## Dioptricae pars prima continens librum primum, de explicatione principiorum, ex quibus constructio tam telescopiorum quam microscopiorum est petenda. [Vol. I:] De explicatione principiorum, ex quibus constructio tam telescopiorum quam microscopiorum est petenda. [Vol. II:] De constructione telescopiorum dioptricorum cum appendice de constructione telescopiorum catoptrico-dioptricorum. [Vol. III:] De constructione microscopiorum tam simplicium, quam compositorum.

St. Petersburg: Imperial Academy of Sciences, 1769-1770-1771.

First edition, a beautiful copy in original wrappers, of Euler’s *magnum opus* on optics, “widely known and important in the physics of the eighteenth century,” which “laid the foundations of the calculation of optical systems” (DSB). “The *Dioptricae* presented a universal optics with practical applications. Volume 1 explained the general theory of optics and covered the construction of dioptric instruments in general, including visual confusions in working with them. In the mathematical description of optics, Euler noted, the geometrical side dominated. In elementary geometric optics, Euler’s formulas described properties of lenses and the passage of light through a system of them; his was the first such complete theory. Volumes 2 and 3 presented his research on perfecting optical instruments and explained rules that applied to them. The second volume concentrated on building the telescope, including scopes with convex ocular lenses; the third dealt with the construction of simple and composite microscopes. Euler’s research made possible a considerable improvement of these instruments” (Calinger, pp. 470-1). “His book *Dioptricae* deals with the determination of the path of a ray of light through a system of diffracting spherical surfaces. In the first approximation, Euler discovered the familiar formulas of elementary optics, and in the second approximation, he took into account the spherical and chromatic aberrations with the spherical aberration errors of the third order’ (Debnath, p. 370). “Next to the lunar theory, the most important subject which exercised the genius of [18th century] mathematicians was the improvement of the achromatic telescope” (*Edinburgh Encyclopedia*, Vol. 6). “In geometrical optics [Euler] invented the achromatic lens. His design for it required glasses of high, distinct, and reproducible quality; attempts to construct lenses according to his prescriptions have been adduced as impulses to the rise of the optical industry in Germany, which was supreme in precision for at least a century” (Dunham, p. 17). It is worth remarking that geometrical optics continued to exercise the minds of the greatest mathematicians – seventy years after *Dioptricae *was appeared Carl Friedrich Gauss published *Dioptrische Untersuchungen*, which built upon Euler’s work.

“From 1766 to 1777 Euler concluded roughly forty years of intermittent studies on geometrical optics, and was the first natural philosopher to construct a mathematical pulse theory of light. Elevated by their experimental component, his optical studies included probes of reflection, the dispersion of light, the phenomena of colors, the course of light rays in the atmosphere, and refraction in different fluids. Upon returning to St. Petersburg [in 1766], Euler kept dioptrics a major topic in his studies. Dioptrics, the branch of optics that examines the refraction of light through different surfaces and their systems, is often connected with studies of the eye; it investigates the properties of the eye as an optical instrument. Among Euler’s predecessors in this subject were Johannes Kepler and Descartes” (Calinger, pp. 469-70).

“Although Euler’s intense interest in the science of optics appeared before he was 30 and remained with him almost until his death, there is still no monographic evaluation of his contributions to the wide field of physical and geometrical optics. Part of Euler’s work is best described by Habicht:

‘In the second half of his life, from 1750 on and throughout his sixties, Leonhard Euler worked intensively on problems in geometric optics. His goal was to improve in several ways optical instruments, in particular, telescopes and microscopes. Besides the determination of the enlargement, the light intensity and the field of view, he was primarily interested in the deviations from the point-by-point imaging of objects (caused by the diffraction of light passing through as system of lenses), and also in the even less tractable deviations which arise from the spherical shape of the lenses… As was his custom, he collected his results in a grandly conceived textbook, the *Dioptrica* (1769-1771). This book deals with the determination of the path of a ray of light through a system of diffracting spherical surfaces, all of which have their centres on a line, the optical axis of the system. In a first approximation, Euler obtains the familiar formulae of elementary optics. In a second approximation he takes into account the spherical and chromatic aberrations. After passing through a diffracting surface, a pencil of rays issuing from a point on the optical axis is spread out in an interval on the optical axis; this is the so-called ‘longitudinal aberration’. Euler uses the expression ‘espace de diffusion’. If the light passes through several diffracting surfaces, the ‘espace de diffusion’ is determined using a principle of superposition.

‘Euler had great expectations for his theory, and believed that using his recipes, the optical instruments could be brought to ‘the highest degree of perfection.’ Unfortunately, the practical realization of his systems of lenses did not yield the hoped-for success. He searched for the causes of failure in the poor quality of lenses on the one hand, and also in basic errors in the laws of diffraction which were determined experimentally in a manner completely unsatisfactory from a theoretical point of view. Because of the failure of his prediction, Euler’s *Dioptricae* is often underrated.’

“Habicht notes that Euler’s theory can be modified to obtain the general imaging theories developed in the nineteenth century. The crucial gap in Euler’s treatment consist in neglecting those aberrations which are caused by the distance of the object and its images from the optical axis; with modification it is possible to determine the spherical aberration errors of the third order directly from Euler’s formulas” (Dunham, pp. 83-4).

One of Euler’s successes in the field of dioptrics was in the field of colour dispersion – different colours of light are refracted by different amounts when passing from one medium into another. Isaac Newton had claimed that it was impossible to avoid this ‘chromatic aberration’ “Subsequent to the utilization of the refractor telescope by Galileo and Harriot at the beginning of the 17^{th} century, the then unavoidable colour rings in the picture field proved to be very disturbing. Because of this, David Gregory and Newton turned to the (in this respect) better reflector telescope. Only on the basis of Newton’s examination of the dispersion of light in a prism could the possibility of eliminating the chromatic errors be envisaged. Newton himself initially considered it impossible to reach achromasy by employing materials of different refractive index” (Fellmann, p. 7).

Euler noted that the human eye refracts light without colour dispersion, and reasoned that it should therefore be possible to correct chromatic aberration in optical instruments. “Since the time of Huygens and Newton theoretical optics had not progressed any further than applied optics. In particular no one had re-examined Newton’s demonstration of the impossibility of correcting chromatic aberration in lenses. In Proposition III, Experiments 7 and 8 in his *Opticks*, Newton examined the possibility of suppressing chromatic aberration in telescope objectives by using a lens system consisting of two lenses of different refractive indices. The refrangibility of one substance cancelling the dispersion provoked by the other, one obtained at the end of the objective reconstituted white light, but this would only occur if he employed lenses of infinite focal length – an impossibility. This result caused him to abandon the refracting telescope and to construct a reflecting one.

“Newton’s work had such authority that for more than thirty years no one thought of reviewing his conclusions. Physicists and mathematicians held to the opinion that it was impossible to make an achromatic lens by associating two different substances… [Euler] began at the point where Newton left off, and produced a lens-combination formed of two concave lenses whose intervening space was filled with water. Studying refraction in each medium and for each colour he showed that it was possible to correct colour dispersion and gave the corresponding formulae” (Dumas, *Scientific Instruments of the Seventeenth and Eighteenth Century and their Makers*, pp. 153-4).

“A responsible evaluation of Euler’s contributions to optics will be possible only after Euler’s unpublished letters and manuscripts are edited and made generally accessible. E. A. Fellmann provides an example of Euler’s method which helps to place Euler’s contribution in a historic context. The problem of diffraction in the atmosphere is one which was first seriously considered by Euler:

‘He began by deriving a very general differential equation; naturally, it turned out not to be integrable – it would have been a miracle had that not happened. Then he searched for conditions which make a solution possible, and finally he solved the problem in several cases under practically plausible assumptions.

‘Euler frequently expressed the opinion that the phenomena in optics, electricity and magnetism are closely related (as states of the ether), and that therefore they should receive simultaneous and equal treatment. This prophetic dream of Euler concerning the unity of physics could only be realized after the construction of bridges (experimental as well as theoretical) which were missing in Euler’s time. These were later built by Faraday, W. Weber and Maxwell’” (Dunham, p. 84).

*Becker Collection* 126; *British Optical Association Library and Museum Catalogue* I, p. 65; Brunet 1093; DSB IV, 482; Eneström, 367, 386 & 404; Poggendorff I, 689-703; Roller-Goodman I, 374. Calinger, *Leonhard Euler*,* Mathematical Genius in the Enlightenment*, 2016. Debnath, *The Legacy of Leonhard Euler*, 2009. Dunham, *The Genius of Euler*, 2007. Fellmann, ‘Leonhard Euler 1707-1783,’ *Europhysics News*, vol. 14 (1983), pp. 6-7. W. Habicht (ed.), *Opera Omnia*, Series Tertia, vol. 9: *Commentationes Opticae*, vol. 5, 1973.

Three volumes, large 4to (280 x 228 mm), pp. [iv], 337; [vi], 592 (recte 584, pagination jumps 240-249 but signatures Gg4-Hh1 continuous); [viii], 440, with six folding engraved plates (minor damp stain to a few of the plates in Volume I, contemporary red ownership stamp to verso of each title). Original wrappers (small repair to spine of Volume II). A completely unsophisticated copy, entirely uncut and mostly (2 of the 3 volumes) unopened. Preserved in a custom clamshell box.

Item #5225

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Price:
$22,500.00
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