2008, ISBN: 9780847832095

Paris: Firmin-Didot, 1826. First edition. FOURIER'S PRIZE ESSAY ON FOURIER SERIES: PRECURSOR TO THÃORIE ANALYTIQUE DE LA CHALEUR . First printing of Fourier's prize essay on Fourier seri… More...

Paris: Firmin-Didot, 1826. First edition. FOURIER'S PRIZE ESSAY ON FOURIER SERIES: PRECURSOR TO THÃORIE ANALYTIQUE DE LA CHALEUR . First printing of Fourier's prize essay on Fourier series, and their application to the mathematical theory of heat, composed some five years before his epoch-making Théorie analytique de la chaleur. "The mathematical parts of this paper were expanded into Fourier's most famous work, the Théorie analytique de la chaleur(1822). The physical aspects were intended for re-examination in a companion monograph, but this was never accomplished" (DSB). "This work marks an epoch in the history of both pure and applied mathematics. It is the source of all modern methods in mathematical physics ... The gem of Fourier's great book is 'Fourier series'" (Cajori, A History of Mathematics, p. 270). "The methods that Fourier used to deal with heat problems were those of a true pioneer because he had to work with concepts that were not yet properly formulated. He worked with discontinuous functions when others dealt with continuous ones, used integral as an area when integral as an anti-derivative was popular, and talked about the convergence of a series of functions before there was a definition of convergence ... such methods were to prove fruitful in other disciplines such as electromagnetism, acoustics and hydrodynamics. It was the success of Fourier's work in applications that made necessary a redefinition of the concept of function, the introduction of a definition of convergence, a reexamination of the concept of integral, and the ideas of uniform continuity and uniform convergence. It also provided motivation for the discovery of the theory of sets, was in the background of ideas leading to measure theory, and contained the germ of the theory of distributions" (González-Velasco, p. 428). In December 1807, Fourier submitted a large manuscript, entitled Sur la propagation de la chaleur, to the Institut de France in Paris, "but although Laplace, Lacroix and Monge were in favour of publishing it, Lagrange blocked publication, apparently because its treatment of trigonometric series differed markedly from the way he, Lagrange, had stipulated in the 1750s [it was not actually published until 1972]. Another chance came in 1810, when the Academy of Sciences announced a prize competition on heat diffusion. Fourier submitted a revised memoir, which won [in 1811], but was criticised for a lack of rigour and generality. Fourier thought the criticism unfair, but revised it again, and the resulting book [Théorie analytique] came out in 1822 (after Lagrange's death and when Fourier's standing was rising in the Academy)" (Gray, p. 14). The two offered papers constitute the first publication of Fourier's 1811 prize essay. ABPC/RBH lists the sale of only one copy (the March 1808 issue extracted from the yearly volume, in a modern binding). ABPC/RBH lists only two copies in the last 75 years, both rebound extract of the two journal articles. Born in Auxerre, France, Fourier (1768-1830) was in 1795 appointed an assistant lecturer at the Ãcole Polytechnique, working under Lagrange and Monge. In 1798 Monge, a prominent supporter of Napoleon, selected Fourier to go on the French expedition to Egypt. After the British defeated them there, Fourier returned to France in 1801, hoping to resume his work at the Ãcole Polytechnique, but Napoleon had been impressed by his organisational talents and sent him instead to be the prefect of the Department of Isère. Despite these administrative duties, Fourier managed to pursue scientific research in his spare time, and on 21 December 1807, he sent a paper to the mathematical and physical section of the Institut de France in Paris presenting some of his discoveries. The paper was a large one: 234 pages of text, with many complicated equations, several diagrams of strange mathematical functions, and, in the last part, a few tables of experimental results. "The secrétaire perpétuel of the mathematical and physical section, Delambre, sent it to the Institut's foremost mathematical minds-Lagrange, Laplace, Monge and Lacroix-for examination. The topic was novel and ambitious, for it purported to take the mathematical analysis of physical phenomena outside the terms of reference of Newton's law of universal gravitation; the theoretical investigation of the propagation of heat. Little had been achieved on this problem, although it was known that Biot and Poisson, two of Paris's rising young scientists, were interested in it. Now Fourier, a man in his fortieth year who had published only one paper in his life-a study of the Principle of Virtual Work ten years previously-was submitting his own ideas on the subject ... "There was much for the examiners to ponder over; but the main bone of contention was Lagrange's doubt over the use of all those trigonometric series in forming general solutions to the partial differential equations. Further explanations were called for ... Finally after some coercion, the examiners proposed a prize problem on 2 January 1810: 'Give the mathematical theory of heat and compare the result of this theory with exact experiments.' "The entries had to be in by 1 October 1811. Fourier revised the old paper, reordering some of its material and suppressing many of its diagrams, but preserving all the main results and adding some new sections; and he managed to get the paper, to Paris just in time. Haüy and Malus replaced Monge on the examiners' panel, but the most important judges were still Laplace and Lagrange. Laplace seems to have been quite pleased-he had already made one encouraging reference to the original paper in 1809-but Lagrange was still hostile, and the examiners' report of the 6 January 1812, expressed reservations: ' . . . This work contains the true differential equations of the transmission of heat, both in the interior of the bodies and at their surface, and the novelty of the purpose adjoined to its importance has determined the class [of the Institut] to crown this work, observing, however, that the manner of arriving at its equations is not free from difficulties and its analysis of integration still leaves something to be desired, both relative to its generality and on the side of rigour. The author of this paper is the Baron Fourier, Member of the Legion of Honour, Baron of the Empire.' "So Fourier had won the prize-but with criticism, which he always resented. And still there appeared to be no prospect of getting the paper published in the journals of the Institut. So he began a third version of the work, this time in the form of a book which he would publish separately. This was near completion by 1814 when the biggest upset of his life occurred-the fall of Napoleon" (Grattan-Guinness 1969, p. 250). "Fourier began by exploring the known properties and parameters for the study of heat diffusion. There were three main ones of the latter: conduction internally within a solid body and externally through its surface or boundary into the environment; and specific heat. Assuming them to be constant, he used them to define quantity of heat at a point or section of the body. He took the flow of heat to be uniform, and temperature change linear with respect to distance. He drew upon Newton's law of cooling, that the flow of heat through a domain was proportional to the temperature difference across it ... To mathematize the phenomenon Fourier used the standard differential and integral calculus in the version developed by Euler" (Landmark Writings, p. 356). Fourier was led to the 'heat diffusion equation': in the simplest case of heat flow through a body in one dimension, the temperature T at a distance x along a line at time t satisfies the differential equation d2T/dx2 = KdT/dt, where K is a constant which depends on the physical parameters of the body. For heat flow in bodies of more than one dimension, there was a corresponding partial differential equation. The essay concluded with a section on Fourier's experimental findings. To solve the heat diffusion equation, Fourier used 'separation of variables': he assumed a solution of the form T(x,t) = U(x)V(t), which led to ordinary differential equations for U and V; the solutions for U were trigonometric functions. Since the heat diffusion equation is linear, superposition of such solutions will also be a solution. Fourier thus arrived at solutions of the form T(x,t) = Σ (ar cos rx + br sin rx) exp(-r2Kt), where the infinite sum is over r = 0, 1, 2, 3, ... and the coefficients ar, br are determined by the 'boundary conditions', e.g., the given values of T at certain values of x and t. "There had been a long 18th-century debate about trigonometric series in connection with solutions to the wave equation and the shape of a vibrating string. On the one hand it seemed reasonable that a string could have any continuous initial shape - that was Euler's view - on the other hand the equation could only be solved by functions to which the calculus applied ... Fourier proposed to reopen the debate by boldly asserting that any solution to the heat equation, which he was the first to derive, could be written as an infinite sum of sines and cosines for the simple reason that any function could be written that way. This is a dramatic claim, and it was still more so in his day, because the consensus was that however broadly a function might be defined all the functions that arise in practice are finite sums of familiar ones: polynomials, sines, cosines, exponentials and logarithms, nth roots, and the like. They could also be infinite power series, and indeed infinite trigonometric series, but nonetheless they had the usual sorts of properties, such as smoothly varying graphs. No-one said so in so many words, but it is clear that the expectation was there, and Fourier in particular simply assumed that every function is continuous, as is clear from his account of the coefficients of a Fourier series ... One of the dramas introduced by Fourier's series was that they readily flout all these expectations ... at various stages in the 19th century they provided fresh, and disturbing, examples of just what functions could do. Contrary to what Fourier himself believed, if Cauchy's work began the exploration of what rigorous mathematics can do, Fourier series can indicate just what theory is up against" (Gray, pp. 13-14). To give some indication of Fourier's originality and technical expertise, one problem he considered led to the equation 1 = a1 cos x + a3 cos 3x + a5 cos 5x + ..., from which the coefficients a1, a3, a5, ... had to be determined. Fourier solved these equations by repeated differentiation, followed by putting y = 0. This led to an infinite set of linear equations for a1, a3, a5, ... He took the first n of these equations, truncated them by omitting all but the first n coefficients, solved the resulting finite set of equations, and finally let n tend to infinity. Using John Wallis's expression for Ϥ as an infinite product, this gave a1 = 4/Ϥ, a3 = - 1/3. 4/Ϥ, a5 = 1/5. 4/Ϥ, ... and hence Ϥ/4 = cos x - 1/3 cos 3x + 1/5 cos 5x - ... This formula illustrates an important point which Fourier was the first to understand: the representation of a function by its Fourier series is valid only in a restricted range. For example, the preceding series is valid only when x lies between -Ϥ/2 and Ϥ/2: in fact, if x is between Ϥ/2 and 3Ϥ/2, the sum of the series is -Ϥ/4! One of Lagrange's criticisms was that Fourier series, being periodic functions, are not sufficiently general to represent a 'general' function. Fourier realized that "periodicity is no handicap to generality when the range of values required of the variable equals that period; what happens outside that range is irrelevant to the physical problem, and therefore to the mathematics used to describe it. All this is common wisdom today, but it is the wisdom that Fourier created; Euler and Lagrange wrote under and indeed did much to create an algebraic approach to the theory of functions, and one of its most profound features was that if the algebraic expression f(x) took real values over a particular range of values of x then it must be used, or at least thought of, over the whole of that range. Therefore a 'general' function would have a 'general' range as well as a 'general' shape, and so the restricted range of trigonometric series would in itself exclude their candidature for generality ... It is this profound mistake over the kind of generality demanded of a solution of the wave equation which was as responsible as any other cause for the subsidence into failure of the 18th-century discussion of the vibrating string problem ... The vibrating string analysis was Fourier's great predecessor in the field of linear partial differential equations, and Fourier enriched it by solving the generality problem and introducing into the theory of functions the specification of a range of values to a function independent of its shape or equation" (Grattan-Guinness 1969, pp. 241-242).  Remarkable as the prize essay was for its originality in the introduction and application of Fourier series, it actually went beyond standard Fourier series in its discussion of heat flow in bodies with curved boundaries. The study of heat flow in a sphere led to non-periodic series such as a1 sin n1x + a2 sin n2x + a3 sin n3x + ..., where n1, n2, n3, ..., instead of being integers (or integer multiples of a fixed quantity), are roots of the equation nX / tan nX = constant (where X is a constant). When Fourier considered heat flow in a cylinder, trigonometric series did not work: they had to be replaced by what are now known as 'Bessel functions', and Fourier developed many of their basic properties more than a decade before Friedrich Wilhelm Bessel introduced them in his astronomical work. From a modern point of view, some of Lagrange's criticisms were justified, particularly those relating to the question of convergence of Fourier series and of whether 'any' function could be expanded in a Fourier series. These questions would only be answered decades later, especially by Lejeune Dirichlet. "Fourier was not a naive formalist: he could handle problems of convergence quite competently, as in his discussion of the series for the saw-tooth function. The leading technical ideas of several basic proofs, such as that of Dirichlet on the convergence of the Fourier series, can be found in his work. Moreover, he saw, long before anyone else, that term-by-term integration of a given trigonometric series, to evaluate the coefficients, is no guarantee of its correctness; the completeness of a series is not to be assumed. The great shock caused by his trigonometric expansions was due to his demonstration of a p, Firmin-Didot, 1826, 0, Paris: David l'ainé, 1744. First edition. 'D'ALEMBERT'S PRINCIPLE' APPLIED TO HYDRODYNAMICS . First edition of this continuation of d'Alembert's classic Traité de dynamique published in the previous year. "The 'Treatise on Dynamics' was d'Alembert's first major book and it is a landmark in the history of mechanics. It reduces the laws of the motion of bodies to a law of equilibrium. Its statement that 'the internal forces of inertia must be equal and opposite to the forces that produce the acceleration' is still known as 'd'Alembert's principle'. This principle is applied to many phenomena and, in particular, to the theory of the motion of fluids" (PMM 195). D'Alembert had applied his principle to fluid mechanics in a brief section at the end of the Traité de dynamique, but in the present work he gives a far more detailed treatment."In 1744 d'Alembert published a companion volume to his first work, the Traité de l'équilibre et du mouvement des fluides. In this work d'Alembert used his principle to describe fluid motion, treating the major problems of fluid mechanics that were current. The sources of his interest in fluids were many. First, Newton had attempted a treatment of fluid motion in his Principia, primarily to refute Descartes's tourbillon theory of planetary motion. Second, there was a lively interest in fluids by the experimental physicists in the eighteenth century, for fluids were most frequently invoked to give physical explanations for a variety of phenomena, such as electricity, magnetism, and heat. There was also the problem of the shape of the earth: What shape would it be expected to take if it were thought of as a rotating fluid body? Clairaut published a work in 1744 which treated the earth as such, a treatise that was a landmark in fluid mechanics. Furthermore, the vis viva controversy was often centered on fluid flow, since the quantity of vis viva was used almost exclusively by the Bernoullis in their work on such problems. Finally, of course, there was the inherent interest in fluids themselves. D'Alembert's first treatise had been devoted to the study of rigid bodies; now he was giving attention to the other class of matter, the fluids. He was actually giving an alternative treatment to one already published by Daniel Bernoulli [Hydrodynamica, 1738], and he commented that both he and Bernoulli usually arrived at the same conclusions. He felt that his own method was superior. Bernoulli did not agree" (DSB). D'Alembert himself gives an account of the Traité des fluides in the article 'Hydrodynamique' in the Encyclopédie. "My object in this book has been to reduce the laws of fluid equilibrium and motion to the least possible number and to determine by an extremely simple general principle, everything that is concerned with the motion of fluid bodies. I have examined the theories given by M. Bernoulli and M. Maclaurin and I believe that I have revealed the difficulties as well as confusion. I also believe that on certain occasions M. Daniel Bernoulli has used the principle of live forces in cases where he should not have done so. I must add that this great geometer has used this principle without having proved it, or rather that the proof that he has provided is unsatisfactory. However this should not stop from providing this work with the merit that other scientists as well as I should give to this work. I deal as well in this work on the resistance of fluids to bodily motion, of refraction or the motion of a body as it enters into a fluid and finally concerning laws of motion governing fluids which move in vortices" (The Encyclopedia of Diderot and d'Alembert Collaborative Translation Project). The Traité des fluides is based on the principle set forth in the Traité de dynamique. In the first part of the earlier work, "d'Alembert developed his own three laws of motion. It should be remembered that Newton had stated his laws verbally in the Principia, and that expressing them in algebraic form was a task taken up by the mathematicians of the eighteenth century. D'Alembert's first law was, as Newton's had been, the law of inertia. D'Alembert, however, tried to give an a priori proof for the law, indicating that however sensationalistic his thought might be he still clung to the notion that the mind could arrive at truth by its own processes. His proof was based on the simple ideas of space and time; and the reasoning was geometric, not physical, in nature. His second law, also proved as a problem in geometry, was that of the parallelogram of motion. It was not until he arrived at the third law that physical assumptions were involved. "The third law dealt with equilibrium, and amounted to the principle of the conservation of momentum in impact situations. In fact, d'Alembert was inclined to reduce every mechanical situation to one of impact rather than resort to the effects of continual forces; this again showed an inheritance from Descartes. D'Alembert's proof rested on the clear and simple case of two equal masses approaching each other with equal but opposite speeds. They will clearly balance one another, he declared, for there is no reason why one should overcome the other. Other impact situations were reduced to this one; in cases where the masses or velocities were unequal, the object with the greater quantity of motion (defined as mv) would prevail. In fact, d'Alembert's mathematical definition of mass was introduced implicitly here; he actually assumed the conservation of momentum and defined mass accordingly. This fact was what made his work a mathematical physics rather than simply mathematics. "The principle that bears d'Alembert's name was introduced in the next part of the Traité. It was not so much a principle as it was a rule for using the previously stated laws of motion. It can be summarized as follows: In any situation where an object is constrained from following its normal inertial motion, the resulting motion can be analyzed into two components. One of these is the motion the object actually takes, and the other is the motion "destroyed" by the constraints. The lost motion is balanced against either a fictional force or a motion lost by the constraining object. The latter case is the case of impact, and the result is the conservation of momentum (in some cases, the conservation of vis viva as well). In the former case, an infinite force must be assumed. Such, for example, would be the case of an object on an inclined plane. The normal motion would be vertically downward; this motion can be resolved into two others. One would be a component down the plane (the motion actually taken) and the other would be normal to the surface of the plane (the motion destroyed by the infinite resisting force of the plane)" (DSB). "The Traité de dynamique permeates a large part of his work, quite explicitly so in the case of the Traité des fluides" (Crépel, p. 165). "At the end of his treatise on dynamics, d'Alembert considered the hydraulic problem of efflux through the vessel ... D 'Alembert intended his new solution of the efflux problem to illustrate the power of his principle of dynamics. He clearly relied on the long-known analogy with a connected system of solids. Yet he believed this analogy to be imperfect. Whereas in the case of solids the condition of equilibrium was derived from the principle of virtual velocities, in the case of fluids d'Alembert believed that only experiments could determine the condition of equilibrium. As he explained in his treatise of 1744 on the equilibrium and motion of fluids, the interplay between the various molecules of a fluid was too complex to allow for a derivation based on the only a priori known dynamics, that of individual molecules. "In this second treatise, d'Alembert provided a similar treatment of efflux, including his earlier derivations of the equation of motion and the conservation of live forces, with a slight variant: he now derived the equilibrium condition by setting the pressure acting on the bottom slice of the fluid to zero. Presumably, he did not want to base the equations of equilibrium and motion on the concept of internal pressure, in conformance with his general avoidance of internal contact forces in his dynamics. His statement of the general conditions of equilibrium of a fluid, as found at the beginning of his treatise, only required the concept of wall pressure ... "In the rest of his treatise, d'Alembert solved problems similar to those of Daniel Bernoulli's Hydrodynamica, with nearly identical results. The only important difference concerned cases involving the sudden impact of two layers of fluids. Whereas Daniel Bernoulli still applied the conservation of live forces in such cases (save for possible dissipation into turbulent motion), d'Alembert's principle of dynamics there implied a destruction of live force. Daniel Bernoulli disagreed with these and a few other changes. In a contemporary letter to Euler he expressed his exasperation over d'Alembert's treatise: 'I have seen with astonishment that apart from a few little things there is nothing to be seen in his hydrodynamics but an impertinent conceit. His criticisms are puerile indeed, and show not only that he is no remarkable man, but also that he never will be.' "In this judgment, Daniel Bernoulli overlooked that d'Alembert's hydrodynamics, being based on a general dynamics of connected systems, lent itself to generalizations beyond parallel-slice flow. D'Alembert offered striking illustrations of the power of his approach in a prize-winning memoir published in 1747 on the cause of winds [Réflexions sur la cause générale des vents, 1747]" (Darrigol, pp. 14-16). "D'Alembert's Traité des fluides was largely a criticism of Bernoulli's Hydrodynamica. Where Bernoulli had used the conservation of vis viva to arrive at his results, d'Alembert employed his 'Principle', first used successfully in the Traité de dynamique. On a few points of detail d'Alembert's criticisms were valid (as, for instance, his clarification of negative pressures), but he retained Bernoulli's hypothesis of parallel sections (that is, the assumption that a fluid moving through any conduit may be divided into layers perpendicular to its axis of flow and that these layers always retain a plane surface perpendicular to the axis), and therefore his method failed just where Bernoulli's had failed. What particularly annoyed Bernoulli was d'Alembert's complete disregard for all the experimental evidence that he had brought forward in his own work - a criticism of d'Alembert that later became quite characteristic. Bernoulli was more favourably impressed by d'Alembert's Traité de dynamique which he had received after the Traité des fluids. He told Euler that this work had given him a 'rather good opinion' of its author, although he had not changed his mind about d'Alembert's hydrodynamics" (Hankins, p. 45). In Book I of the Traité des fluides, d'Alembert discusses various cases of fluid equilibrium such as fluid equilibrium with immersed solids, pressure distribution in the fluid layers with gravity in a constant direction, the equilibrium of fluids of different densities, the law relating gravity and density in different layers of a fluid, the equilibrium of a fluid in which the layers vary in density, the "adherence" of fluids, the equilibrium of a fluid with a curved upper surface (with application to the figure of the earth), and the equilibrium of elastic fluids. Book II is devoted to the movement of fluids contained in vessels. D'Alembert contrasts his own approach with that in Bernoulli's Hydrodynamica, and also with that in Colin Maclaurin's Treatise of Fluxions (1742). Book III deals with the resistance experienced by bodies moving through fluids. It ends with a chapter on vortex flow, including the motion of bodies in rotating fluid masses. "A natural son of the chevalier Destouches and Mme. De Tencin, D'Alembert was born on 16 or 17 November 1717 and was placed (rather than abandoned) on the steps of the church of Saint-Jean-le-Rond in Paris-whence his given name, although much later he preferred 'Daremberg', then 'Dalembert' or 'D'Alembert'. He followed his secondary studies at the Quatre-Nations College in Paris, and later studied law and probably a little medicine. His first memoir was submitted to the Académie des Sciences in Paris in 1739, and he became a member of that institution in 1741. The Traité de dynamique was D'Alembert's first major work, to be followed by many others in the 1740s and early 1750s. He was co-editor with Dénis Diderot of the Encyclopédie, for which he wrote the introduction (1751) and around 1700 articles, mainly scientific, the majority of them before the work was banned following his article 'Genève' in 1758-1759. He was appointed to membership of the Académie Française in 1754 and quickly became second to Voltaire in the group for philosophes. In 1772 he became permanent secretary of this academy (but not that for sciences). He died of gall-stones on 29 October 1783" (Crépel, p. 160). Bibliotheca Mechanica, pp. 7-8; En français dans le texte, p. 167; Honeyman 7; Norman 33; Sotheran I, 74. Darrigol, Worlds of Flow, 2008. Hankins, Jean d'Alembert, 1970. Crépel, 'Jean le Rond d'Alembert, Traité de dynamique,' Chapter 11 in Landmark Writings in Western Mathematics 1640-1940 (Grattan-Guinness, ed.), 2005. 4to (220 x 169 mm), pp. xxxii, [8], 458, [2], with engraved printer's device on title and 10 folding engraved plates. Contemporary vellum., David l'ainé, 1744, 0, Powerful, beautiful, wild, fragile, and elegant, horses are as diverse and as enigmatic as people. This oversized luxuriously illustrated book, designed by Sam Shahid, is a celebration of the physical beauty of the animal, of what horses can do, and the sense of wonder and awe that the horse evokes. A competitive amateur show-jumper since childhood, Kelly Klein is a highly respected horsewoman, as well as a renowned fashion stylist. In this stunning collection of more than 250 selected photographs, including many previously unpublished, she conveys her very intimate and personal fascination with horses, and the intense vulnerability that counters their natural power and majesty. Mingling high fashion images with vintage shots of races and rodeos, fine art with amateur photography, this anthology is as provocative as it is beautiful, and reveals the extraordinary spectrum of emotions horses inspire in us. With photographs by Helmut Newton, Annie Leibowitz, Bruce Weber, Robert Mapplethorpe, Chris Makos, Richard Prince, Bob Richardson, and Ellen von Unwerth, among many others, Horse is a definitive reflection of an indefinable love and a passionate tribute to a uniquely beautiful animal. Horse is also available in a deluxe slipcased edition limited to 500 copies, each signed by Kelly Klein., Rizzoli, 2008, 0<

2008, ISBN: 9780847832095

Powerful, beautiful, wild, fragile, and elegant, horses are as diverse and as enigmatic as people. This oversized luxuriously illustrated book, designed by Sam Shahid, is a celebration of… More...

Powerful, beautiful, wild, fragile, and elegant, horses are as diverse and as enigmatic as people. This oversized luxuriously illustrated book, designed by Sam Shahid, is a celebration of the physical beauty of the animal, of what horses can do, and the sense of wonder and awe that the horse evokes. A competitive amateur show-jumper since childhood, Kelly Klein is a highly respected horsewoman, as well as a renowned fashion stylist. In this stunning collection of more than 250 selected photographs, including many previously unpublished, she conveys her very intimate and personal fascination with horses, and the intense vulnerability that counters their natural power and majesty. Mingling high fashion images with vintage shots of races and rodeos, fine art with amateur photography, this anthology is as provocative as it is beautiful, and reveals the extraordinary spectrum of emotions horses inspire in us. With photographs by Helmut Newton, Annie Leibowitz, Bruce Weber, Robert Mapplethorpe, Chris Makos, Richard Prince, Bob Richardson, and Ellen von Unwerth, among many others, Horse is a definitive reflection of an indefinable love and a passionate tribute to a uniquely beautiful animal. Horse is also available in a deluxe slipcased edition limited to 500 copies, each signed by Kelly Klein., Rizzoli, 2008, 0<

2008, ISBN: 9780847832095

Hardcover

Rizzoli International Publications, Hardcover, Auflage: 01, 272 Seiten, Publiziert: 2008-10-28T00:00:01Z, Produktgruppe: Book, 7.17 kg, Verkaufsrang: 10809230, Plants & Animals, Nature & … More...

Rizzoli International Publications, Hardcover, Auflage: 01, 272 Seiten, Publiziert: 2008-10-28T00:00:01Z, Produktgruppe: Book, 7.17 kg, Verkaufsrang: 10809230, Plants & Animals, Nature & Wildlife, Photography & Video, Arts & Photography, Subjects, Books, Horses, Mammals, Animal Sciences, Biological Sciences, Science, Nature & Maths, Rizzoli International Publications, 2008<