circle and fall upon the lines themselves; for our geometrical terms should be subject to analogy. Kepler dearly loves analogies, his most trusty teachers, acquainted with all the secrets of nature, ‘omnium naturae arcanorum conscios.’ And they are to be especially regarded in geometry as, by the use of ‘however absurd expressions,’ classing extreme limiting forms with an infinity of intermediate cases, and placing the whole essence of a thing clearly before the eyes. Here, then, we find formulated by Kepler the doctrine of the concurrence of parallels at a single point at infinity and the principle of continuity (under the name analogy) in relation to the infinitely great” (Britannica).

Caspar 18; Cinti 13; Garrison p. 260; Hirschberg 308; Houzeau-Lancaster I, 2842; Krivatsy 6343; Lalande 141; Zinner 3993; VD17 39:121965W. Donahue, Johannes Kepler Optics, 2000. Sotheran 10, 097 (“[C]ontains the first correct physiological explanation of the defects of sight, with a theory of vision, the first suggestion of the undulatory theory of light, an approximately correct formula of refraction (pointing out the relation between the sine of incident and refracted rays), the first announcement of one of the principal axioms of photometry, his method of calculating eclipses, still in use, etc., etc.”); Swinden, ‘Johann Kepler: Paralipomena ad Vitellionem,’ Mathematical Gazette 38 (1954), pp. 44-46. For detailed accounts of the content of this work, see Darrigol, A History of Optics (2012), pp. 26-33; Lindberg, Theories of Vision from Al-Kindi to Kepler (1976), pp. 185-208.

4to (203 x 160 mm), pp. [xvi], 449, [18], [1, blank], with one engraved plate (with adjacent unsigned and unpaginated leaf of explanation), two folding letterpress tables (between pp. 424 and 425), woodcut printer’s device on title and numerous woodcut diagrams in text (some leaves browned, as usual, due to the quality of the paper). Contemporary green limp vellum. Housed in a green cloth clamshell case with morocco gilt lettering label.

Item #5230

Price: $50,000.00