Optice; sive de reflexionibus, refractionibus, inflexionibus & coloribus lucis libri tres.
London: Samuel Smith and Benjamin Walford, 1706. First Latin edition of the Opticks, the extremely rare first issue with Ss1 in its original state (cancelled in almost all copies). Of Newton’s three greatest contributions to science – his theory of gravity, his theories of light and colour, and the invention of calculus – the first was published for the first time in the Principia (1687), and the other two in the Opticks (1704), “one of the supreme productions of the human mind” (Andrade). “Newton’s Opticks did for light what his Principia had done for gravitation, namely, placed it on a scientific basis” (Babson, p. 66).“One of the supreme productions of the human mind” (Andrade), “All previous philosophers and mathematicians had been sure that white light is pure and simple, regarding colors as modifications or qualifications of the white. Newton showed that the opposite is true … Natural white light, far from being simple, is a compound of many pure elementary colors which can be separated and recombined at will” (PMM). The Optice contains translations not only of the Opticks itself but also of the two appended mathematical tracts, Tractatus de quadratura curvarum and Enumeratio linearum tertii ordinis. The former is Newton’s first publication of his method of fluxions, or calculus, which he developed in terms of ‘prime and ultimate ratios’, an early version of the theory of limits; it includes the first published statement of the general binomial theorem and of ‘Taylor’s theorem’ on series expansions. The real importance of this Latin edition is the seven new ‘Queries’ it contains: “The Queries contain some of Newton’s most influential and speculative writing” (Gjertsen, p. 519). The purpose of the original 16 queries in the Opticks was principally to compensate for the many years’ delay between the writing of Opticks and its publication, during which many discoveries had been made (by Newton and others). Each of the new Queries, with one exception, is longer than the original 16 taken together. “In the new Queries, Newton expressed fundamental views on the nature of light, on the nature of bodies, on the relation of God to the physical universe, and on the presence in nature of a whole range of forces which furnish the activity necessary for the operation of the world and for its permanence. At the last moment, he dared even a bit more, and inserted three further speculative passages in the Addenda to the volume. The new Queries were the most informative of the speculations that Newton ever published.” (Westfall, p. 644). “Th[is] edition is known in two states. In query 20 Newton had written of space: ‘Annon spatium universuum, sensorium est entis incorporei, viventis, et intelligentis?’ (Is not infinite space the sensorium of a Being incorporeal, living and intelligent?). It must have struck Newton that to call space ‘the sensorium of God’, without any qualification, was too bold a claim. Consequently, he chose to substitute for page 315 a cancel in which he spoke of infinite space (‘spatio infinito’), as ‘tanquam sensorio suo’ (which is as it were his sensorium). He failed, however, to modify the whole edition and copies with the missing tanquam been found in the Babson collection, the Bodleian library, and [Cambridge University Library]. But worse, from Newton’s point of view, an uncancelled copy found its way to Leibniz, who lost no time in accusing Newton of claiming that space is an organ of God” (Gjertsen, p. 413). Some of the other added Queries contain remarkably prescient speculations. Query 23 “was an extended version of the speculations on forces that Newton had once planned to insert in the Principia. Heavily, indeed overwhelmingly, chemical in content, it was arguably the most advanced product of seventeenth-century chemistry” (Westfall, p. 644). “In a remarkable paragraph [in Query 22, pp. 320-321] which did not survive into subsequent English editions he compared the force of attraction in proportion to size in particles of light and gross bodies by comparing velocities and radii of curvature of rays of light and projectiles. He concluded that the force of attraction in particles of light is more powerful by a factor of 1015, that is, the short-range forces are immensely more powerful than gravity” (ibid., p. 646). “Newton wrote most of the Opticks between 1687 and early 1692. He wrote Book I, Parts I and II, expounding his new theory of light and colour, in 1687. He then appears to have set aside the Opticks for about three years, but by the late summer or autumn of 1691, he had considered it – at least for a few months – to be complete. It is most likely that he carried out new research and wrote the remainder of the Opticks – that is, Books II and III – in the winter or spring of 1692, or perhaps six months earlier. At some time between late August 1691 and late February 1692, Newton decided to revise the draft significantly. After this effort he brought it close to its published form except for the brief last book on diffraction [which Newton called ‘inflexion’] and the queries which were not prepared for publication until shortly before publication in 1704. “The composition of Book II in 1690 or 1691 at first went very quickly. Newton made so few changes in the text that he was able to mark up the manuscript of the [‘Discourse of] Observations’ from 1675 for his amanuensis to copy for the Opticks. This formed Parts I and II and much of Part III … After revising the ‘Observations’, Newton was confronted with a decision on how to end his book. At first he planned to follow this material with a new fourth book or part on diffraction, but he was also toying with the idea of a speculative ‘Fourth Book’. Newton soon reined in his more speculative tendencies and turned to more empirical optical investigations. He continued experiments on diffraction and also discovered an entirely new phenomenon: coloured rings produced in transparent thick plates. By the autumn of 1691, Newton had completed and written up his investigations of thick plates as Book IV, Part I, which, together with his research on diffraction, Book IV, Part II, was to form the concluding book of the Opticks. “Between late August 1691 and late February 1692, Newton removed the two parts of the new Book IV from the manuscript and set about revising them. The part on diffraction was troublesome and remained incomplete until shortly before publication. Within six months, however, he revised the part on the colours of thick plates, incorporated it into Book III because of their affinity to those of thin films, and essentially put it into its published state. During this revision, Newton also introduced his theory of fits – an immaterial vibration to explain the physical cause of periodicity in light that replaced his earlier aetherial and corpuscular vibrations” (Shapiro, pp. 187-188). On 15 November 1702, according to a memorandum by the Scottish mathematician and Oxford Professor of Astronomy David Gregory, Newton “promised Mr Roberts, Mr Fatio, Capt. Hally & me to publish his Quadratures, his treatise of Light, & his treatise of the Curves of the 2d Genre” [i.e., cubic curves]. The book appeared by 16 February 1704, when Newton presented a copy to the Royal Society” (ibid., p. 196). In the published work, “Newton presented his main discoveries and theories concerning light and color in logical order, beginning with eight definitions and eight axioms … Eight propositions follow, the first stating that ‘Lights which differ in Colour, differ also in Degrees of Refrangibility.’ In appended experiments Newton discussed the appearance of a paper colored half red and half blue when viewed through a prism and showed that a given lens produces red and blue images, respectively, at different distances. The second proposition incorporates a variety of prism experiments as proof that ‘The Light of the Sun consists of Rays differently refrangible.’ “The figure given with experiment 10 of this series illustrates ‘two Prisms tied together in the form of a Parallelopiped’. Under specified conditions, sunlight entering a darkened room through a small hole F in the shutter would not be refracted by the parallelopiped and would emerge parallel to the incident beam, from which it would pass by refraction through a third prism, which would by refraction ‘cast the usual Colours of the Prism upon the opposite Wall.’ Turning the parallelopiped about its axis, Newton found that the rays producing the several colors were successively ‘taken out of the transmitted Light’ by ‘total Reflexion’; first ‘the Rays which in the third Prism had suffered the greatest Refraction and painted [the wall] with violet and blew were … taken out of the transmitted Light, the rest remaining,’ then the rays producing green, yellow, orange, and red were ‘taken out’ as the parallelopiped was rotated yet further. Newton thus experimentally confirmed the ‘experimentum crucis,’ showing that the light emerging from the two prisms ‘is compounded of Rays differently Refrangible, seeing [that] the more Refrangible Rays may be taken out while the less Refrangible remain’ … In proposition 6 Newton showed that, contrary to the opinions of previous writers, the sine law [of refraction] actually holds for each single color. The first part of book I ends with Newton’s remarks on the impossibility of improving telescopes by the use of color corrected lenses and his discussion of his consequent invention of the reflecting telescope. “In the second part of book I, Newton dealt with colors produced by reflection and refraction (or transmission), and with the appearance of colored objects in relation to the color of the light illuminating them. He discussed colored pigments and their mixture and geometrically constructed a color wheel, drawing an analogy between the primary colors in a compound color and the “seven Musical Tones or Intervals of the eight Sounds, Sol, la, fa, sol, la, mi, fa, sol….” “Proposition 9, ‘Prob. IV. By the discovered Properties of Light to explain the Colours of the Rain-bow,’ is devoted to the theory of the rainbow. Descartes had developed a geometrical theory, but had used a single index of refraction in his computation of the path of light through each raindrop. Newton’s discovery of the difference in refrangibility of the different colors composing white light, and their separation or dispersion as a consequence of refraction, on the other hand, permitted him to compute the radii of the bows for the separate colors. He used 108:81 as the index of refraction for red and 109:81 for violet, and further took into consideration that the light of the sun does not proceed from a single point. He determined the widths of the primary and secondary bows to be 2°15' and 3°40', respectively, and gave a formula for computing the radii of bows of any order n (and hence for orders of the rainbow greater than 2) for any given index of refraction … “Book II, which constitutes approximately one third of the Opticks, is devoted largely to what would later be called interference effects, growing out of the topics Newton first published in his 1675 letter to the Royal Society. Newton’s discoveries in this regard would seem to have had their origin in the first experiment that he describes (Book II, Part 1, Observation 1); he had, he reported, compressed ‘two Prisms hard together that their sides (which by chance were a very little convex) might somewhere touch one another’ (as in the figure provided for Experiment 10 of Book I, Part 1). He found ‘the place in which they touched’ to be ‘absolutely transparent,’ as if there had been one ‘continued piece of Glass,’ even though there was total reflection from the rest of the surface; but ‘it appeared like a black or dark spot, by reason that little or no sensible light was reflected from thence, as from other places’ … Rotating the two prisms around their common axis (Observation 2) produced ‘many slender Arcs of Colours’ which, the prisms being rotated further, ‘were compleated into Circles or Rings.’ In Observation 4 Newton wrote that ‘To observe more nicely the order of the Colours … I took two Object-glasses, the one a Plano-convex for a fourteen Foot Telescope, and the other a large double Convex for one of about fifty Foot; and upon this, laying the other with its plane side downwards, I pressed them slowly together, to make the Colours successively emerge in the middle of the Circles, and then slowly lifted the upper Glass from the lower to make them successively vanish again in the same place.’ It was thus evident that there was a direct correlation between particular colors of rings and the thickness of the layer of the entrapped air … Furthermore, as he noted in Observation 13, ‘the Circles which the red Light made’ were ‘manifestly bigger than those which were made by the blue and violet’ … He concluded that the rings visible in white light represented a superimposition of the rings of the several colors, and that the alternation of light and dark rings for each color must indicate a succession of regions of reflection and transmission of light, produced by the thin layer of air between the two glasses … “Book II, Part 2, of the Opticks has a nomogram in which Newton summarized his measures and computations and demonstrated the agreement of his analysis of the ring phenomenon with his earlier conclusions drawn from his prism experiments – ‘that whiteness is a dissimilar mixture of all Colours, and that Light is a mixture of Rays endued with all those Colours.’ The experiments of Book II further confirmed Newton’s earlier findings ‘that every Ray have its proper and constant degree of Refrangibility connate with it, according to which its refraction is ever justly and regularly perform’d,’ from which he argued that ‘it follows, that the colorifick Dispositions of Rays are also connate with them, and immutable.’ The colors of the physical universe are thus derived ‘only from the various Mixtures or Separations of Rays, by virtue of their different Refrangibility or Reflexibility’; the study of color thus becomes ‘a Speculation as truly mathematical as any other part of Opticks.’ “In Part 3 of Book II, Newton analyzed ‘the permanent Colours of natural Bodies, and the Analogy between them and the Colours of thin transparent Plates.’ He concluded that the smallest possible subdivisions of matter must be transparent, and their dimensions optically determinable. A table accompanying Proposition 10 gives the refractive powers of a variety of substances ‘in respect of … Densities.’ Proposition 12 contains Newton’s conception of ‘fits’: ‘Every Ray of Light in its passage through any refracting Surface is put into a certain transient Constitution or State, which in the progress of the Ray returns at equal Intervals, and disposes the Ray at every return to be easily transmitted through the next refracting Surface, and between the returns to be easily reflected by it.’ The succeeding definition is more specific: ‘The returns of the disposition of any Ray to be reflected I will call its Fits of easy Reflection, and those of its disposition to be transmitted its Fits of easy Transmission, and the space it passes between every return and the next return, the Interval of its Fits.’ The ‘fits’ of easy reflection and of easy refraction could thus be described as a numerical sequence; if reflection occurs at distances 0, 2, 4, 6, 8, …, from some central point, then refraction (or transmission) must occur at distances 1, 3, 5, 7, 9, …. Newton did not attempt to explain this periodicity, stating that ‘I do not here enquire’ into the question of ‘what kind of action or disposition this is’ … Newton thus integrated the periodicity of light into his theoretical work … His work was, moreover, based upon extraordinarily accurate measurements – so much so that when Thomas Young (1773-1829) devised an explanation of Newton’s rings based on the revived wave theory of light and the new principle of interference, he used Newton’s own data to compute the wavelengths and wave numbers of the principal colors in the visible spectrum and attained results that are in close agreement with those generally accepted today. “In Part 4 of Book II, Newton addressed himself to ‘the Reflexions and Colours of thick transparent polish’d Plates.’ This book ends with an analysis of halos around the sun and moon and the computation of their size, based on the assumption that they are produced by clouds of water or by hail. This led him to the series of eleven observations that begin the third and final book, ‘concerning the Inflexions of the Rays of Light, and the Colours made thereby,’ in which Newton took up the class of optical phenomena previously studied by Grimaldi, in which ‘fringes’ are produced at the edges of the shadows of objects illuminated by light ‘let into a dark Room through a very small hole.’ Newton discussed such fringes surrounding the projected shadows of a hair, the edge of a knife, and a narrow slit” (DSB). “Since Newton published the Opticks without a complete investigation into diffraction, which he had hoped would support a corpuscular theory of light in which light corpuscles were acted on by short-range forces of matter” (Shapiro, p. 196), “Newton concluded the first edition of the Opticks with a set of sixteen queries, introduced ‘in order to a further search to be made by others.’ He had at one time hoped he might carry the investigations further, but was ‘interrupted,’ and wrote that he could not ‘now think of taking these things into farther Consideration.’ In the eighteenth century and after, these queries were considered the most important feature of the Opticks … The original sixteen queries at once go beyond mere experiments on diffraction phenomena. In Query 1, Newton suggested that bodies act on light at a distance to bend the rays; and in Queries 2 and 3, he attempted to link differences in refrangibility with differences in ‘flexibility’ and the bending that may produce color fringes. In Query 4, he inquired into a single principle that, by ‘acting variously in various Circumstances,’ may produce reflection, refraction, and inflection, suggesting that the bending (in reflection and refraction) begins before the rays ‘arrive at the Bodies.’ Query 5 concerns the mutual interaction of bodies and light, the heat of bodies being said to consist of having ‘their parts [put] into a vibrating motion’; while in Query 6 Newton proposed a reason why black bodies ‘conceive heat more easily from Light than those of other Colours.’ He then discussed the action between light and ‘sulphureous’ bodies, the causes of heat in friction, percussion, putrefaction, and so forth, and defined fire (in Query 9) and flame (in Query 10), discussing various chemical operations. In Query 11, he extended his speculations on heat and vapors to sun and stars. The last four queries (12 to 16) of the original set deal with vision, associated with ‘Vibrations’ (excited by ‘the Rays of Light’) which cause sight by ‘being propagated along the solid Fibres of the optick Nerves into the Brain.’ In Query 13 specific wavelengths are associated with each of several colors. In Query 15 Newton discussed binocular vision, along with other aspects of seeing, while in Query 16 he took up the phenomenon of persistence of vision” (DSB). Newton appended to the Opticks two mathematical tracts, of which the first, Tractatus de quadratura curvarum, is Newton’s first published account of the calculus of fluxions. In Newton’s time, finding the ‘quadrature’ of a curve meant finding the area enclosed or subtended by it, which for us is a problem of integral calculus and for Newton one of the ‘inverse method of fluxions’. Newton wrote three extended treatises on fluxions. The first of these, ‘De analysi per aequationes numero terminorum infinitas,’ was composed in 1669 and treats Newton’s general methods of infinite series. It was not published until 1711, when William Jones included it, along with a number of other tracts, in his Analysis per quantitatum series. In ‘De analysi,’ however, Newton “did not explicitly make use of the fluxionary notation or idea. Instead, he used the infinitely small, both geometrically and analytically, in a manner similar to that found in Barrow and Fermat, and extended its applicability by the use of the binomial theorem” (Boyer, The Concept of Calculus, p. 191). It was in the second of Newton’s calculus treatises, ‘De methodus fluxionum’, composed in 1671 but not published until 1736, that he first “introduced his characteristic notation and conceptions. Here he regarded his variable quantities as generated by the continuous motion of points, lines, and planes, rather than as aggregates of infinitesimal elements, the view which had appeared in ‘De analysi’. … In the ‘Methodus fluxionum’ Newton stated clearly the fundamental problem of the calculus: the relation of quantities being given, to find the relation of the fluxions of these; and conversely” (ibid., pp. 192-3), i.e., the processes that we call differentiation and integration. De quadratura was the first of Newton’s treatises on fluxions to be published, but the last to be composed, so that it represents his most mature view of the subject. It was prompted by a letter from David Gregory, on 7 November 1691, sending Newton “my method of squaring figures, published three years ago but now clarified by examples. If only I might be allowed to know your method too, which, as I have subsequently gathered, differs little from mine.” “De quadratura contained the first published statement of the binomial theorem, discovered by Newton some forty years before. The text of De quadratura, in its published form, is in two parts. In the first part Newton, in the manner of De analysi, demonstrated how infinite series could be deployed to determine the quadrature and rectification of curves. In the second part he returned to the topic of fluxions, discussed at greater length in his then unpublished De methodis [eventually published as The method of fluxions and infinite series in 1736]” (Gjertsen, p. 579). But perhaps “Newton’s most important achievement in his ‘De quadratura’ [was] the first explicit enunciation of the Taylor expansion of a general function – Newton deduced the particular ‘Maclaurin’ form in his Corollary 3 (by successive differentiation, it would seem) and then passed to the general theorem in his Corollary 4” (Papers VII, pp. 18-19). The expansion was rediscovered by Brook Taylor in 1715. The second appended mathematical treatise, Enumeratio linearum tertii ordinis, was composed in summer 1695, although it was based on researches carried out intermittently over the previous three decades. “In some ways the Enumeratio is the most original of Newton’s mathematical works. It had no predecessors, met with no rivals claiming to have anticipated the results, or few even who acknowledged its results” (Gjertsen, p. 187). Since the inception of analytic geometry – most notably with Descartes’s Géométrie (1637), which Newton carefully studied in its Latin translation (1659-61) – European mathematicians became interested in the algebraic representation of plane curves. As Descartes showed, and John Wallis further developed, conic sections can be represented by second-degree polynomial equations in two variables (in Cartesian coordinates, as we would say nowadays), and they can be divided into circle, parabola, ellipse and hyperbola. The question naturally arises of how to move a step further and study the graphs of third-degree polynomials. In the Enumeratio, Newton gave a classification of cubic curves analogous to the classification of conic sections. He identified 72 species of cubic curves, mostly classified in terms of the properties of their diameters and asymptotes. There are, in fact, 78 species: four were added by James Stirling in his Lineae tertii ordinis Newtonianae (1717), and the remaining two by François Nicole and Nicolas I Bernoulli in the 1730s. Newton uses oblique Cartesian axes (something Descartes did not do) and has no qualms in using negative coordinates (a novelty at the time). Newton also demonstrates deep geometrical insights, stating a general theorem according to which all cubic curves can be obtained by centrally projecting the five ‘divergent parabolas’, very much as all conics can be obtained by projecting the circle; this was proved by Nicole and Alexis-Claude Clairaut in 1731. In the final section of the work, Newton shows how the real roots of polynomial equations of degree up to 9 can be found from the points of intersection of cubic curves with lines, conics or other cubic curves. Newton gave almost no proofs of his claims but Stirling revealed the methods Newton had used: algebra and infinite series. Newton’s published treatise is “a marvellous epitome of results whose subtleties were only just becoming to be understood by mathematicians in the last decade of Newton’s life, half a century after their initial discovery” (Papers VII, p. 588 n1). Gjertsen (p. 520) summarizes the content of the seven new Queries added to the Optice as follows: In Query 20, “the refutation of wave theories of light led Newton into an argument against the possibility of a dense, Cartesian ether filling the heavens, and thence into an explication of his ultimate objection against conventional mechanical philosophies, their tendency to make nature self-sufficient and thus to dispense with God. Some ancient philosophers, he argued, took atoms, the void, and the gravity of atoms as the first principles of their philosophy and attributed gravity to some other cause than matter. ‘Latter Philosophers banish the Consideration of such a Cause out of natural Philosophy, feigning Hypotheses for explaining all things mechanically, and referring other Causes to Metaphysicks: Whereas the main Business of natural Philosophy is to argue from Phenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical; and not only to unfold the Mechanism of the World, but chiefly to resolve these and such like Questions. What is there in places empty of Matter, and whence is it that the Sun and Planets gravitate towards one another, without dense Matter between them? Whence is it that Nature doth nothing in vain; and whence arises all that Order and Beauty which we see in the World? . . . How do the Motions of the Body follow from the Will, and whence is the Instinct in Animals? Is not infinite Space the Sensorium of a Being [Annon Spatium Universum, Sensorium est Entis] incorporeal, living, and intelligent, who sees the things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself …’ “David Gregory, who held an extensive discussion of the new Queries with Newton on 21 December 1705, recorded the interpretation of this passage in a memorandum. ‘His Doubt was whether he should put the last Quaere thus. What the space that is empty of body is filled with. The plain truth is, that he believes God to be omnipresent in the literal sense; And that as we are sensible of Objects when their Images are brought home within the brain, so God must be sensible of every thing, being intimately present with every thing: for he supposes that as God is present in space where there is no body, he is present in space where a body is also present. But if this way of proposing this his notion be too bold, he thinks of doing it thus. What Cause did the Ancients assign of Gravity. He believes that they reckoned God the Cause of it, nothing els, that is no body being the cause; since every body is heavy.’ “At the last moment, after the last moment really, Newton decided that he had indeed been too bold. He tried to recall the whole edition; and from all the copies he could lay his hands on, he cut out the relevant page, and pasted in a new one which asserted, not that infinite space is the sensorium of God, but that ‘there is a Being incorporeal, living, intelligent, omnipresent, who in infinite Space, as it were in his Sensory, [tanquam Sensorio suo] sees the things themselves intimately …’ Alas, he failed to alter every copy, and one of the originals made its way to Leibniz, who did not fail to hold up to ridicule the concept of space as the sensorium of God. In its initial form the passage recalled ‘De gravitatione,’ the beginning of Newton's rebellion against Cartesian philosophy because of its atheistical tendencies. Following the implications of the rebellion, he had traveled far. In the Latin edition of the Opticks, he gave the fullest exposition of his own conception of nature he would ever put in print before, in his old age, he tried to placate critics by seeming retreats to more conventional positions. “In addition to its importance for Newton’s philosophy, the Latin edition of the Opticks also provided the occasion for a graceful personal relation. Abraham De Moivre saw it through the press. Every evening, according to the story, Newton would wait for him in a coffeehouse where De Moivre would go as soon as he finished the mathematical lessons with which he supported himself. Newton would take him home, and the two would spend the evening in philosophical discussion. De Moivre was one of the young men in London, disciples really, with whom Newton found companionship possible in a way it had never been in Cambridge. Another young disciple, Samuel Clarke, translated the Opticks into Latin and received £500 for his pains: £100 for each of his five children” (Westfall, pp. 646-8). Babson 137; Honeyman 2326; Poggendorff II, 277; Wallis 179. Gjertsen, The Newton Handbook, 1986. Shapiro, ‘Newton’s Optics,’ pp. 165-198 in: The Oxford Handbook of the History of Physics (Buchwald & Fox, eds.), 2013. Westfall, Never at Rest, 1980.
4to (??? mm), pp. [xiv], 348, [2], 24, [2], 43 [recte 47], with 19 engraved plates. Contemporary calf.
Item #6373
Price: $12,500.00
