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Méchanique analitique. [Bound with:] Théorie des fonctions analytiques

Méchanique analitique. [Bound with:] Théorie des fonctions analytiques

LAGRANGE, Joseph Louis de An exceptional volume, in a fine contemporary binding, containing the first edition of Lagrange's masterpiece, the Méchanique, "one of the outstanding landmarks in the history of both mathematics and mechanics" (Sarton, p. 470) and "perhaps the most beautiful mathematical treatise in existence, together with the corrected second printing of the Théorie, containing Lagrange's formulation of calculus in terms of infinite series, which provided the basis for Augustin-Louis Cauchy's development of complex function theory in the first decades of the next century. The Méchanique contains the discovery of the general equations of motion, the first epochal contribution to theoretical dynamics after Newton's Principia" (Evans). "Lagrange's masterpiece, the Méchanique Analitique (Paris, 1788), laid the foundations of modern mechanics, and occupies a place in the history of the subject second only to that of Newton's Principia" (Wolf). "The year 1797 . saw the appearance of the famous work of Lagrange, Théorie des fonctions analytiques . This book developed with care and completeness the characteristic definition and method in terms of 'fonctions dérivées,' based upon Taylor's series, which Lagrange had proposed in 1772 . Lagrange's Théorie des fonctions was only one, but by far the most important, of many attempts made about this time to furnish the calculus with a basis which would logically modify or supplant those given in terms of limits and infinitesimals" (Cajori). "With the appearance of the Mécanique Analytique in 1788, Lagrange proposed to reduce the theory of mechanics and the art of solving problems in that field to general formulas, the mere development of which would yield all the equations necessary for the solution of every problem . [it] united and presented from a single point of view the various principles of mechanics, demonstrated their connection and mutual dependence, and made it possible to judge their validity and scope. It is divided into two parts, statics and dynamics, each of which treats solid bodies and fluids separately. There are no diagrams. The methods presented require only analytic operations, subordinated to a regular and uniform development. Each of the four sections begins with a historical account which is a model of the kind." (DSB). "In [Méchanique Analitique] he lays down the law of virtual work, and from that one fundamental principle, by the aid of the calculus of variations, deduces the whole of mechanics, both of solids and fluids. The object of the book is to show that the subject is implicitly included in a single principle, and to give general formulae from which any particular result can be obtained. The method of generalized co-ordinates by which he obtained this result is perhaps the most brilliant result of his analysis. Instead of following the motion of each individual part of a material system, as D'Alembert and Euler had done, he showed that, if we determine its configuration by a sufficient number of variables whose number is the same as that of the degrees of freedom possessed by the system, then the kinetic and potential energies of the system can be expressed in terms of those variables, and the differential equations of motion thence deduced by simple differentiation . Amongst other minor theorems here given I may mention the proposition that the kinetic energy imparted by the given impulses to a material system under given constraints is a maximum, and the principle of least action. All the analysis is so elegant that Sir William Rowan Hamilton said the work could only be described as a 'scientific poem'" (Rouse Ball, A Short Account of the History of Mathematics). The Méchanique analitique "was certainly regarded as the most important unification of rational mechanics at the turn of the 18th century and as its 'crowning' (Dugas). This achievement of unification and the abstract-formal nature of the work, physically reflected in immediate applications, earned the extravagant praise of Ernst Mach: 'Lagrange [.] strove to dispose of all necessary considerations once and for all, including as many as possible in one formula. Every case that arises can be dealt with according to a very simple, symmetric and clearly arranged scheme [.] Lagrangian mechanics is a magnificent achievement in respect of the economy of thought' (Mach, Die Mechanik in ihrer Entwicklung, 1933, 445)" (Pulte, p. 220). "Lagrange produced the Méchanique analitique during his time in Berlin. He referred as early as 1756 and 1759 to an almost complete textbook of mechanics, now lost; a later draft first saw the light of day in 1764. But it was not until the end of 1782 that Lagrange seems to have put the textbook into an essentially complete form, and the publication of the book was delayed a further six years" (Pulte, p. 209). "By 1790 a critical attitude had developed both within mathematics and within general scientific culture. As early as 1734 Bishop George Berkeley in his work The Analyst had called attention to what he perceived as logical weaknesses in the reasonings of the calculus arising from the employment of infinitely small quantities. Although his critique was somewhat lacking in mathematical cogency, it at least stimulated writers in Britain and the Continent to explain more carefully the basic rules of the calculus. In the 1780s a growing interest in the foundations of analysis was reflected in the decisions of the academies of Berlin and Saint Petersburg to devote prize competitions to the metaphysics of the calculus and the nature of the infinite. In philosophy Immanuel Kant's Kritik der reinen Vernunft (1787) set forth a penetrating study of mathematical knowledge and initiated a new critical movement in the philosophy of science . "The full title of the Théorie explains its purpose: 'Theory of analytical functions containing the principles of the differential calculus disengaged from all consideration of infinitesimals, vanishing limits or fluxions
Geometria

Geometria, aÌ Renato Des Cartes Anno 1637 GalliceÌ edita; nunc autem cum notis Florimondi De Beaune, in curia Bloesensi consilliari regii, in linguam Latinam versa, & commentariis illustrata, operâ atque studio Francisci aÌ Schooten.

DESCARTES, René First separate edition of Descartes's magnum opus (DSB), the invention of coordinate geometry and one of the key texts in the history of mathematics - this is an exceptional copy, uncut in the original interim boards. The Geometry was originally published in French as the third part of the Discours de la Méthode; the French text was not issued separately until 1664. Descartes' "application of modern algebraic arithmetic to ancient geometry created the analytical geometry which was the basis of the post-Euclidean development of that science" (PMM). It "rendered possible the later achievements of seventeenth-century mathematical physics" (M. B. Hall, Nature and nature's laws (1970), p. 91). "Inspired by a specific and novel view of the world, Descartes produced his Géométrie, a work as exceptional in its contents (analytic geometry) as in its form (symbolic notation), which slowly but surely upset the ancient conceptions of his contemporaries. In the other direction, this treatise is the first in history to be directly accessible to modern-day mathematicians. A cornerstone of our 'modern' mathematical era, the Géométrie thus paved the way for Newton and Leibniz" (Serfati, p. 1). "Divided into three books, it opens with the claim that 'Any problem in geometry can easily be reduced to such terms that a knowledge of the lengths of certain lines is sufficient for its construction.' In this spirit, Book I is concerned with 'Problems which can be constructed by the aid of circles and straight lines.' The highlight of Book I is the solution, by algebraic means, of the problem, outstanding since the time of Euclid, of the four-line locus. Book II contains a little-used classification of curves, and Descartes' method of drawing tangents. The final Book III deals with the solution of higher-order equations, as well as Descartes' rule of signs" (Gjertsen, Newton Handbook, p. 170). It was through this Latin translation, with its extensive commentary by Frans van Schooten and Florimonde De Beaune, that Newton and other contemporary mathematicians acquired an understanding of Descartes's work. It is also the most accessible edition for bibliophiles, the Discours now commanding a six-figure sum. We have never seen another copy uncut in original boards, and none is recorded on ABPC/RBH. Descartes' interest in geometry was stimulated when, in 1631, Jacob Golius (1596-1667), a professor of mathematics and oriental languages at Leyden, sent Descartes a geometrical problem, that of 'Pappus on three or four lines'. It had originally been posed and solved shortly before the time of Euclid in a work called Five books concerning solid loci by Aristaeus, and was then studied by Apollonius and later by Pappus. But the solution was lost in the 17th century, and the problem became an important test case for Descartes. Claude Hardy, a contemporary at the time of its solution, later reported to Leibniz the difficulties that Descartes had met in solving it (it took him six weeks), which 'disabused him of the small opinion he had held of the analysis of the ancients'. The Pappus problem is a thread running through the entire work. Book One is entitled 'Problems the construction of which requires only straight lines and circles,' and it is in this opening book that Descartes details his geometrical analysis, that is, how geometrical problems are to be formulated algebraically. It begins with the geometrical interpretation of algebraic operations, which Descartes had already explored in the early period of his mathematical research. However, what we are presented in 1637 is a "gigantic innovation" both over Descartes' previous work and the work of his contemporaries (Guicciardini, p. 38). On the one hand, Descartes offers a geometrical interpretation of root extraction and thus treats five arithmetical operations. Crucially, he also uses a new exponential notation (e.g. x3), which replaces the traditional cossic notation of early modern algebra, and allows Descartes to tighten the connection between algebra and geometry. Descartes proceeds to describe how one is to give an algebraic interpretation of a geometrical problem: 'If, then, we wish to solve any problem, we first suppose the solution already effected, and give names to all the lines that seem needful for its construction, to those that are unknown as well as to those that are known. Then, making no distinction between unknown and unknown lines, we must unravel the difficulty in any way that shows most naturally the relations between these lines, until we find it possible to express a single quantity in two ways. This will constitute an equation, since the terms of one of these two expressions are together equal to the terms of the other.' Descartes applies his geometrical analysis to solve the four-line case of the Pappus problem, and shows how the analysis can be generalized to apply to the general, n-line version of the problem, which had not been solved by the ancients. Book Two, entitled 'On the Nature of Curved Lines,' commences with Descartes' famous distinction between 'geometric' and 'mechanical' curves. For Pappus, 'plane' curves were those constructible by ruler and compass, 'solid' curves were the conic sections, and 'linear' curves were the rest, such as the conchoids, the spiral, the quadratrix and the cissoid. The linear curves were also called 'mechanical' by the ancient Greeks because instruments were needed to construct them. Following Descartes, the supremacy of algebraic criteria became established: curves were defined by equations with integer degrees. Algebra thus brought to geometry the most natural hierarchies and principles of classification. This was extended by Newton to fractional and irrational exponents, and by Leibniz to 'variable' exponents (gradus indefinitus, or transcendental in modern terminology). Book Three, entitled 'The construction of solid, and higher than solid problems,' is devoted to the theory of equations and the geome
De Ovi Mammalium et Hominis Genesi Epistolam ad Academiam Imperialem Scientiarum Petropolitanam dedit Carolus Ernestus a Baer

De Ovi Mammalium et Hominis Genesi Epistolam ad Academiam Imperialem Scientiarum Petropolitanam dedit Carolus Ernestus a Baer

BAER, Karl Ernst von First edition, rare, especially in original boards as here, of von Baer's landmark paper, in which he announced the discovery of the mammalian ovum. The idea that all animals begin as eggs had been current at least since the seventeenth century, when William Harvey, in his De Generatione Animalium (1651), defended it against the false notions of spontaneous generation and the "preformation" of the foetus. Harvey's theory was strengthened in 1672, when Reinier de Graaf published his observations of the Graafian vesicle (which contains the ovum) and the process of ovulation; and in 1825, when Johann Evangelista Purkinje announced his discovery of the germinal vesicle in the embryo. However, the mammalian ovum itself remained unobserved until von Baer, in his experiments with dogs and other mammals, "plot[ted] the course of ovulation and fertilization from its later stages back to the ovary and there . identif[ied] the minute cell which was the ovum" (PMM). In von Baer's own words, "when I observed the ovary . . . I discovered a small yellow spot in a little sac, then I saw these same spots in several others, and indeed in most of them-always in just one little spot. How strange, I thought, what could it be? I opened one of these little sacs, lifting it carefully with a knife onto a watchglass filled with water, and put it under the microscope. I shrank back as if struck by lightening, for I clearly saw a minuscule and well developed yellow sphere of yolk" (quoted in Baer, 'On the Genesis of the Ovum of Mammals and Man,' tr. O'Malley, Isis 47 (1956), p. 120). Von Baer concluded that every sexually reproducing animal - including man - develops originally from an egg cell, "a unifying doctrine whose importance cannot be overemphasized" (DSB). For this concept and for his further researches in embryology, contained in his monumental Entwickelungsgeschichte der Thiere (1828--1837), Garrison and Morton have named von Baer "the father of modern embryology." ABPC/RBH list only two copes in original boards in the last 35 years (Sotheby's, June 8, 2011, lot 65, £15,000 (rebacked); Sotheby's NY, November 16, 2001, lot 7, $30,650 (Friedman copy)). "Earlier researchers had used microscopes to look at eggs and to try to explain early development. Mid-17th century scientists, such as Marcello Malpighi and Nicolas Steno, both in Italy, claimed that living beings developed from a corpuscular element called the ovum, which in Latin means egg, as its function corresponded to the birds' eggs . In 1651, the physician William Harvey had employed the Latin word ovum to refer to the beginning of animal life in his Exercitationes de generatione animalium (Exercises on Animal Generation). Harvey provided no evidence for such a claim. From the 17th to the 19th century, other scholars in Europe, such as Regner de Graaf, William Cruikshank, Jean-Luis Prévost, and Jean-Baptiste André Dumas had observed the ovum in mammals. However, their contributions were imprecise about the place in which the ovum was likely generated . "The pamphlet has an introduction and six chapters. In the introduction, von Baer first praises the Imperial Academy of Sciences in Saint Petersburg, Russia, and the works of its scholars. Second, he outlines the conceptual background of his discovery, in particular the debate about the relationship between Graafian follicles and the ovum. Scholars involved in that debate either argued that a Graafian follicle was actually the ovum, as had de Graff in 1672, or that it did not correspond to the ovum, as had Cruikshank argued in 1797 and Prévost and Dumas in 1824. Third, von Baer states that the goal of his research is to resolve that debate by assessing the relationship between a Graafian follicle and the ovum. After introducing the historical context, von Baer writes that the main organism he used for his research was the dog. "In Chapters One and Two, von Baer describes the first stages of development in the dog embryo, and he names its different parts. He writes about the first stages of development, and he describes the embryo's shape, color, and position of the anatomical structures. Additionally, von Baer notes that in more advanced stages of development the ovum lies in the uterus, while in less advanced stages it lies in the oviducts. His observations, and the similarity of the ovum between the early and later stages, enabled von Baer to infer that the ovum passes through the oviducts before reaching the uterus. "In Chapter Three, von Baer writes about the dog's ovum as he found it in the ovary. Von Baer claims that the ovum is not exactly the same as the Graafian follicle, as some scholars had thought, and that it lies inside the follicle. In Chapter Four, von Baer describes the formation of the Graafian follicle by comparing how that phenomenon occurs in different mammals. Such a comparison demonstrated that in all of those mammals the ovum is formed in the same way. In Chapter Five and Six, von Baer describes the development of mammals in general, and he summarizes the course of the ovum from the ovary to the oviducts to the uterus. Additionally, he compares the ovum of mammals with the ovum of other animals, such as birds. Von Baer concludes that all animals develop from an ovum. Von Baer's statement that reproduction begins with a corpuscular element rather than with liquid matter influenced debates concerning generation, because it disproved a claim of Albrecht von Haller's, who worked in Switzerland, that development starts from fluids . "Although von Baer was skeptical of common ancestry and natural selection, Charles Darwin's portrayal of development in The Origin of Species was the same as von Baer's: branching and epigenetic. Darwin also provided the same critiques of recapitulation as had von Baer; Darwin said that adult forms of one animal do not show themselves in other animal's development, and that only the embryos look similar to one another. Darwin also wrote that embryology p
Theorie der Parallellinien

Theorie der Parallellinien

LAMBERT, Johann Heinrich First edition, very rare, and a copy with excellent provenance, of one of the most important works on non-Euclidean geometry preceding those of Bolyai and Lobachevsky half a century later. Lambert derived several fundamental results in this subject, and "no one else came so close to the truth without actually discovering non-Euclidean geometry" (Boyer, History of Mathematics, p. 504). "The memoir Theorie der Parallellinien (Theory of parallel lines) by Johann Heinrich Lambert (1727-1777), written probably in 1766, is a masterpiece of mathematical literature, and its author is one of the most outstanding minds of all times" (Papadopoulos & Théret). "In the introductory part of his treatise Lambert wrote: 'This work deals with the difficulty encountered in the very beginnings of geometry and which, from the time of Euclid, has been a source of discomfort for those who do not just blindly follow the teachings of others but look for a basis for their convictions and do not wish to give up the least bit of the rigor found in most proofs. This difficulty immediately confronts every reader of Euclid's Elements, for it is concealed not in his propositions but in the axioms with which he prefaced the first book'" (Rosenfeld, A History of Non-Euclidean Geometry, p. 99). This difficulty was the question of whether Euclid's 'Parallel Postulate' - that through any given point not on a given straight line one can draw exactly one straight line that is parallel to (i.e., which does not intersect) the given line - could be deduced from the other axioms of Euclidean geometry. Girolamo Saccheri, in his Euclides ab omni naevo vindicatus (1733), had deduced many interesting consequences of denying the parallel postulate, but had ultimately concluded, erroneously, that denying it led to a contradiction. Lambert was the first to realize "that Euclid's Parallel Postulate cannot be proved from the other Euclidean postulates and that it is possible to build a logically consistent system satisfying the other postulates but explicitly rejecting the Parallel Postulate" (Parkinson, Breakthroughs, 1766 & 1786). OCLC lists no copies in US; no copies on ABPC/RBH. Provenance: Max Steck (1907-71), German-Swiss mathematician and mathematical historian (bookplate on front paste-down). Steck was the editor of Johann Heinrich Lambert: Schriften zur Perspektive (Berlin, 1943), which contains a Bibliographia Lambertiana (reprinted separately, Hildesheim, 1970). Lambert became interested in the parallel postulate after having heard of Georg Simon Klügel's dissertation Conatuumpraecipuorum theoriam parallelarum demonstrandi from 1763, in which he had shown the flaws of all proofs so far of the parallel postulate. This inspired Lambert to take up the subject himself. Like Saccheri's Euclides vindicatus, "Lambert wrote his Theorie der Parallellinien in an attempt to prove, by contradiction, the parallel postulate. He deduced remarkable consequences from the negation of that postulate. These consequences make his memoir one of the closest (probably the closest) text to hyperbolic geometry, among those that preceded the writings of Lobachevsky, Bolyai and Gauss. We recall by the way that hyperbolic geometry was acknowledged by the mathematical community as a sound geometry only around the year 1866, that is, one hundred years after Lambert wrote his memoir. "To give the reader a feeling of the wealth of ideas developed in Lambert's memoir, let us review some of the statements of hyperbolic geometry that it contains. Under the negation of Euclid's parallel postulate, and if all the other postulates are untouched, the following properties hold: (1) The angle sum in an arbitrary triangle is less than 180°. (2) The area of triangles is proportional to angle defect, that is, the difference between 180° and the angle sum. (3) There exist two coplanar disjoint lines having a common perpendicular and which diverge from each other on both sides of the perpendicular. (4) Given two coplanar lines d1 and d2 having a common perpendicular, if we elevate in the same plane a perpendicular d3 to d1 at a point which is far enough from the foot of the common perpendicular, then d3 does not meet d2. (5) Suppose we start from a given point in a plane the construction of a regular polygon, putting side by side segments having the same length and making at the junctions equal angles having ascertain value between 0 and 180°. Then, the set of vertices of these polygons is not necessarily on a circle. Equivalently, the perpendicular bisectors of the segment do not necessarily intersect. (6) There exist canonical measures for length and area. "Property (6) may need some comments. There are several ways of seeing the existence of such a canonical measure. For instance, we know that in hyperbolic geometry, there exists a unique equilateral triangle which has a given angle which we can choose in advance (provided it is between 0 and 60°). This establishes a bijection [one-to-one correspondence] between the set of angles between 0 and 60° and the set of lengths. We know that there is a canonical measure for angles (we take the total angle at each point to be equal to four right angles.) From the above bijection, we deduce a canonical measure for length. This fact is discussed by Lambert in §80 of his memoir. Several years after Lambert, Gauss noticed the same fact. In a letter to his friend Gerling, dated April 11, 1816 (cf. C. F. Gauss, Werke, Vol. VIII, p. 168), he writes: "It would have been desirable that Euclidean geometry be not true, because we would have an a priori universal measure. We could use the side of an equilateral triangle with angles 59°59'59,9999" as a unit of length". We note by the way that there is also a canonical measure of lengths in spherical geometry, and in fact, a natural distance in this geometry is the so-called 'angular distance'. "It also follows from Lambert's memoir that in some precise sense there are exactly three geometries
Sketch of the Analytical Engine invented by Charles Babbage Esq. By L. F. Menabrea of Turin

Sketch of the Analytical Engine invented by Charles Babbage Esq. By L. F. Menabrea of Turin, Officer of the Military Engineers, with Notes by the Translator

LOVELACE, Lady Ada Augusta [MENABREA, Luigi] First edition, journal issue, of the best contemporary description of Babbage's Analytical Engine, the first programmable (mechanical) computer. It is a translation by Lovelace of a report by Menabrea of a series of lectures given by Babbage while he was in Turin. At Babbage's suggestion, Lovelace added seven explanatory notes; as a result, the translation is three times as long as the original. Two of these notes are essentially programs for the Analytical Engine; their inclusion has given rise to the claim that Lovelace was the first computer programmer. "In the fall if 1841, after eight years of work, Babbage described his landmark Analytical Engine at a seminar in Turin. Although the Engine was never constructed, there is no doubt that in conception and design, it embodied all of the essential elements of what is recognized today as a general-purpose digital computer. L.F. Menabrea, an Italian military engineer who attended the seminar, reported the presentation the following year in an obscure Swiss serial, and Babbage urged Ada Lovelace to translate the report into English. In fact, Lovelace undertook a far larger task: adding to her translation a series of important explanatory 'Notes' substantially longer than Menabrea's article" (Grolier Extraordinary Women, p. 122). The collaboration "between Byron's celebrity daughter and Babbage is one of the more unusual in the history of science . Ada's translation of Menabrea's paper, with its lengthy explanatory notes, represents the most complete contemporary account in English of the intended design and operation of the first programmable digital computer. Babbage considered this paper a complete summary of the mathematical aspects of the machine, proving 'that the whole of the development and operations of Analysis are now capable of being executed by machinery.' As part of his contribution to the project, Babbage supplied Ada with algorithms for the solution of various problems. These he had worked out years ago, except for one involving Bernoulli numbers, which was new. Ada illustrated these algorithms in her notes in the form of charts detailing the stepwise sequence of events as the hypothetical machine would progress through a string of instructions input from punched cards" (Swade, p. 165). These procedures, and the procedures published in the original edition of Menabrea's paper, were the first published examples of computer 'programs.' "Ada also expanded upon Babbage's general views of the Analytical Engine as a symbol-manipulating device rather than a mere processor of numbers. She brought to the project a fine sense of style that resulted in the frequently quoted analogy, 'We may say most aptly that the Analytical Engine weaves algebraic patterns just as the Jacquard-loom weaves flowers and leaves.' She suggested that . 'Many persons who are not conversant with mathematical studies, imagine that because the business of the engine is to give its results in numerical notation, the nature of its processes must consequently be arithmetical and numerical, rather than algebraical and analytical. This is an error. The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact it might bring out its results in algebraical notation, were provisions made accordingly' (p. 713)" (OOC). Lady Lovelace signed these notes 'A.A.L.,' masking her class and gender in deference to the conventions of the time. ABPC/RBH list only the OOC copy (Christie's, 23 February 2005, lot 32, $10,800). In 1828, during his grand tour of Europe, Babbage had suggested a meeting of Italian scientists to the Grand Duke of Tuscany. On his return to England Babbage corresponded with the Duke, sending specimens of British manufactures and receiving on one occasion from the Duke a thermometer from the time of Galileo. In 1839 Babbage was invited to attend a meeting of Italian scientists at Pisa, but he was not ready and declined. "In 1840 a similar meeting was arranged in Turin. By then Babbage did feel ready, and accepted the invitation from [Giovanni] Plana (1781-1864) to present the Analytical Engine before the assembled philosophers of Italy . In the middle of August 1840, Babbage left England . "Babbage had persuaded his friend Professor MacCullagh of Dublin to abandon a climbing trip in the Tyrol to join him at the Turin meeting. There in Babbage's apartments for several mornings met Plana, Menabrea, Mosotti, MacCullagh, Plantamour, and other mathematicians and engineers of Italy. Babbage had taken with him drawings, models and sheets of his mechanical notations to help explain the principles and mode of operation of the Analytical Engine. The discussions in Turin were the only public presentation before a group of competent scientists during Babbage's lifetime of those extraordinary forebears of the modern digital computer. It is an eternal disgrace that no comparable opportunity was ever offered to Babbage in his own country . "The problems of understanding the principles of the Analytical Engines were by no means straightforward even for the assembly of formidable scientific talents which gathered in Babbage's apartments in Turin. The difficulty lay not as much in detail but rather in the basic concepts. Those men would certainly have been familiar with the use of punched cards in the Jacquard loom, and it may reasonably be assumed that the models would have been sufficient to explain the mechanical operation in so far as Babbage deemed necessary. Mosotti, for example, admitted the power of the mechanism to handle the relations of arithmetic, and even of algebraic relations, but he had great difficulty in comprehending how a machine could handle general conditional operations: that is to say what the machine does if its course of action must be determined by results arising from its own previous calculations. By a series of particular examples, Babbage gradually led his audience to understa
Eine neue Art von Strahlen [wrapper title]. Offprint from Sitzungs-Bericht der physikalisch-medicinische Gesellschaft zu Würzburg

Eine neue Art von Strahlen [wrapper title]. Offprint from Sitzungs-Bericht der physikalisch-medicinische Gesellschaft zu Würzburg, no. 9 (1895). [With:] Eine neue Art von Strahlen. II. Mittheilung. Offprint from ibid., nos. 1 & 2 (1896)

RÖNTGEN, Wilhelm Conrad First editions, first issues, and fine copies, of the rare offprints of Röntgen's discovery of X-rays, the most important contribution to medical diagnosis in a century, and a key to modern physics. "While performing experiments with a Crookes vacuum tube, a type of cathode-ray tube, Röntgen observed that some agent produced in the tube was causing barium platinocyanide crystals to fluoresce. Upon investigation he found that the fluorescence was caused by unknown rays (which he named 'X-rays') originating from the spot where cathode rays hit the glass wall of the vacuum tube. He announced his discovery in the present paper, which described the rays' photographic properties and their amazing ability to penetrate all substances, even living flesh. Although he was unable to determine the true physical nature of the rays, Röntgen was certain that he had discovered something entirely new, a belief soon confirmed by the work of other scientists such as Becquerel, Laue and the Curies. For his discovery, Röntgen was awarded the Nobel Prize in physics for 1901" (Norman 1841). "Röntgen's second paper on X-rays reported his latest findings: that X-rays render air conductive (a phenomenon already recognized), and that the target of the rays does not have to be simultaneously the anode of the cathode-ray tube. He described a scale for measuring X-ray intensity, along with other innovations in equipment designed for the optimal production of X-rays" (Norman 1842). "Their importance in surgery, medicine and metallurgy is well known. Incomparably the most important aspect of Röntgen's experiments, however, is his discovery of matter in a new form, which has completely revolutionized the study of chemistry and physics. Laue and the Braggs have used the X-rays to show us the atomic structure of crystals. Moseley has reconstructed the periodic table of the elements. Becquerel was directly inspired by Röntgen's results to the investigation that discovered radioactivity. Finally J.J. Thomson enunciated the electron theory as a result of investigating the nature of the X-rays" (PMM). "The discovery by Professor Röntgen of a new kind of radiation from a highly exhausted tube through which an electric discharge is passing has aroused an amount of interest unprecedented in the history of physical science" (J.J. Thomson, 'On cathode rays,' Report of the Sixty-sixth Meeting of British Association for the Advancement of Science, 1896). "It was this separate printing [of the first paper], and the following four additional printings in five issues, that were primarily responsible for the rapid dissemination of the news of Röntgen's discovery" (Klickstein, Röntgen, p. 62). "On Friday evening, 8 November 1895, Wilhelm Röntgen remained long hours in his laboratory and was late for dinner ? so the story goes. He had been kept by a most puzzling observation he made while repeating some of Heinrich Hertz's and Philipp Lenard's recent experiments on cathode rays. "His apparatus was very simple and standard; it consisted of a Ruhmkorff spark coil with a mercury interrupter and a Hittorf discharge tube. That evening, in preparing for his next experiment, he had carefully covered the tube with black cardboard and drawn the curtains of the windows. He hoped to be able to detect some fluorescence coming from the tube with a fluorescent screen made of a sheet of paper painted with barium platinocyanide. That screen, which he intended to bring close to the tube later on, was lying on the table at some distance. Röntgen wanted to test the tightness of the black shield around the tube. He operated the switch of the Ruhmkorff spark coil, producing high-voltage pulses of cathode rays and looked for any stray light coming from the glass tube. He then happened to notice out of the corner of his eye a faint glimmer towards the end of his experimentation table. He switched off the coil, the glimmer disappeared. He switched the coil back on, the glimmer reappeared. He repeated the operation several times, the glimmer was still there. He looked for its source and found that it came from the fluorescent screen. "In the interview he granted in March 1896 to H. J. Dam, a London-based American reporter for the American magazine, McClures, Röntgen was asked: 'What did you think?' His answer was: 'I did not think, I investigated. I assumed that the effect must have come from the tube since its character indicated that it could come from nowhere else'. Röntgen found that the intensity of the fluorescence increased significantly as he brought the screen close to the discharge tube. More baffling, the propagation of this 'radiation' was not hampered if he put a piece of cardboard between the screen and the tube, or other objects such as a pack of cards, a thick book or a wooden board two or three centimetres thick. Then he moved the screen farther and farther away, even as far as two metres, and, his eyes being well accustomed to obscurity, he could still see the very faint glimmer. As an added fortunate circumstance, according to H. H. Seliger, Röntgen being colour-blind, his eyes had enhanced sensitivity in the dark. "After dinner, Röntgen went back down to his laboratory and repeated his experiment, now putting various sheets of materials such as aluminium, copper, lead or platinum in front of the screen. Only lead and platinum absorbed the radiation completely, and lead glass was found to be more absorbing than ordinary glass. Röntgen held a small lead disk in front of the screen and was very surprised to see not only the shadow of the disk, but also the shadow of the bones of his own hand! He also found that photographic plates were sensitive to this unknown radiation. "In the days that followed, Röntgen told no one of his startling observations, neither his assistants nor his wife. He was morose and abstracted, according to his wife, and often ate and even slept in his laboratory. The discovery was so astounding, so unbelievable, that he would
Epistola docens venam axillarem dextri cubiti j in dolore laterali secandam: et melancholicum succum ex venae porto ramis ad sedem pertinentibus purgari. [Bound with:] GUENTHER

Epistola docens venam axillarem dextri cubiti j in dolore laterali secandam: et melancholicum succum ex venae porto ramis ad sedem pertinentibus purgari. [Bound with:] GUENTHER, Johann. Anatomicarvm institvtionvm ex Galeni sententia libri IIII . His accesserunt Theophili Protospatarii de Corporis humani fabrica Libri V, Iunio Paulo Crasso Patauino interprete. Item. Hippocratis Coi de Medicamentis purgatorijs libellus, nunquam ante nostra tempora in lucem editus, eodem Iun. Paulo Crasso interprete. Basel: [colophon: Robert Winter, June 1539]. [Bound with:] FUCHS, Leonhart. L. F. . libri IIII., difficilium aliquot quæstionum, et hodie passim controversarum explicationes continents . aucti et recogniti. (Adversus G. Puteanum, . falsam Joannis Mesues sententiam, Aloen aperire ora venarum, tuentem, apologia. Apologia adversus aliquot palam insanas et convitiis plenas S. Montui Dialexeis, nonnulla Paradoxorum capita temere perstringentes. Apologia adversus H. Thriverum Brachelium . qua docet

VESALIUS, Andreas First edition, and a truly wonderful copy in a dated contemporary binding, of Vesalius's 'venesection letter,' one of his rarest works, embodying what may be the earliest approach to an area of medicine which may be called scientific in the modern sense. This is a fine copy, complete with the final leaf (the Cushing and Waller copies both lack it); it is almost never found in a contemporary binding as here. This copy is doubly interesting for preserving its original context - that of a 16th-century physician's compendium of texts which attempted to condense and survey the most important elements of contemporary medical knowledge in a single volume: Vesalius' work is here accompanied by two other medical works from the same press, published within a year of Vesalius' Epistola. The letter on venesection "was written for Nicolas Flourens, physician to Charles V, who had queried Vesalius regarding the notes on the azygos vein in Tabulae anatomicae sex [published by Vesalius in 1538]; Flourens wished to know what relation the vein had to the question of bloodletting in cases of pleurisy and pneumonia. Vesalius' letter advocated the new 'classical' method of letting blood near the site of the affliction, a method arousing great controversy among the medical community as it was directly opposed to the traditional 'revulsive' bleeding taught by the Arabic authorities. Although the classical method was derived from a more accurate reading of Hippocrates and Galen . the importance of Vesalius' defense of it lies in the authority he gave to his own knowledge of the structure of the venous system ? an important step in his movement away from traditional anatomical concepts" (Norman). "In this letter we perceive the first steps in the slow and gradual loosening of traditional bonds whence eventually emerged the principle that the validity of a hypothesis rests solely upon facts established by observation. Here Vesalius asks a first tentative question 'whether the method of an anatomy could corroborate speculation'; a question not without moment in a day when principles based solely upon the power of the intellect were enshrined as truth . Vesalius's fame rests upon his anatomical contributions, but he was as fully concerned with the problem of practical medicine . The venesection letter strongly suggests that it was Vesalius's preoccupation with such clinical problems which provided the insight that enabled him to shake off the dead hand of Galen's pronouncements and make the production of the Fabrica possible" (Saunders & O'Malley, pp. 5-6). "Out of the venesection controversy came as a purely incidental finding the discovery of the venous valves . which in the consciousness of Harvey was to provide the key to unlocking the door to the circulation" (ibid., p. 20). The Anatomicarum institutionum is the only quarto edition (third overall) of the great textbook of Johann Guenther [Winter] of Andernach, who taught Vesalius anatomy at Paris. The first edition, published (in 8vo) at Basel in 1536, contains the first mention of Vesalius in print; a second edition (16mo), revised by Vesalius himself, was published at Venice in 1538. "Of all the many commentaries on Galen's innumerable works that followed rapidly on the heels of one another during the late Renaissance, few proved more popular than Guenther's manual of four books" (Cushing, p. 44). The final work in the volume is the first edition of Fuchs' pharmacological treatise 'Four books on some difficult questions', which gives a commentary on the indications and dosages of prescriptions of Ibn Sina (Avicenna) and of Masawaih al-Mardini (Mesue the Younger), and praises the work of Galen. ABPC/RBH list only two copies of the venesection letter since 1929, both in modern bindings: the Norman copy (Christie's New York, 18 March 1998, lot 212, $33,350) and the Blondelet copy (Sotheby's Paris, 31 May 2016, lot 50, ?65,000). "In 1538 Vesalius visited Matteo Corti, professor of medicine in Bologna, and discussed the problems of therapy by venesection. Differences of opinion between the two men seem to have been the impulse behind Vesalius' next book, Epistola docens venam axillarem dextri cubiti in dolore laterali secundam (Basel, 1539), written in support of the revived classical procedure first advocated in a posthumous publication (1525) of the Parisian physician Pierre Brissot. In this procedure blood was drawn from a site near the location of the ailment, in contrast to the Muslim and medieval practice of drawing blood from a distant part of the body. As the title of his book indicates, Vesalius sought to locate the precise site for venesection in pleurisy within the framework of the classical method. The real significance of the book lay in Vesalius' attempt to support his arguments by the location and continuity of the venous system rather than by an appeal to earlier authority. Despite his own still faulty knowledge, his method may be called scientific in relation to that of others; certainly it was nontraditional and required that his opponents resort to the same method if they wished to reply effectively. With this novel approach to the problem of venesection Vesalius posed the then striking hypothesis that anatomical dissection might be used to test speculation. Here too he declared clearly, on the basis of vivisection, that cardiac systole was synchronous with arterial expansion and for the first time mentioned his initial efforts in the preparation of the anatomical monograph that was ultimately to take shape as De humani corporis fabrica" (DSB). "Since remote antiquity, venesection had occupied a unique and important position in the minds of physicians as the sheet anchor of therapeutics. In the sixteenth century the subject had become one of violent and bitter controversy. The humanists in clearing away the rubbish of Arabian compilations and scholastic commentary had exposed how far current practice had deviated from the teachings of Hippocrat
On Aerial Navigation

On Aerial Navigation

CAYLEY, George First edition, journal issues in the original printed wrappers, extremely rare thus, of "the first and the greatest classic of aviation history, laying the foundations of the science of aerodynamics" (PMM) and setting out the correct conception of the modern aeroplane. "'The true inventor of the aeroplane and one of the most powerful geniuses in the history of aviation': these are the words used by the French historian Charles Dollfus to describe Sir George Cayley (1773-1857), a scholarly Yorkshire baronet who until recently was virtually ignored by historians of applied science. Cayley, who lived and did most of his work at Brompton Hall, near Scarborough, first had his aeronautical investigations fired by the invention of the balloon in 1783 - when he was ten - and his active concern with flying lasted until his death in 1857. In the year 1796 he made a helicopter model on the lines of that invented by Launoy and Bienvenu, a device he later improved and modified. Then, within a few years, with no previous workers to guide him or suggest the lines of approach, he arrived at a correct conception of the modern aeroplane, and so laid the secure foundations for all subsequent developments in aviation. It was in the year 1799 that Cayley took his first and most decisive step towards inaugurating the concept of the modern aeroplane: the proper separation of the system of thrust from the system of lift. This was the crucial breakaway from the ornithopter tradition of previous centuries: it meant picturing the bird with its wings held rigid as if in gliding flight, and propelled by some form of auxiliary mechanism. Then, during the most fruitful decade of his life (1799-1809), Cayley made his basic experiments, which included testing both model and full-size gliders, and arrived at his mature conception of aircraft and aerodynamics. It was almost an accident that he gathered together his notes and published them. For it was in Nicholson's Journal, for November 1809, February 1910, and March 1810, that there appeared Cayley's triple paper 'On Aerial Navigation'" (ibid.). ABPC/RBH lists only three copies in the last half-century, none of them in original printed wrappers. "The 2007 discovery of sketches in Cayley's school notebooks (held in the archive of the Royal Aeronautical Society Library) revealed that even at school Cayley was developing his ideas on the theories of flight. It has been claimed that these images indicate that Cayley identified the principle of a lift-generating inclined plane as early as 1792" (Wikipedia, accessed May 15, 2019). "It was in 1804 that Cayley began to write his famous paper on Aerial Navigation, a work he was not able to complete for four years . One hundred and fifty years after Cayley began his essay, von Karman wrote in his book Aerodynamics (published this year [1954]), 'The idea that sustentation can be accomplished by moving inclined surfaces in the flight direction, provided we have mechanical power to compensate for the air resistance, was probably clearly defined for the first time by an Englishman, Sir George Cayley, in his papers published in 1809-10 on aerial navigation . in his paper he clearly defined and separated the problem of sustentation, or in modern scientific language the problem of lift, from the problem of drag' . It was after a brief but significant discussion on the forces on a bird in gliding flight that Cayley made the statement: 'The whole problem is confined within these limits-To make a surface support a given weight by the application of power to the resistance of the air.' This paper provided the first clarification of ideas about mechanical flight and was the first to lay down the main principles. "The resistance of a plane in a moving stream of air, at various angles of incidence, was unknown. In his paper Cayley refers to 'many carefully repeated experiments' to obtain the pressures on a plane, but it was not until the discovery of his note-book in 1933 that it was known how astonishing these experiments were. Cayley records that they were made with a home-made whirling arm apparatus, to find the pressure on a flat plate, one foot square, at angles of incidence from 3 deg to 18 deg, in 3 deg steps. He was well aware of the difficulties of obtaining exact results, and carried out further tests, using a model glider, with an adjustable tailplane and a movable centre of gravity, to test his results. "In this paper Cayley briefly touches upon the helicopter, the principle of which he demonstrates with a model using two sets of contra-rotating airscrews made from birds' feathers. 'For the mere purpose of ascent this is perhaps the best apparatus,' he declares, 'but speed is the great object of this invention, and this requires a different structure.' He discusses the problem of the lateral and longitudinal stability of a fixed-wing machine and 'aided by a remarkable circumstance that experiment alone could point out,' shows that at very acute angles of incidence the centre of pressure moves considerably in front of the centre of gravity of a wing. This was the first statement made of the centre-of-pressure movement. Light construction, light engines, and minimum forward resistance were the key features of all Cayley's ideas about heavier-than-air craft. 'In thinking of how to construct the lightest possible wheel for aerial navigation cars,' he wrote in 1808, 'an entirely new mode of manufacturing this most useful part of locomotive machines occurred to me-vide, to do away with wooden spokes altogether, and refer the whole firmness of the wheel to the strength of the rim only, by the intervention of tight cording.' In a later paper he pointed out that the wheel was an incumbrance during flight, a cogent reason why it should be as light as possible" (Pritchard, pp. 701-2). "His emphasis on lightness led him to invent a new method of constructing lightweight wheels which is in common use today. For his landing wheels, he shifted th
On the action of the rays of the solar spectrum on vegetable colours

On the action of the rays of the solar spectrum on vegetable colours, and on some new photographic processes

HERSCHEL, John Frederick William, Sir First edition, extremely rare offprint, of this seminal early work of photography, the invention of the world's first photocopying process, 'cyanotype,' later called 'blue-printing'; this remained by far the most important reprographic process for more than a century after the publication of Herschel's paper. This is an extraordinary presentation copy, inscribed by Herschel to the great French colour theorist Michel-Eugène Chevreul. "Photography in Prussian blue was discovered in 1842 by Sir John Herschel just three years after Louis Daguerre and Henry Talbot had announced their independent inventions of photography in silver, using metal and paper substrates, respectively. Their successes in finally securing silver photographs represented the fruition of an idea that had been gestating for more than a century in the minds and laboratories of many noted natural philosophers. In contrast, the birth of cyanotype came, literally and metaphorically, 'out of the blue', to a single parent . As one of the leading physical scientists of his day, Herschel was driven by the urge to understand photochemical phenomena, and to harness them as tools for probing the electromagnetic spectrum beyond the narrow optical limits imposed by human vision. Using light-sensitive coatings on paper, he sought to venture below the shortwave end of the visible spectrum, into the region of the ultra-violet or 'actinic' rays discovered in 1801 by Johann Ritter; and above the longwave visible limit, into the region of the infra-red or 'thermic' rays, which had been discovered in 1800 by his father, Sir William Herschel . There is no compelling evidence to suggest that he was in pursuit of commercially useful methods of reprography, unlike Talbot, whose clear aim was to multiply his photographic images in printer's ink. It is therefore a happy irony that Herschel should have been responsible for inventing the first process for photocopying" (Ware, Cyanotype: the history, science and art of photographic printing in Prussian blue (1999), p. 11). "Only in 1872, one year after Herschel died, was the cyanotype revived, when the Paris-based Marion and Company renamed his invention 'ferro-prussiate paper' and began marketing it for the replication of architectural plans. (Previously, they had been copied by hand, which was expensive and prone to human error.) At the 1876 Philadelphia Centennial Exposition, the process reached American shores, where it finally met success as the blueprint, the first inexpensive means of duplicating documents. All that was required was a drawing traced on translucent paper. Pressed against a second sheet coated with Herschel's chemical under glass, the drawing was exposed to sunlight, then washed in water. The blueprint paper recorded the drawing in reverse, black lines appearing white against a cyan background" (Keats, 'The Blueprint,' Scientific American 301 (2009), p. 90. ABPC/RBH list only a copy offered by Goldschmidt in 1936 (not a presentation copy). We have located only one other copy in commerce, offered by Ernst Weil in his Catalogue 7 (ca. 1946). Provenance: Michel-Eugène Chevreul (inscribed by Herschel on title 'M. Chevreul with the authors respects' and on original front wrapper 'M. Chevreul Membre de l'Inst[itut] &c &c. Paris'). "As a scientist Sir John Herschel was naturally more interested in the theory of photography than in its practice. Photography is indebted to him for a wealth of ideas, but those who developed them often neglected to acknowledge their originator. Herschel was of a retiring disposition and never pushed forward his claims; indeed, we marvel at the restraint with which he bore the incorrect behaviour of Talbot who, thwarted in his desire for public acclaim, hastened to the Patent Office with more than one idea which Herschel had freely published. "Herschel's photographic researches are concentrated within the first few years after the discovery of photography, and the genius and energy which he displayed were overwhelming. For him, it would have been an easy matter to invent a photographic process earlier had he felt, like Niépce, any urge to do so, or had he believed that it would facilitate his work, as Daguerre and Talbot and Reade did. As far back as 1819 Herschel discovered the property of the hyposulphites as solvents for silver salts, whereas ignorance of this fact had proved the stumbling-block to other investigators in photography for a long time. Herschel's scientific knowledge was indeed so great that on merely receiving a note, on 22 January 1839, from Captain (later Admiral) Beaufort telling him the bare fact of Daguerre's discovery, 'a variety of processes at once presented themselves,' and only a week later Herschel succeeded in producing his first photograph" (Gernsheim & Gernshein, The History of Photography1685-1914 (1969), p. 95). Herschel learned of Talbot's competing process just a few days after Daguerre's. "In January of 1839, stimulated by Talbot's announcement of his invention of photogenic drawing, Herschel took up the study of photographic phenomena. Within a week he had solved the problem of silver fixation. In contrast to Talbot's single-minded pursuit of the silver image, however, Herschel soon began to widen his investigations in the search for other viable photographic systems . To the enduring benefit of the embryonic science of photography, the spring of 1840 was remarkably brilliant. Herschel had already initiated a new series of exposure tests of 'vegetable colours' using extracts of the juices of plants and flowers, but this work was interrupted in March by the removal of the family home from Slough in Buckinghamshire to Hawkhurst in Kent. Once resettled, Herschel resumed his experiments in August, but by then he frequently found the sun to be 'pale' or 'desultory', requiring long exposures for these very insensitive processes. He pursued them nonetheless, during the very poor summer of 1841 that followed . In the early spr
Exercitationes de generatione animalium. Quibus accedunt quaedum de partu: de membranis ac humoribus uteri: & de conceptione

Exercitationes de generatione animalium. Quibus accedunt quaedum de partu: de membranis ac humoribus uteri: & de conceptione

HARVEY, William John Evelyn's copy, and possibly the unique copy containing the portrait of Harvey, of the first edition of "the most important book on [embryology] to appear during the seventeenth century" (Garrison-Morton). In this work, "he rejected the prevailing doctrine of the preformation of the fetus, and advanced the theory, radical for its time, of epigenesis, that all living beings derive from the ovum 'by the gradual building up and aggregation of its parts'. Regarding Harvey's theory of epigenesis, Thomas Henry Huxley (1825-95) claimed this should "give him an even greater claim to the veneration of posterity than his better known discovery of the circulation of the blood" (Keynes, Bibliography, p. 47). Harvey reported a wealth of observations on many aspects of reproduction in a wide variety of species. As representatives of vivipara, his attention was chiefly devoted to the deer, while that for ovipara was the domestic fowl. For Harvey, all life develops from the egg. This is expressed on the frontispiece which depicts the supreme Roman god Jupiter [Jove] opening a large egg, inscribed with the fundamental dictum of embryology, ex (upper half of egg shell) ovo omnia (lower half of egg shell), which translates as, 'from the egg everything,' and from which the liberated animals and insects fly . An opponent of the theory of spontaneous generation, Harvey speculated that humans and other mammals must reproduce through the joining of an egg and sperm. No other theory was credible. By positing and demonstrating for viviparous animals the same mechanism of reproduction as that observed in oviparous animals, he thus initiated the search for the mammalian ovum" (Longo & Reynolds, p. 272). Harvey was persuaded to publish this work by his colleague Dr. George Ent, who wrote the preface addressed to the College of Physicians and saw the book through the press. "Ent reports in his dedication the conversations with Harvey in which he secured his consent to publication, and remarks at the end that 'as our author writes a hand which no one without practice can easily read, I have taken some pains to prevent the printer committing any very grave blunders through this'" (Keynes, Bibliography, p. 46). The text comprises seventy-two 'Exercises' and extended chapters on parturition, the uterus, and conception. In Exercise 51 he formulates the theory of epigenesis, and his chapter 'De partu' is the first published essay on midwifery by an Englishman. The importance of Harvey's text was immediately recognized, and it was reprinted three times in the year of its issue. The scarce portrait of Harvey inserted in the Evelyn copy was in fact intended to be published in this edition of De generatione animalium, as a letter to Evelyn from Dr. Jasper Needham quoted by Keynes (Life, p. 333) demonstrates: 'Dr. Harvey's picture is etcht by a friend of mine and should have been added to his work, but that resolution altered: however I'll send you a proof with your book that you may bind it up with his book De Generatione. I'm sure 'tis exactly like him, for I saw him sit for it.' Keynes refers to the present copy (then in Christ Church College, Oxford) for the portrait. Provenance: 1. John Evelyn (1620-1706), bound for him and with press-marks in his hand, N3 (deleted) and L.27. Also on the recto of A4 is a note to the binder in the hand of Evelyn's calligrapher and amanuensis, Richard Horae, Veau Harveius de Generatione. Descended through: 2. The Evelyn family library, with further press-mark G4.7, subsequently housed in Christ Church College, Oxford, sold by the Evelyn trustees in Christie's London rooms, 1 December 1977, lot 713, £3800 = $7044, to Zeitlin & Ver Brugge. 3. Haven O'More (bookplate, sale Garden Ltd., Sotheby's New York, 10 November 1989, lot 115, $15,400). "Harvey had for a great number of years experimented and recorded his observations on the development of the chick embryo and of other animals. There are many references to the subject in his writings on the heart and circulation of the blood . It is evident from references in the sixth Exercise of this work that this interest in the subject of generation had been initiated by his association with the great Fabricius when he was at Padua, 1598-1602" (Keynes, Bibliography, p. 46). "While Harvey's general biological interests developed in Padua, there is no adequate evidence that he played an active part in Fabricius's embryological studies. Nevertheless, he consciously based his own studies on Aristotle and Fabricius, the latter's De formation ovi et pulli of 1621 being particularly important. Thus, it is probable that Harvey's serious investigations of the embryology of the chick, which formed the basis of De generatione, began shortly after he had read Fabricius's book. "Evidence from De generatione suggests that Harvey was actively engaged in collecting materials relating to generation between 1625 and 1637. De motu cordis indicates that, by 1628, he had recognized the important theoretical implications of studies on generation and was already engaged on a major treatise on this subject. "First, he was determined to resolve the contradictions in the various descriptions of the chick embryology. This in turn provided evidence for use in the wider problem of the nature of sexual generation throughout the animal kingdom. The technical and theoretical difficulties involved in this research would cause Harvey to progress slowly. However, it is quite possible that [Sir Thomas] Browne and [Sir Kenelm] Digby saw major sections of the work in about 1638 and this may have been the stimulus to their own embryological investigations. "After 1638, Harvey probably continued modifying his work and compiling additional material relating to this inexhaustible subject. The study of insects and other invertebrates would have been a particularly demanding study. However, soon the continuity of his labour was interrupted, with the outbreak of the civil war in 1642. He vac
Solutio Problematis ad Geometriam Situs Pertinentis

Solutio Problematis ad Geometriam Situs Pertinentis

EULER, Leonhard First edition of "one of Euler's most famous papers-the Königsberg bridge problem. It is often cited as the earliest paper in both topology and graph theory" (Euler Archive, E53). The city of Königsberg is situated on the River Pregel, across which seven bridges had been built in Euler's time, most of which connected to the island of Kneiphof; the problem asked whether it was possible to devise a route that would allow one to cross each of the bridges exactly once. "When reading Euler's original proof, one discovers a relatively simple and easily understandable work of mathematics; however, it is not the actual proof but the intermediate steps that make this problem famous. Euler's great innovation was in viewing the Königsberg bridge problem abstractly, by using lines and letters to represent the larger situation of landmasses and bridges. He used capital letters to represent landmasses, and lowercase letters to represent bridges. This was a completely new type of thinking for the time, and in his paper, Euler accidentally sparked a new branch of mathematics called graph theory, where a graph is simply a collection of vertices and edges.Today a path in a graph, which contains each edge of the graph once and only once, is called an Eulerian path, because of this problem. From the time Euler solved this problem to today, graph theory has become an important branch of mathematics, which guides the basis of our thinking about networks" (MAA). Although Euler felt that the Königsberg bridge problem was trivial, he was still intrigued by it, and believed it was related toLeibniz's geometria situs, or geometry of position, although today Leibniz's ideas are viewed as an anticipation of the subject of topology, whereas the bridge problem is one of graph theory. After Euler's paper, graph theory developed rapidly with major contributions made by Augustin-Louis Cauchy, William Rowan Hamilton, Arthur Cayley, and Gustav Kirchhoff, among many others. "In March 1736 Karl Ehler, the mayor of Dantzig (now Gdansk), a city eighty miles from Königsberg, imparted to Euler his thoughts on a recreational puzzle about the seven bridge of Konigsberg. It was part of their ongoing correspondence, which covered such items as artillery, real and imaginary numbers, and the rectification of curves. Ehler called the bridges problem 'an outstanding example of the calculus of position.' Euler had already solved it. The city of Konigsberg in East Prussia (now Kaliningrad in Russia) comprises four sections. At the center is an island in the Pregel River, and in Euler's time seven bridges spanning the river connected the island with the other three sections. The question was whether someone could pass over the bridges in a connected walk, crossing each bridge once, and return to the same spot. The puzzle itself, unrelated to Euler's mathematical research, was among several problems that he addressed only once. While Leibniz and Wolff posed problems of this type, Euler seems to have learned of them from Johann I Bernoulli. Finding the Königsberg Bridge Problem simple, Euler solved it negatively - not with mathematics but with reasoning alone. The article 'Solutio problematis ad geometriam situs pertinentis' (Solution of a problem relating to the geometry of position) gave his conclusion. Submitted the next year for volume 8 of the Commentarii, it was not published until 1741 in an issue containing thirteen mathematical articles - two by Daniel Bernoulli and eleven by Euler [see below]. "'Solutio problematis' contains no graphs but is considered the first work in graph theory. The requisite type of graphs to represent the possible Königsberg walk under the given conditions did not appear until the nineteenth century. Euler divided this paper into twenty-one numbered paragraphs. After paragraph 3 rejects as unworkable any attempt to solve the problem by checking all possible paths, the paper considers the transit entrances to land regions rather than the crossing of bridges" (Calinger, pp. 130-131). The four regions were denoted by the capital letters A, B, C, D (A being the island) and the seven bridges by lower case letters a, b, c, d, e, f, g: a & b connected A to B; c & d connected A to C; e connected A to B; f connected B to D and g connected C to D. "Euler noted that, if a region had an odd number of bridges (k), then the letter of that region must appear (k + 1)/2 times in the string of capital letters that represent the entire journey . Since five bridges connect the island to the city's other regions, the frequency [of A in the tour] will be (5 + 1)/2 = 3. The frequency for B, C and D, there being three bridges, is (3 + 1)/2 = 2. The sum of these frequencies is nine [3 + 2 + 2 + 2], but the sum for a path crossing each of the seven bridges only once is eight [because each bridge separates two regions]; the Königsberg tour under the given conditions is this impossible; the problem has no solution" (ibid.). Of the other ten papers by Euler in this volume, the most significant is 'Theorematum quorundam ad numeros primos spectantium demonstratio' (pp. 141-146), in which Euler proves 'Fermat's Little Theorem.' This was first stated the theorem in a letter dated October 18, 1640, to his friend and confidant Frénicle de Bessy. Fermat did not send Frénicle the proof, only writing 'I would send you a demonstration of it, if I did not fear going on for too long.' Euler was the first to publish a proof, in the present paper. "Number theory continued to be Euler's passion and a wellspring of challenging problems; its higher degrees of abstraction attracted him. Among the circle of scholars he met or corresponded regularly with were Goldbach and Krafft, both of whom particularly discussed number theory with him, and by 1736 Euler was inventing ways to prove its theorems by introducing the concepts, definitions, and methods required to complete these theorems; he assiduously tried to consolidate the methods. "After beginning with
Recueil d'observations electro-dynamiques

Recueil d’observations electro-dynamiques

AMPERE, Andre-Marie; Jöns Jacob von BERZELIUS; Michael FARADAY; Auguste de la RIVE; Félix SAVARY A beautiful copy bound in contemporary red morocco of the definitive version of this continually evolving collection of important memoirs on electrodynamics by Ampère (1775-1836) and others. "Ampère had originally intended the collection to contain all the articles published on his theory of electrodynamics since 1820, but as he prepared copy new articles on the subject continued to appear, so that the fascicles, which apparently began publication in 1821, were in a constant state of revision, with at least five versions of the collection appearing between 1821 and 1823 under different titles" (Norman). Some of the 25 pieces in the collection are published here for the first time, others appeared earlier in journals such as Arago's Annales de Chimie et de Physique and the Journal de Physique. But even the articles that had appeared earlier are modified for the Receuil, or have additional notes by Ampère, to reflect his progress and changes in viewpoint in the intervening period. Many of the articles that are new to the present work concern Ampère's reaction to Faraday's first paper on electromagnetism, 'On some new electro-magnetical motions, and on the theory of magnetism', originally published in the 21 October 1821 issue of the Quarterly Journal of Science, which records the first conversion of electrical into mechanical energy and contains the first enunciation of the notion of a line of force. Faraday's work on electromagnetic rotations would lead him to become the principal opponent of Ampère's mathematically formulated explanation of electromagnetism as a manifestation of currents of electrical fluids surrounding 'electrodynamic' molecules. The Receuil contains the first French translation of Faraday's paper followed by extended notes by Ampère and his brilliant student Félix Savary (1797-1841). Ampère's reaction to Faraday's criticisms are the subject of several of the articles in the second half of the Receuil. The collection also includes Ampère's important response to a letter from the Dutch physicist Albert van Beek (1787-1856), in which "Ampère argued eloquently for his model, insisting that it could be used to explain not only magnetism but also chemical combination and elective affinity. In short, it was to be considered the foundation of a new theory of matter. This was one of the reasons why Ampère's theory of electrodynamics was not immediately and universally accepted. To accept it meant to accept as well a theory of the ultimate structure of matter itself" (DSB). The volume concludes with a résumé of a paper read by Savary to the Académie des Sciences on 3 February 1823, and a letter from Ampère to Faraday, dated 18 April 1823 (which does not appear in the Table of Contents), showing that this definitive version of the Receuil was in fact published in 1823. Only three other copies of this work listed by ABPC/RBH. Provenance: Marcel Gompel (1883-1944) (ex-libris on front paste-down - Répertoire général des ex-libris français: G1896). A Jewish professor at the Collège de France, Gompel worked in the Laboratoire d'Histoire naturelle des corps organisés from 1922 to 1940, under the direction of André Mayer. In World War II he became a hero of the French resistance and was finally tortured and executed on orders from Klaus Barbie, the chief of the Gestapo in Lyon. When Barbie came to trial, the prosecutors used Gompel's case as a particularly clear and egregious example of his guilt of crimes against humanity. The collection opens with the 'Premier Mémoire' [1] (numbering as in the list of contents, below), first published in Arago's Annales at the end of 1820. This was Ampère's "first great memoir on electrodynamics" (DSB), representing his first response to the demonstration on 21 April 1820 by the Danish physicist Hans Christian Oersted (1777-1851) that electric currents create magnetic fields; this had been reported by François Arago (1786-1853) to an astonished Académie des Sciences on 4 September. In this memoir Ampère "demonstrated for the first time that two parallel conductors, carrying currents traveling in the same direction, attract each other; conversely, if the currents are traveling in opposite directions, they repel each other" (Sparrow, Milestones, p. 33). The first quantitative expression for the force between current carrying conductors appeared in Ampère's less well-known 'Note sur les expériences électro-magnétiques' [2], which originally appeared in the Annales des Mines. Ampère stated, without proof, that, if two infinitely small portions of electric current A and B, with intensities g and h, separated by a distance r, set at angles ? and ? to AB and in directions which created with AB two planes at an angle ? with each other, the action they exert on each other is gh (sin ? sin ? sin ? + k cos ? cos ?)/r2, where k is an unknown constant which he stated could 'conveniently' be taken to be zero. This last assumption was an error which significantly retarded his progress in the next two years before he stated correctly that k = ? 1/2 in his article [13], published for the first time in the Receuil. This article comprised 'notes' on a lecture [12] delivered to the Institut in April 1822 in which he surveyed experimental work carried out by himself and others since 1821 (he also published for the first time there the words 'electro-static' and 'electro-dynamic'). The full theoretical and experimental proof of the correct value of k appeared in two articles in Arago's Annales in 1822, [19] and [20], in an article by Savary [22], and in experiments with de la Rive [17] (see below). On 20 January 1821 Ampère performed an experiment together with César-Mansuète Despretz (1798-1863) intended to support his own theory of the interaction of electric currents against a rival theory of Jean-Baptiste Biot (1774-1862) and Félix Savart (1791-1841) presented to the Académie on 30 October 1820. This was reported in article [21], the first "experimentally based semi-ax
Die gegenwartige Situation in der Quantenmechanik

Die gegenwartige Situation in der Quantenmechanik

SCHRÖDINGER, Erwin First edition, journal issues, very rare in the original printed wrappers, of the papers in which Schrödinger gave his definitive views on the nature of quantum mechanics, illustrating them with one of the most famous thought experiments in the history of physics, 'Schrödinger's cat.' "A cat is locked in a steel box with a small amount of a radioactive substance such that after one hour there is an equal probability of one atom either decaying or not decaying. If the atom decays, a device smashes a vial of poisonous gas, killing the cat. However, until the box is opened and the atom's wave function collapses, the atom's wave function is in a superposition of two states: decay and non-decay. Thus, the cat is in a superposition of two states: alive and dead. Schrödinger thought this outcome 'quite ridiculous,' and when and how the fate of the cat is determined has been a subject of much debate among physicists" (Britannica). "From the late 1930s to the early 1960s the thought experiment was little mentioned, except sometimes as a classroom anecdote. For instance, Columbia professor and Nobel laureate T. D. Lee would tell the tale to his students to illustrate the strange nature of quantum collapse . Renowned Harvard philosopher Hilary Putnam - who learned about the conundrum from physicist colleagues, was one of the first scholars outside the world of physics to analyze and discuss Schrödinger's thought experiment. He described its implications in his classic paper 'A philosopher looks at quantum mechanics'. When the paper was mentioned the same year in a Scientific American book review, the term 'Schrödinger's cat' entered the realm of popular science. Over the decades that followed, it crept into culture as a symbol of ambiguity and has been mentioned in stories, essays and verse" (Halpern, Einstein's Dice and Schrödinger's Cat, 2015). ABPC/RBH list only one copy of this three-part paper in the original printed wrappers (Sotheby's, June 18, 2002, lot 95, $2390). "Motivated by the EPR paper [A. Einstein, B. Podolsky & N. Rosen, 'Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?', Physical Review, vol. 47 (1935), pp. 777-780], Schrödinger published in 1935 a three-part essay in Die Naturwissenschaften on 'The present situation in quantum mechanics.' He said he did not know whether to call it a 'report' or a 'general confession'. It is written in a sardonic style, which suggests that he found the 'present situation' to be less than satisfactory. "He first explained in detail how physics, on the basis of experimental data, creates models, which are presentations of natural objects idealized or simplified so that mathematical analysis can be applied to them. The deductions from such analysis are then tested by experiments, the results of which may lead to refinement or even drastic alteration of the model. The model can be described in terms of certain specifications/ For example, the Rutherford model of the hydrogen atom consists of two mass points, and the specifications might be the two times three coordinates of these mass points, and their two times three components of momentum. Such specifications are often called variables . In classical physics one can define a state of the model by giving the values of the twelve specification variables. In quantum mechanics, however, not all the variables can be simultaneously specified. If one measures exact values for the position coordinates, one can determine nothing about the values of the six momentum components. This situation is a result of the Heisenberg uncertainty relation, which is derived directly from the operators for position q and momentum p do not commute. It is, however, possible to measure values of q and p that fall within certain ranges in accordance with the uncertainty relation, so that one can speak of the specification variables of the model as being washed out or blurred. "Nevertheless the wave function ? defines the state of the model unequivocally. It constitutes a complete catalog of the probabilities of finding any specified result for a measurement made upon the physical system for which the model was designed . "In Section 5 of his paper, Schrödinger asks 'are the variables really blurred?' He points out that the classical description with its sharp values for the variables can be replaced by the ?-function as long as the blurring is restricted to atomic dimensions which escape our direct control. But when the uncertainty includes visible and tangible things, the expression 'blurring' becomes simply wrong. 'One can even construct quite burlesque cases. A cat is shut up in a steel chamber, together with the following diabolical apparatus (which one must keep out of the direct clutches of the cat): in a Geiger tube there is a tiny mass of radioactive substance, so little that in the course of an hour perhaps one atom of it disintegrates, but also with equal probability not even one; if it does happen, the counter responds and through a relay activates a hammer that shatters a little flask of prussic acid. If one has left this entire system to itself for an hour, then one will say to oneself that the cat is still living, if in that time no atom has disintegrated. The first atomic disintegration would have poisoned it. The ?-function of the whole system would express this situation by having the living and the dead cat mixed or smeared out (pardon the expression) in equal parts. 'It is typical of such cases that an uncertainty originally restricted to the atomic domain has become transformed into a macroscopic uncertainty, which can then be resolved through direct observation. This inhibits us from accepting in a naïve way a 'blurred model' as an image of reality . There is a difference between a shaky or not sharply focused photograph and a photograph of clouds or fogbanks.' "This conclusion has been called 'the principle of state distinction': states of a macroscopic system which could be t
Teoria Generale delle Equazioni

Teoria Generale delle Equazioni, in cui si dimostra impossibile la soluzione algebraica dell equazioni generali di grado superiore al quarto

RUFFINI, Paolo First edition, very rare, of the first statement and proof that the general equation of degree five or more cannot be solved algebraically. This is a remarkable author's presentation copy, uncut in the publisher's printed wrappers. "One of the most fascinating results in the realm of algebra - indeed in all of mathematics - is the theorem that the general polynomial of degree ? 5 is not solvable by radicals. Its discovery at the very end of the 18th century went counter to the belief and expectations of mathematical scholars; it came as a great surprise and was naturally met with scepticism . this revolutionary idea was not accepted without a great deal of resistance" (Ayoub, p. 253). An exception was the great French mathematician Augustin-Louis Cauchy, who wrote to Ruffini in 1821: "Your memoir on the general resolution of equations is a work that has always seemed to me worthy of the attention of mathematicians and one that, in my opinion, demonstrates completely the impossibility of solving algebraically equations of higher than the fourth degree." In Ruffini's arguments one can now see the beginnings of modern group theory. "Ruffini's methods began with the relations that Lagrange had discovered between solutions of third- and fourth-degree equations and permutations of three and four elements, and Ruffini's development of this starting point contributed effectively to the transition from classical to abstract algebra and to the theory of permutation groups. This theory is distinguished from classical algebra by its greater generality: it operates not with numbers or figures, as in traditional mathematics, but with indefinite entities, on which logical operations are performed" (DSB). "Ruffini is the first to introduce the notion of the order of an element, conjugacy, the cycle decomposition of elements of permutation groups and the notions of primitive and imprimitive. He proved some remarkable theorems [in group theory]" (MacTutor). Ruffini's proof did, in fact, have a gap which was filled in 1824 by Niels Henrik Abel (although Abel's proof also had a gap), and the insolvability of quintic equations is now known as the Ruffini-Abel theorem. This is a very rare book on the market in any form (ABPC/RBH list only a single copy) and we have never before seen nor heard of a copy in publisher's wrappers, or a presentation copy. Provenance: Author's presentation copy ("dono dell'autore" written on the front fly-leaf of both volumes). The method of solving quadratic equations was known to the Baghdad mathematician and astronomer Al-Khwarizmi (c. 780-850), and the formula involving square roots is now taught to every student in high school. Similar formulas for solving cubic and quartic equations were not found until the 16th century, by Scipione del Ferro (1465-1525), Lodovico Ferrari (1522-60), and Niccolo Tartaglia (1506-59), and were first published by Girolamo Cardano (1501-76) in his Ars magna (1545). These formulas expressed the solutions in terms of 'radicals,' i.e., expressions involving rational functions (ratios of polynomials) of the coefficients of the equation and their square-, cube-, and higher roots. The search for a similar formula for quintic equations proved fruitless. "For two centuries thereafter, the resolution of the enigma was regarded as one of the most important problems of algebra and occupied the attention of the leading mathematicians of this epoch" (Ayoub, p. 257). The most important work on the problem preceding Ruffini's was Lagrange's remarkable memoir 'Réflexions sur la résolution algébrique des equations, published in the Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Berlin in 1770-71. Katz & Parshall (p. 298) remark that "his introduction of the notion of permutations proved crucial to the ultimate proof that there was no algebraic solution of a fifth-degree polynomial equation," but Lagrange himself still believed that a solution of the quintic would be found. "He concludes with this statement: 'There, if I am not mistaken, are the true principles of the resolution of equations, and the most appropriate analysis which leads to solutions; all reduces, as we see, to a type of calculus of combinations by which we find results which we might expect a priori. It would be pertinent to make application to equations of the fifth and higher degrees whose solution is, up to the present, unknown: but this application requires a large number of combinations whose success is, however, very doubtful. We hope to return to this question at another time and we are content here in having given the fundamentals of a theory which appears to us new and general.' So in spite of past failures in solving the quintic, Lagrange still harbors the hope that a careful analysis of his method will achieve the goal. "Did no one suspect that the solution of the quintic was impossible? Apparently not until 1799 when Ruffini published his book on the theory of equations: 'General theory of equations in which it is shown that the algebraic solution of the general equation of degree greater than 4 is impossible.' Parenthetically, we note that in the same year the young Carl Friedrich Gauss (1777-1855) wrote in his dissertation (in which he proved the fundamental theorem of algebra) as follows: 'After the labors of many geometers left little hope of ever arriving at the resolution of the general equation algebraically, it appears more and more likely that the resolution is impossible and contradictory . Perhaps it will not be so difficult to prove, with all rigor, the impossibility for the fifth degree. I shall set forth my investigations of this at greater length in another place. Here it is enough to say that the general solution of equations understood in this sense [i.e., by radicals] is far from certain and this assumption [i.e., that any equation is solvable by radicals] has no validity at the present time.' Gauss published nothing more on the subject. "Ruf
De iis quae vehuntur in aqua libri duo. A Federico Commandino Urbinate in pristinum nitorem restituti

De iis quae vehuntur in aqua libri duo. A Federico Commandino Urbinate in pristinum nitorem restituti, et commentariis illustrati. [Bound with:] COMMANDINO. Liber de centro gravitatis solidorum

ARCHIMEDES [COMMANDINO, Federico] First edition of both works, a spectacular copy in a mid-seventeenth century red morocco armorial binding from the Library of Felipe Ramirez de Guzmán (ca. 1600-1668), Duke of Medina de las Torres, Viceroy of Naples. The first work is the first complete edition of the foundation work of hydrostatics, Archimedes' On Floating Bodies, which includes the eponymous 'Archimedes' principle' of buoyancy; the second is the first published work on centres of gravity of solid bodies. "Archimedes ? together with Newton and Gauss ? is generally regarded as one of the greatest mathematicians the world has ever known, and if his influence had not been overshadowed at first by Aristotle, Euclid and Plato, the progress of modern mathematics might have been much faster . In hydrostatics [Archimedes] described the equilibrium of floating bodies and stated the famous proposition - known by his name - that, if a solid floats in a fluid, the weight of the solid is equal to that of the fluid displaced and, if a solid heavier than a fluid is weighed in it, it will be lighter than its true weight by the weight of the fluid displaced" (PMM, p. 44). For his edition of On Floating Bodies, Commandino (1509-75) used a Latin translation, from a now lost Greek text, by Flemish Dominican William of Moerbeke (1215-86) in 1269 (Moerbeke's holograph remains intact in the Vatican library, Codex Ottobonianus Latinus 1850); for this work he had no access to a Greek text, unlike the five other Archimedean works he had previously translated. But the Greek text used by Moerbeke was corrupt and lacked the proofs of two crucial propositions. In addition, Archimedes used certain results on the centres of gravity of solid bodies, but his work on this subject has not survived. Commandino not only cleaned up the corrupted text, he also supplied the missing proofs and further took it upon himself to prove the necessary results about centres of gravity in the form of a self-contained treatise, De Centro Gravitatis Solidorum. Commandino uses the Archimedean methods of exhaustion and reductio ad absurdum, and De Centro Gravitatis Solidorum may justly be regarded as a reconstruction of Archimedes' lost work on centres of gravity. Their very close relationship makes it particularly appropriate to find these two works bound together, as here. A second translation of On Floating Bodies, published by Curtius Trioianus from the legacy of Niccoló Tartaglia (1499-1557), appeared in the same year (the brief Book I had been published in 1543), but according to Rose (p. 153) this is a direct transcript of a copy of the Moerbeke translation, retaining all the errors and making no attempt to fill in the lacunae. Commandino's "masterful version . was far more influential than the version of On Floating Bodies . published under Tartaglia's direction" (Clagett). "In the sixteenth century, Western mathematics emerged swiftly from a millennial decline. This rapid ascent was assisted by Apollonius, Archimedes, Aristarchus, Euclid, Eutocius, Hero, Pappus, Ptolemy, and Serenus - as published by Commandino" (DSB). Born in Urbino, Commandino studied Latin and Greek at Fano, then returned to Urbino where he studied mathematics. Later he studied medicine at Padua, and after returning home again he became personal physician to the Duke of Urbino. There he met Cardinal Ranuccio Farnese, the brother of the Duke's wife, who was to become his most important patron. In the early 1550s the Cardinal persuaded Commandino to move to Rome as his personal physician; while there he became friendly with Cardinal Cervini, who was elected Pope Marcello II in 1555. But following Cervini's death shortly after his election, both Commandino and Farnese returned to Urbino, where Commandino continued in the service of the Duke and Cardinal. But Commandino's true love was mathematics, and in 1558 he published his edition of Archimedes' Opera, which he dedicated to Farnese (this did not contain any of Archimedes' works on mechanics). Also in 1558 Commandino published a work he had begun in Rome, namely Commentarius in Planisphaerium Ptolemaei, in which he gave an account of Ptolemy's stereographic projection of the celestial sphere. In 1562 he published his edition of Ptolemy's work on the calibration of sundials, De Analemmate. "In July 1564 Ranuccio Farnese was appointed to the see of Bologna and by 1565 the Cardinal and Commandino were settled there. At Bologna in that year Commandino published his edition of Archimedes' On Floating Bodies together with his own De Centro Gravitatis. Since the Greek text of the Archimedean work was then unknown, Commandino availed himself of the same manuscript of the Moerbeke translation that he had used for his 1562 edition of Ptolemy's De Analemmate . in the dedication to De Centro Gravitatis, Commandino states that Cervini, when still a Cardinal, had given Commandino the early Latin version. This immediately raises the problem of precisely which manuscript Commandino received from Cervini. There are indeed very few codices of the Moerbeke translation . the probability seems to me to be that Cervini loaned, rather than gave, Commandino the autograph Ottob. Lat. 1850 . "The dedication to Ranuccio Farnese explains that the delay in publishing On Floating Bodies is due to the far greater difficulty of the material and the corruption of the text. Here especially he has felt the lack of a Greek text. But even so, Commandino has seen that the earlier translator's (Moerbeke's) Greek text must have been corrupt and defective since two of the proofs are missing, thus disturbing the admirable sequence of mathematical argument. This problem was enhanced by Archimedes' accepting as evident a great many proofs and facts on conics which had been discovered by earlier mathematicians. The ideas in question, however, are not so evident to moderns and so in order to render the text fully intelligible Commandino has had to resort often to the Conics of Apollonius. Bu
Idealtheorie in Ringbereichen

Idealtheorie in Ringbereichen

NOETHER, Emmy First edition, very rare offprint, of one of the most important works of "the most significant creative mathematical genius thus far produced since the higher education of women began" (Einstein, obituary in The New York Times, May 5, 1935). In the same year, but before she died, Norbert Wiener wrote: "Miss Noether is . the greatest woman mathematician who has ever lived; and the greatest woman scientist of any sort now living, and a scholar at least on the plane of Madame Curie." "The prominent algebraist Irving Kaplansky called Emmy Noether the 'mother of modern algebra.' The equally prominent Saunders MacLane asserted that 'abstract algebra,' as a conscious discipline, starts with Noether's 1921 paper 'Ideal Theory in Rings' [the offered paper]. Hermann Weyl claimed that she 'changed the face of algebra by her work'" (Kleiner, p. 91). "During the period from 1920 to 1926, she attracted numerous mathematicians and students - she was the doctoral advisor for ten - to her research program and she became a leader in the development of modern abstract algebra" (Grolier). A ring is an algebraic object which shares some, but not all, of the properties of the integers (whole numbers): it has addition and multiplication (and the result of these operations does not depend on the order in which they are performed), there are 0 and 1, but division is not usually possible and indeed the product of non-zero elements can be zero. The integers form the simplest example of a ring, but many other examples arise from geometry and number theory, as well as other areas of mathematics. In the present paper Noether extends to the general setting of a ring some well-known properties of the factorization of integers into products of prime numbers. It turns out that this cannot usually be done with the elements of the ring - rather it is the 'ideals' of the ring which enjoy good factorization properties (an ideal is a subset of the ring with certain properties - see below). "Formulating geometry and number theory in the language of rings is currently a massive mathematical operation, and Noether's work is a turning point in that endeavour" (Gray, p. 295). No copies located on OCLC or in auction records. According to Emmy Noether's student and successor Bartel van der Waerden, "the essence of Noether's mathematical credo is contained in the following maxim: 'All relations between numbers, functions and operations become perspicuous, capable of generalization, and truly fruitful after being detached from specific examples, and traced back to conceptual connections.' We identify these ideas with the abstract, axiomatic approach in mathematics. They sound commonplace to us. But they were not so in Noether's time. In fact, they are commonplace today in considerable part because of her work. "Algebra in the nineteenth century was concrete by our standards. It was connected in one way or another with real or complex numbers. For example, some of the great contributors to algebra in the nineteenth century, mathematicians whose works shaped the algebra of the twentieth century, were Gauss, Galois, Jordan, Kronecker, Dedekind, and Hilbert. Their algebraic works dealt with quadratic forms, cyclotomy, field extensions, permutation groups, ideals in rings of integers of algebraic number fields, and invariant theory. All of these works were related in one way or another to real or complex numbers. "Moreover, even these important works in algebra were viewed in the nineteenth century, in the overall mathematical scheme, as secondary. The primary mathematical fields in that century were analysis (complex analysis, differential equations, real analysis), and geometry (projective, non-euclidean, differential, and algebraic). But after the work of Noether and others in the 1920s, algebra became central in mathematics . "Noether contributed to the following major areas of algebra: invariant theory (1907-1919), commutative algebra (1920-1929), non-commutative algebra and representation theory (1927-1933), and applications of non-commutative algebra to problems in commutative algebra (1932-1935). ['Commutative' here means that the order in which any two elements of the algebra are multiplied has no effect on the result.] . The two major sources of commutative algebra are algebraic geometry and algebraic number theory. Emmy Noether's two seminal papers of 1921 and 1927 on the subject can be traced, respectively, to these two sources. In these papers, entitled, respectively, 'Ideal Theory in Rings' and 'Abstract Development of Ideal Theory in Algebraic Number Fields and Function Fields,' she broke fundamentally new ground, originating 'a new and epoch-making style of thinking in algebra' (Weyl)" (Kleiner, pp. 91-94). "[A] fundamental concept which she highlighted in the 1921 paper was that of a ring. This concept, too, did not originate with her. Dedekind (in 1871) introduced it as a subset of the complex numbers closed under addition, subtraction, and multiplication, and called it an 'order.' Hilbert, in his famous Report on Number Theory (Zahlbericht) of 1897, coined the term 'ring,' but only in the context of rings of integers of algebraic number fields. Fraenkel (in 1914) gave essentially the modern definition of ring, but postulated two extraneous conditions. Noether in her 1921 paper gave the definition in current use" (Kleiner, p. 95). "As she stated in opening [the offered] paper, 'the aim of the present work is to translate the factorization theorems of the rational integer numbers and of the ideals in algebraic number fields into ideals of arbitrary integral domains and domains of general rings.' Drawing on Fraenkel's formulation of a ring, Noether made the key observation that the abstract notion of ideals in rings could be seen not only to lay at the heart of prior work on factorization in the context of algebraic number fields and of polynomials (in the work of Hilbert, Francis Macaulay (1862-1937), and Emmanuel Lasker (
Photometria sive de mensura et gradibus luminis

Photometria sive de mensura et gradibus luminis, colorum et umbrae

LAMBERT, Johann Heinrich First edition, and a remarkable fine copy, of this cornerstone of modern optics, with applications which touch on astronomy and photography; this is one of the rarest of modern science books of this stature. "It established a complete system of photometric quantities and principles; using them to measure the optical properties of materials, quantify aspects of vision, and calculate illumination" (Wikipedia, accessed 13/05/19). Lambert's discoveries "are of fundamental importance in astronomy, photography and visual research generally . Both Kepler and Huygens had investigated the intensity of light, and the first photometer had been constructed by Pierre Bouguer (1698-1758); but the foundation of the science of photometry - the exact scientific measurement of light - was laid by Lambert's 'Photometry' . In the Photometria he described his photometer and propounded the law of the absorption of light named after him. He investigated the principles and properties of light, of light passing through transparent media, light reflected from opaque surfaces, physiological optics, the scattering of light passing through transparent media, the comparative luminosity of the heavenly bodies and the relative intensities of coloured lights and shadows" (PMM). "In his famous Photometria sive de mensure et gradibus luminis, colorum et umbrae (Augsburg, 1760), Lambert laid the foundation for this branch of physics . [he] carried out his experiments with few and primitive instruments, but his conclusions resulted in laws that bear his name. The exponential decrease of the light in a beam passing through an absorbing medium of uniform transparency is often named Lambert's law of absorption, although Bouguer discovered it earlier. Lambert's cosine law states that the brightness of a diffusely radiating plane surface is proportional to the cosine of the angle formed by the line of sight and the normal to the surface. Such a diffusely radiating surface does therefore appear equally bright when observed at different angles, since the apparent size of the surface also is proportional to the cosine of the said angle" (DSB). ABPC/RBH record the sale of four copies in the last 30 years (Christie's, November 23, 2011, lot 66, £27,500 = $43,118; Christie's NY, June 16, 1998, lot 591, $32,200 (Norman copy); Sotheby's, March 14, 1996, lot 229, £24,150 = $36,899 (Madsen copy); Christie's NY, April 22, 1994, lot 38, $24,150 (Horblit copy)). OCLC lists copies in US at Brown, Harvard Medical School and Oklahoma. "Photometria was the first work to accurately identify most fundamental photometric concepts, to assemble them into a coherent system of photometric quantities, to define these quantities with a precision sufficient for mathematical statement, and to build from them a system of photometric principles. These concepts, quantities, and principles are still in use today. "Lambert began with two simple axioms: light travels in a straight line in a uniform medium and rays that cross do not interact. Like Kepler before him, he recognized that 'laws' of photometry are simply consequences and follow directly from these two assumptions. In this way Photometria demonstrated (rather than assumed) that Illuminance varies inversely as the square of the distance from a point source of light. Illuminance on a surface varies as the cosine of the incidence angle measured from the surface perpendicular. Light decays exponentially in an absorbing medium. "In addition, Lambert postulated a surface that emits light (either as a source or by reflection) in a way such that the density of emitted light (luminous intensity) varies as the cosine of the angle measured from the surface perpendicular. In the case of a reflecting surface, this form of emission is assumed to be the case, regardless of the light's incident direction. Such surfaces are now referred to as 'Perfectly Diffuse' or 'Lambertian'. "Lambert demonstrated these principles in the only way available at the time: by contriving often ingenious optical arrangements that could make two immediately adjacent luminous fields appear equally bright (something that could only be determined by visual observation), when two physical quantities that produced the two fields were unequal by some specific amount (things that could be directly measured, such as angle or distance). In this way, Lambert quantified purely visual properties (such as luminous power, illumination, transparency, reflectivity) by relating them to physical parameters (such as distance, angle, radiant power, and color). Today, this is known as 'visual photometry.' Lambert was among the first to accompany experimental measurements with estimates of uncertainties based on a theory of errors and what he experimentally determined as the limits of visual assessment. "Although previous workers had pronounced photometric laws 1 and 3, Lambert established the second and added the concept of perfectly diffuse surfaces. But more importantly, as Anding pointed out in his German translation of Photometria [Leipzig, 1892], 'Lambert had incomparably clearer ideas about photometry' and with them established a complete system of photometric quantities. Based on the three laws of photometry and the supposition of perfectly diffuse surfaces, Photometria developed and demonstrated the following: Just noticeable differences. In the first section of Photometria, Lambert established and demonstrated the laws of photometry. He did this with visual photometry and to establish the uncertainties involved, described its approximate limits by determining how small a brightness difference the visual system could determine. Reflectance and transmittance of glass and other common materials. Using visual photometry, Lambert presented the results of many experimental determinations of specular and diffuse reflectance, as well as the transmittance of panes of glass and lenses. Among the most ingenious experiments he conducted was that to determine the
Autograph letter signed

Autograph letter signed, with important scientific content concerning the ?vis viva’ controversy, from Basel, dated 27 July 1728, to Gabriel Cramer, ?Professor of Mathematics,’ presently in London

BERNOULLI, Johann An important autograph letter from Johann Bernoulli (1667-1748), then one of the elder scientific statesmen of Europe, and still one of its greatest mathematicians, to his gifted student Gabriel Cramer (1704-52), who despite his youth had been appointed to the chair of mathematics at Geneva the previous year, but was now traveling through Europe and England making the acquaintance of the leading mathematicians of the day. The letter concerns the problem of vis viva ('forces vives', 'living force'), one of the most controversial topics of the day. This was the question of whether it is (to use modern terminology) momentum ('quantity of motion', mass x velocity) or kinetic energy ('living force', mass x velocity2) which is the true measure of the 'force' between colliding bodies in motion. As with so many other issues, this controversy pitted the supporters of Leibniz against those of Newton. Bernoulli had recently published a major contribution to the dispute, Discours sur les Loix de la Communication du Mouvement (1727), supporting the Leibnizian position, in which he presented an analysis of vis viva in terms of balls moved by releasing compressed springs. This was attacked by the young English Newtonian Benjamin Robins (1707-51) in May 1728 in an article in The Present State of the Republick of Letters, in which he gave a detailed discussion of the impact of elastic bodies. This article won Robins many admirers in England. In the present letter, Bernoulli refutes Robins' article, and writes that an experiment proposed by another English Newtonian, James Jurin (1684-1750), and carried out by the London instrument maker George Graham (1673-1751), involving dropping a lead weight onto an elastic plate, 'prouve rien contre la théorie des forces vives'. Bernoulli also responds to a misunderstanding by Cramer of a point in his Discours which Cramer had raised in an earlier letter. In a postscript, Bernoulli conveys the compliments of his nephew, the mathematician Nicolas Bernoulli (1687-1759). Letters by Bernoulli are rare on the market, particularly those with significant scientific content. Transcription: Monsieur Robert Caille Marchand Banquier, pour faire tenir à Monsieur Cramer, Professeur en mathematique presant à Londres Monsieur, Ce mot de lettre n'est que pour vous don[n]er avis que je vous ecrivis jeudi passé une reponse à la votre du 22. Juin, que j'ai adressée à Mr. de Mairan à Paris. Elle contient quelques reflexions generales sur la piece de Mr. Robins, et une reponse à l'objection tirée de l'experience avec la plaque de cuivre par laquelle étant en oscillation on laisse tomber un poids de plomb. J'ai fait voir que cette experience ne prouve rien contre la theorie des forces vives, et qu'elle est semblable à celle qu'on feroit avec deux corps sans ressort dont l'un en mouvement choqueroit directement l'autre en repos, auquel si le choquant étoit egal, ne lui com[m]uniqueroit que la moitié de la vitesse et iroit avec lui après le choc de compagnie, en sorte que la moitié de la force vive paroitra étre perdue. Je vous avois aussi ecrit une tres grande lettre datée du 23. Mai en reponse à vos deux precedentes du 10. Mars et 15 Avril, mais de laquelle vous ne faites pas mention dans votre derniere du 22 Juin, auquel temps vous prairés [pourriez] déjà avoir reçû la mienne; ce silence me mettant en peine, je vous prie de m'en tirer au plutot pour savoir si en fin elle vous a été rendue: vous y aurés trouvé bien des choses pour la confirmation de la theorie des forces vives et une ample solution à votre difficulté, qui consistoit à me demander, d'où vient que c'est l'increment de la vitesse, et non pas celui de la force vive, qui dans un temps infiniment petit est proportionel à ce temps et à la pression: c'est-à-dire, pourquoi il faut faire du = pdx/u, et non pas df = pdx/u ? Je finis en vous temoignant que je suis toujours avec la plus parfait consideration Monsieur votre tres humble et tres obeissant serviteur J Bernoulli Bale, ce 27. Juillet 1728 S. Mon neveu vous fait ses compliments; il y a quelques semaines qu'il vous a ecrit une lettre sous l'adresse de Mr. Caille: dont je me sers aussi toujours en vous ecrivant. Translation: Mr Robert Caille Merchant Banker, for the attention of Mr. Cramer, Professor in mathematics present in London Sir, This brief letter is only meant to give notice that I wrote you last Thursday a reply to your letter of 22 June which I addressed to Monsieur de Mairan in Paris. It contains some general reflections on Mr. Robins' essay, and a response to the objection derived from the experiment with an oscillating copper plate on which a lead weight is dropped. I have shown that this experiment proves nothing against the theory of the live force, and that it is similar to that which would be made with two inelastic bodies, one of which in motion would directly collide with the other at rest. If the colliding body was equal to the one at rest, it would convey to it only half the speed and go with it after the collision, so that half the force will appear to be lost. I also wrote you a very long letter dated 23 May in reply to your two previous ones of 10 March and 15 April, which you do not mention in your last letter of 22 June, though at that time you may have already received mine; this silence is distressing and I beg you to put an end to it and let me know if eventually it was delivered to you: you will have found [in it] many things confirming the theory of live forces and an ample solution to your difficulty, which consisted in asking me, how come that it is the increment of speed, and not that of the live force, which in an infinitely small time interval is proportional to this interval and to pressure; that is to say, why should we do du = pdx/u, not df = pdx/u? I am ending this letter with the renewed assurance that I remain, with the most perfect consideration Your very humble and very obedient servant J Bernoulli Basel, 27 July 1728 P.S. My nephe
Elementary Principles in Statistical Mechanics Developed with Especial Reference to the Rational Foundation of Thermodynamics

Elementary Principles in Statistical Mechanics Developed with Especial Reference to the Rational Foundation of Thermodynamics

GIBBS, Josiah Willard First edition, inscribed presentation copy to the great French mathematician and mathematical physicist Henri Poincaré. "Of Gibbs [Einstein] wrote in 1918: '[His] book is . a masterpiece, even though it is hard to read and the main points are found between the lines'" (Pais, Subtle is the Lord (1983), p. 73). This book was "a major advance in statistical mechanics, the branch of science in which a purely mechanical view of natural phenomena is replaced by one combining mechanics with probability" (Norman). Gibbs' book was "a triumph of the rigorous axiomatic method, which placed him beside Clausius, Maxwell, and Boltzmann as one of the principal founders of statistical mechanics" (Mehra, p. 1786). "Albert Einstein - who independently developed his own version of statistical mechanics from 1902 to 1904, having no knowledge of Gibbs' work - remarked in 1910 'Had I been familiar with Gibbs' book at that time, I would not have published those papers at all, but would have limited myself to the discussion of just a few points'" (Inaba, p. 102). "Gibbs' book on statistical mechanics became an instant classic and has remained so for almost a century" (Mehra). In this book, Gibbs formulated statistical mechanics in terms of 'ensembles' of systems, which were collections of large numbers of copies of the system of interest, all identical except for their physical properties (volume, temperature, etc.). "In most of his elegant Principles in Statistical Mechanics of 1902, [Gibbs] described the underlying mechanical system in a formal manner, by generalised coordinates subject to Hamilton's equations . He introduced and systematically studied the three fundamental ensembles of statistical mechanics: the micro-canonical, the canonical, and the grand-canonical ensemble (in which the number of molecules may vary). He examined the relations between these three ensembles and their analogies with thermodynamic systems, including fluctuation formulas" (Buchwald & Fox, p. 784). "A year before his death, Einstein paid Gibbs the highest compliment. When asked who were the greatest men, the most powerful thinkers he had known, he replied 'Lorentz', and added 'I never met Willard Gibbs; perhaps, had I done so, I might have placed him beside Lorentz'" (Pais, p. 73). According to Emilio Segré (From Falling Bodies to Radio Waves (1984), p. 250), "even Jules-Henri Poincaré found [Elementary Principles] difficult to digest" - the present copy is presumably the one Poincaré puzzled over. Although reasonably well represented in institutional collections, this is a very rare book on the market. ABPC/RBH lists only one other copy in the last 35 years (and that copy lacked the dust-jacket). Provenance: Jules-Henri Poincaré (1854-1912), presentation inscription on front free endpaper: 'M. J.-H. Poincaré with the respects of the author'. Poincaré was "one of the greatest mathematicians and mathematical physicists at the end of 19th century. He made a series of profound innovations in geometry, the theory of differential equations, electromagnetism, topology, and the philosophy of mathematics" (Britannica). Although Poincaré did not work directly on statistical mechanics, his work on the three-body problem in celestial mechanics had an important impact upon it. In 1890, he proved his 'recurrence theorem', according to which mechanical systems governed by Hamilton's equations will, after a sufficiently long time, return to a state very close to the initial state. This theorem created serious difficulties for any mechanical explanation of the laws of thermodynamics, as it apparently contradicts the Second Law, which says that large dynamical systems evolve irreversibly towards states with higher entropy, so that if one starts with a low-entropy state, the system will never return to it. "Josiah Willard Gibbs was born in 1839: his father was at that time a professor of sacred literature at Yale University. Gibbs graduated from Yale in 1858, after he had compiled a distinguished record as a student. His training in mathematics was good, mainly because of the presence of H. A. Newton on the faculty. Immediately after graduation he enrolled for advanced work in engineering and attained in 1863 the first doctorate in engineering given in the United States. After remaining at Yale as tutor until 1866, Gibbs journeyed to Europe for three years of study divided between Paris, Berlin, and Heidelberg. Not a great deal of information is preserved concerning his areas of concentration during these years, but it is clear that his main interests were theoretical science and mathematics rather than applied science. It is known that at this time he became acquainted with Möbius' work in geometry, but probably not with the systems of Grassmann or Hamilton. Gibbs returned to New Haven in 1869 and two years later was made professor of mathematical physics at Yale, a position he held until his death [in 1903]. "His main scientific interests in his first year of teaching after his return seem to have been mechanics and optics. His interest in thermodynamics increased at this time, and his research in this area led to the publication of three papers, the last being his now classic 'On the Equilibrium of Heterogeneous Substances,' published in 1876 and 1878 in volume III of the Transactions of the Connecticut Academy. This work of over three hundred pages was of immense importance. When scientists finally realized its scope and significance, they praised it as one of the greatest contributions of the century" (Crowe, p. 151). "During the academic year 1889-1890 Gibbs announced 'A short course on the a priori Deduction of Thermodynamic Principles from the Theory of Probabilities,' a subject on which he lectured repeatedly during the 1890s" (DSB). "Lord Rayleigh, writing on 5 June 1892 about an optical problem to Josiah Willard Gibbs in New Haven, Connecticut, concluded his letter as follows: 'Have you ever thought of bringing out a new edition of, o
Planiglobium coeleste ac terrestre: argentorati quondam . [Planiglobium celeste

Planiglobium coeleste ac terrestre: argentorati quondam . [Planiglobium celeste, Hoc est globus coelestis nove forma ac norma in planum projectus, omnes orbis coelestis lineas, circulos, gradus, partes, stellas, sidera &c. in planis tabulis aeri incises artificiose exhibens. Adjecta succincta tum fabricate tum usus explicatione, omnium Problematum, quae vulgatis hactenus globis, Planisphaeris, Astrolabiis expediri solita sunt, stellas coeli quascunq; cognoscere & denominare possit.] [Planiglobium terrestre. Sive globus terrestris, novo modo, ac method in plano descriptus; omnes Orbis Terrestris lineas, circulos, Regiones, Regna, Provincias, Promontoria, Portus, Insulas, Maria: omnes deniq; Terrae Marisq; tractus & anfractus in tabulis aeri insculptis, accurate monstrans. Annexa simul perspicua tum structurae, tum usue explanation: ubi plurima as usum globorum terrestrium plenius intelligendum hinc inde inseruntur.]

HABRECHT II, Isaac & STURM, Johann Christoph First edition of one of the most beautiful instrument books published in the seventeenth century and certainly one of the rarest, particularly with the full complement of plates. This work is an enlargement, by his student Sturm, of Habrecht's famous treatise on the making of celestial and terrestrial globes, published in 1628/29. Much influenced by Blaeu and Hondius, Habrecht published a pair of printed celestial and terrestrial globes at Strasbourg in 1621. The first edition of Planiglobium included two large planispheres (although they are lacking from almost all copies), these being polar stereographic celestial charts of the northern and southern constellations. In the present edition Sturm augmented the text, reprinted these planispheres from the same plates (one of them is still dated 1628), and added to them a further 12 plates, including two handsome polar projections of the world, and ten engravings showing the various parts of his celestial and terrestrial globes. "The plates, superbly executed by Jacob van der Heyden, were probably intended to be mounted and assembled to form several instruments, each with a revolving plate measuring 27cm in diameter and a movable pointer. Each was to be supported on an approximately 12cm base" (W.P. Watson, Cat. 18). Regarding the two planispheres, Warner writes (TheSky Explored, p. 104): "Habrecht derived the bulk of the information for this globe from Plancius. The origin of Rhombus - a constellation near the south pole that as Reticulum survives today - is unclear. It may perhaps derive from the quadrilateral arrangement of stars seen by Vespucci around the Antarctic pole. In any case, Rhombus as such seems to have made its first appearance on Habrecht's globe." Habrecht added to his celestial globe several cometary paths, an innovation that was followed by many Central European globe makers. Despite being an obvious Americanum (see for example pp. 220, 237, 249, and America pictured on one of the maps), this work is not in Sabin, JCB, Palmer and other standard bibliographies. The Honeyman copy (Sotheby's, November 6, 1979, £1100 = $2346) is the only other complete copy on ABPC/RBH since 1950 and it had significant defects (some plates torn or repaired, title page defective and repaired, O2 torn, one leaf with marginal repair, browned). The Macclesfield copy, sold in 2004 for £3600, lacked the title page. A set of the unfolded plate sheets (without the text) sold at Christie's in 2010 for £10,000. OCLC lists Brown, Harvard (both lacking the plates) and Chicago only in North America. "European discovery of the New World helped to establish the status of the terrestrial globe as equal to its celestial counterpart, for it was ideally suited to whet the imagination of those who remained at home but were eager to learn of the new and hitherto unknown lands and people about whom so much speculation had long existed. This interest stimulated a real boom in the cartographic industry. Map and globe makers set out to produce different versions of the world by adjusting and correcting the existing Ptolemaic picture. Through this process of continual adjustment old and rare terrestrial globes have become valuable artefacts, on which the history of world exploration is recorded both visually, by the tracks of the various epoch-making circumnavigations, and verbally, by lengthy legends inscribed on the globes . "During the fifteenth century, when the first western terrestrial globes emerged in the wake of the Latin translation of Ptolemy's Geography, the Earth was firmly believed to be immobile in the centre of the universe. Thus, as far as models of the Earth are concerned, it would have sufficed to make a terrestrial sphere with a fixed mounting. However, the dominant construction in early globe making was more complex. It consisted of a mobile sphere mounted in a stand with a number of accessories - a movable meridian ring, a fixed horizon ring, and an hour circle with pointer. These accessories served to demonstrate the time-dependent phenomena of the world around us in terms of the then generally accepted Ptolemaic concept of the First Mover and the annual motion of the Sun around the Earth. "In the common pairing of the terrestrial and celestial globes the diurnal motion of the First Mover is realized by the rotation of both spheres around the poles of the world. In use, these spheres always have to be turned from east to west in accordance with the Ptolemaic world system. For a proper understanding of the common Ptolemaic globe, it is particularly important to realize that the mobility of a terrestrial example has nothing whatsoever to do with the motion of the Earth. Neither is it a matter of simple viewing convenience. When the sphere of a terrestrial globe is turned, it is the daily motion of the Sun that is reproduced . Thus, in the terrestrial globe the motion of the First Mover is imparted to the 'sphere of the Sun' and in the celestial globe to the 'sphere of the fixed stars'. With this construction the whole series of phenomena which mattered in daily life as well as in education, such as the rising and setting of the Sun (with the terrestrial globe) and of the stars (with the celestial globe), could be demonstrated. The meridian ring serves to rectify the globe for the latitude of a place. The hour circle with pointer on top of the meridian ring can be set to local time, as measured through the diurnal motion of the Sun. "The annual motion of the Sun around the Earth is realized, only indirectly, by two design features of these globes. First, the ecliptic is drawn on both the terrestrial and the celestial sphere. Second, the position of the Sun in the zodiac throughout the year is displayed graphically on the horizon ring. Having established the Sun's position at a particular time of the year, it can then be located on the ecliptic drawn on the sphere and its motion for that season demonstrated. "Thus, the common terrestrial globe is no
A Treatise on Electricity and Magnetism

A Treatise on Electricity and Magnetism

MAXWELL, James Clerk First edition, first issue, and a very fine copy in a contemporary prize binding, of Maxwell's presentation of his theory of electromagnetism, advancing ideas that would become essential for modern physics, including the landmark "hypothesis that light and electricity are the same in their ultimate nature" (Grolier/Horblit). "This treatise did for electromagnetism what Newton's Principia had done from classical mechanics. It not only provided the mathematical tools for the investigation and representation of the whole electromagnetic theory, but it altered the very framework of both theoretical and experimental physics. It was this work that finally displaced action-at-a-distance physics and substituted the physics of the field" (Historical Encyclopedia of Natural and Mathematical Sciences, p. 2539). "From a long view of the history of mankind - seen from, say, ten thousand years from now - there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics" (R. P. Feynman, in The Feynman Lectures on Physics II (1964), p. 1-6). "[Maxwell] may well be judged the greatest theoretical physicist of the 19th century . Einstein's work on relativity was founded directly upon Maxwell's electromagnetic theory; it was this that led him to equate Faraday with Galileo and Maxwell with Newton" (PMM). "Einstein summed up Maxwell's achievement in 1931 on the occasion of the centenary of Maxwell's birth: 'We may say that, before Maxwell, Physical Reality, in so far as it was to represent the process of nature, was thought of as consisting in material particles, whose variations consist only in movements governed by [ordinary] differential equations. Since Maxwell's time, Physical Reality has been thought of as represented by continuous fields, governed by partial differential equations, and not capable of any mechanical interpretation. This change in the conception of Reality is the most profound and the most fruitful that physics has experienced since the time of Newton'" (Longair). Provenance: Stanley Butter (presentation inscription in Latin on front free endpaper from Exeter College, Oxford, dated Michaelmas [autumn] term 1877). "Maxwell's great paper of 1865 established his dynamical theory of the electromagnetic field. The origins of the paper lay in his earlier papers of 1856, in which he began the mathematical elaboration of Faraday's researches into electromagnetism, and of 1861-1862, in which the displacement current was introduced. These earlier works were based upon mechanical analogies. In the paper of 1865, the focus shifts to the role of the fields themselves as a description of electromagnetic phenomena. The somewhat artificial mechanical models by which he had arrived at his field equations a few years earlier were stripped away. Maxwell's introduction of the concept of fields to explain physical phenomena provided the essential link between the mechanical world of Newtonian physics and the theory of fields, as elaborated by Einstein and others, which lies at the heart of twentieth and twenty-first century physics" (Longair). The 1865 paper "provided a new theoretical framework for the subject, based on experiment and a few general dynamical principles, from which the propagation of electromagnetic waves through space followed without any special assumptions . In the Treatise Maxwell extended the dynamical formalism by a more thoroughgoing application of Lagrange's equations than he had attempted in 1865. His doing so coincided with a general movement among British and European mathematicians about then toward wider use of the methods of analytical dynamics in physical problems . Using arguments extraordinarily modern in flavor about the symmetry and vector structure of the terms, he expressed the Lagrangian for an electromagnetic system in its most general form. [George] Green and others had developed similar arguments in studying the dynamics of the luminiferous ether, but the use Maxwell made of Lagrangian techniques was new to the point of being almost a new approach to physical theory-though many years were to pass before other physicists fully exploited the ground he had broken . "In 1865, and again in the Treatise, Maxwell's next step after completing the dynamical analogy was to develop a group of eight equations describing the electromagnetic field . The principle they embody is that electromagnetic processes are transmitted by the separate and independent action of each charge (or magnetized body) on the surrounding space rather than by direct action at a distance. Formulas for the forces between moving charged bodies may indeed be derived from Maxwell's equations, but the action is not along the line joining them and can be reconciled with dynamical principles only by taking into account the exchange of momentum with the field" (DSB). "Maxwell once remarked that the aim of his Treatise was not to expound the final view of his electromagnetic theory, which he had developed in a series of five major papers between 1855 and 1868; rather it was to educate himself by presenting a view of the stage he had reached in his thinking. Accordingly, the work is loosely organized on historical and experimental, rather than systematically deductive, lines. It extended Maxwell's ideas beyond the scope of his earlier work in many directions, producing a highly fecund (if somewhat confusing) demonstration of the special importance of electricity to physics as a whole. He began the investigation of moving frames of reference, which in Einstein's hands were to revolutionize physics; gave proofs of the existence of electromagnetic waves that paved the way for Hertz's discovery of radio waves; worked out connections between electrical and optical qualities of bodies that would lead to modern solid-state physics; and applied Tait's quaternion formulae to the field equations, out of which Heaviside and Gibbs would develop
Telescopium: sive Ars perficiendi novum illud Galilaei visorium instrumentum ad sydera in tres partes divisa

Telescopium: sive Ars perficiendi novum illud Galilaei visorium instrumentum ad sydera in tres partes divisa

SIRTORI, Girolamo First edition, extremely rare, of "the first book about the telescope, its invention and use" (Zinner). Written by the Milanese scholar Girolamo Sirtori in 1612, only four years after the telescope was invented, it contained a complete set of instructions and diagrams for building a refracting telescope, and gave in the second part the first detailed account of Galileo's telescope. Dedicated to the Grand Duke Cosimo II de' Medici, Telescopium is also one of the most important sources for the history of the invention and first uses of the telescope. Sirtori records the arrival of a telescope in Milan in May 1609, brought by 'a Frenchman' who was an associate of its inventor, Hans Lipperhey, and presented to the Count of Fuentes; this was about a month before Galileo first learned of the invention (according to Siderius Nuncius). Sirtori claims to have seen and handled Lipperhey's very first telescope, but also suggests that the device was known to others before the Dutchman. He also provides an account of a famous meeting organised by Federico Cesi, founder of the Accademia dei Lincei, dated by Rosen to 14 April 1611, at which a select group of natural philosophers and mathematicians, including Sirtori himself, met Galileo and experienced the performance of his telescope in person - this was "the public unveiling of the term telescope" (Rosen, p. 31). Galileo received a copy of Sirtori's work in 1633 from the hands of Cassiano dal Pozzo, his fellow Lincean and great collector and begetter of the 'Museo Cartaceo' (Cassiano Dal Pozzo to Galileo [in Rome], Rome, 18 June 1633, Opere XV, p. 158); this is presumably the copy which belonged to François Arago, cited by both Brunet and Riccardi, and having notes in Galileo's hand. ABPC/RBH list only three other complete copies, two of them in Macclesfield sammelbands, the other an ex-library copy with removed stamps. The Honeyman copy, a presentation copy from the author to Tommaso Mingoni (Menghin), Leibartzt of Rudolph II, and a friend of Kepler, lacked one of the plates. OCLC lists Chicago and Yale only in North America; VD17 gives only 5 locations. "Almost immediately after its invention, the telescope evolved from a mere optical toy into a 'scientific instrument,' an instrument of a new type which at the time was called 'philosophical': the manipulation of such instruments allowed scholars to attain natural philosophical truth. In this way, the telescope paved the way for other scientific instruments which also emerged in the course of the seventeenth century, such as the air pump, the barometer, and the microscope. The emergence of the telescope was an important episode in the history of science and technology not only because it marks the invention of a new device, or because it changed man's image of the universe, but also because it helped change the ways in which natural philosophy was practiced and what counted as 'science' . "The search for the inventor of the telescope has a long tradition which began almost immediately after the invention of the instrument. In Telescopium, the earliest book on the telescope, published in 1618, but composed in 1612, Girolamo Sirtori already doubts whether Lipperhey, the first demonstrator of the instrument, was also the inventor of the device" (Van Helden, Origins, p. 2). Indeed, Sirtori writes (pp. 24-26, translation from Van Helden, Invention, pp. 50-51): 'In the year 1609 [sic, for 1608] there appeared a genius or some other man, as yet unknown, of the race of Hollanders, who, in Middelburg in Zeeland, visited Johannes Lippersein [i.e., Lipperhey], a man distinguished from others by his remarkable appearance, and a spectacle maker. There was no other [spectacle-maker] in that city, and he ordered many lenses to be made, concave as well as convex. On the agreed day he returned, eager for the finished work, and as soon as he had them before him, raising two of them up, namely a concave and a convex one, he put the one and the other before his eye and slowly moved them to and fro, either to test the gathering point or the workmanship, and after that he left, having paid the maker. The artisan, by no means devoid of ingenuity, and curious about the novelty began to do the same and to imitate the customer, and quickly his wit suggested that these lenses should be joined together in a tube. And as soon as he had completed one, he rushed to the court of Prince Maurits and showed him the invention. The prince had one [or, had been acquainted with one] before, and lest it should be suspected that [the device] was of military value, and very necessary, had kept it a secret. But now that he found by chance that it had become known he disguised [his prior knowledge], rewarding the industry and good intentions of the artisan. Thence the novelty of so great a thing was spread through the whole world, and many other telescopes were made. But none of those turned out better or more apt than the first one (which I have seen and handled).' Sirtori goes on to describe his first encounter with a telescope. 'In the month of May [1609] a Frenchman rushed into Milan and offered such a telescope to the Count of Fuentes. He said that he was an associate of the inventor from Holland. When the Count had given it to a silversmith to put it in a silver tube, it came into my hands. I handled it and examined it, and made similar ones, in which I observed that many inconveniences occurred because of the glass. I therefore went to Venice in order to obtain a supply [of lenses] from the artisans there and, being still unskilled in the art, I delivered a finished lens to someone so that he could make similar ones. I squandered some money uselessly and lost the lens, having learned nothing more than that the business is to be perfected by chance and by the laborious selection of lenses. As it happened when I acquired one, I imprudently ascended the tower of St. Mark, in order to try it out at a distance. Someone, having decried the n
De revolutionibus orbium coelestium

De revolutionibus orbium coelestium, libri VI: in quibus stellarum et fixarum et erraticarum motus, ex veteribus atq[ue] recentibus observationibus, restituit hic autor : praeterea tabulas expeditas luculentasq[ue] addidit, ex quibus eosdem motus ad quodvis tempus mathematum studiosus facillime calculare poterit. Item, De libris revolutionum Nicolai Copernici narratio prima, per Georgium Ioachimum Rheticum ad Ioan. Schonerum scripta

COPERNICUS, Nicolaus Second edition of the most important scientific publication of the sixteenth century and a "landmark in human thought" (PMM). De revolutionibus was the first work to propose a comprehensive heliocentric theory of the cosmos, according to which the sun stood still and the earth revolved around it. It thereby inaugurated one of the greatest ever paradigm shifts in the history of human thought. "Renaissance mathematicians, following Ptolemy, believed that the moon, sun and five planets were carried by complex systems of epicycles and deferents about the central earth, the fixed pivot of the whole system. In Copernicus's day it was well known that conventional astronomy did not work accurately . Copernicus, stimulated by the free entertainment of various new ideas among the ancients, determined to abandon the fixity of the earth . With the sun placed at the center, and the earth daily spinning on its axis and circling the sun in common with other planets, the whole system of the heavens became clear, simple and harmonious. The revolutionary nature of his theory is evident in his famous diagram illustrating the concentric orbits of the planets [C1v]" (PMM). The text of the second edition of De revolutionibus follows the 1543 first edition almost exactly, including Andreas Osiander's notorious unsigned preface, in which he attempted to placate potential critics of the work by stating that "these hypotheses need not be true nor even probable" - all that was necessary was that they should allow astronomers to correctly calculate the motions of the heavenly bodies. Petri added, at the end of the 'Index capitulorum', a five-line recommendation by "our leading mathematician" Erasmus Reinhold, extracted from his Tabulae Prutenicae, stating that "all posterity will gratefully remember the name of Copernicus, by whose labor and study the doctrine of celestial motions was again restored from near collapse" (translation from Gingerich, Eye of Heaven, p. 221). This second edition is the first to contain the Narratio prima of Copernicus's disciple George Joachim Rheticus, which summarises and champions the Copernican heliocentric hypothesis, and records Rheticus's indefatigable efforts to persuade Copernicus to publish. The first edition of the Narratio, published at Gdansk in 1540, is virtually unobtainable, and the second edition of 1541 is hardly more procurable. According to Gingerich (Census, p. XIV), about 500-600 copies of this second edition of De revolutionibus were printed, perhaps slightly more than the first edition. "The first speculations about the possibility of the Sun being the center of the cosmos and the Earth being one of the planets going around it go back to the third century BCE. In his Sand-Reckoner, Archimedes (d. 212 BCE), discusses how to express very large numbers. As an example he chooses the question as to how many grains of sand there are in the cosmos. And in order to make the problem more difficult, he chooses not the geocentric cosmos generally accepted at the time, but the heliocentric cosmos proposed by Aristarchus of Samos (ca. 310-230 BCE), which would have to be many times larger because of the lack of observable stellar parallax. We know, therefore, that already in Hellenistic times thinkers were at least toying with this notion, and because of its mention in Archimedes's book Aristarchus's speculation was well-known in Europe beginning in the High Middle Ages but not seriously entertained until Copernicus. "European learning was based on the Greek sources that had been passed down, and cosmological and astronomical thought were based on Aristotle and Ptolemy. Aristotle's cosmology of a central Earth surrounded by concentric spherical shells carrying the planets and fixed stars was the basis of European thought from the 12th century CE onward. Technical astronomy, also geocentric, was based on the constructions of eccentric circles and epicycles codified in Ptolemy's Almagest (2d. century CE). "In the fifteenth century, the reform of European astronomy was begun by the astronomer/humanist Georg Peurbach (1423-1461) and his student Johannes Regiomontanus (1436-1476). Their efforts were concentrated on ridding astronomical texts, especially Ptolemy's, from errors by going back to the original Greek texts and providing deeper insight into the thoughts of the original authors. With their new textbook and a guide to the Almagest, Peurbach and Regiomontanus raised the level of theoretical astronomy in Europe. "Several problems were facing astronomers at the beginning of the sixteenth century. First, the tables (by means of which astronomical events such as eclipses and conjunctions were predicted) were deemed not to be sufficiently accurate. Second, Portuguese and Spanish expeditions to the Far East and America sailed out of sight of land for weeks on end, and only astronomical methods could help them in finding their locations on the high seas. Third, the calendar, instituted by Julius Caesar in 44 BCE was no longer accurate. The equinox, which at the time of the Council of Nicea (325 CE) had fallen on the 21st, had now slipped to the 11th. Since the date of Easter (the celebration of the defining event in Christianity) was determined with reference to the equinox, and since most of the other religious holidays through the year were counted forward or backward from Easter, the slippage of the calendar with regard to celestial events was a very serious problem. For the solution to all three problems, Europeans looked to the astronomers" (Galileo Project). Nicolaus Copernicus was born on 19 February 1473 in Thorn (modern day Torun) in Poland. His father was a merchant and local official. When Copernicus was 10 his father died, and his uncle, a priest, ensured that Copernicus received a good education. In 1491, he went to Krakow Academy, now the Jagiellonian University, and in 1496 travelled to Italy to study law. While a student at the University of Bologna he stayed with
Gliding Experiments. Offprint from: Journal of the Western Society of Engineers

Gliding Experiments. Offprint from: Journal of the Western Society of Engineers, Vol. 2, No. 5, October, 1897 (read 20 October)

CHANUTE, Octave Alexander First edition, extremely rare offprint, of this seminal work in the history of aviation, and a remarkable association copy linking three great early American pioneers of aviation and technology. In this work, Chanute presented his findings from nearly 2,000 flights made at Dune Park, Indiana, on the shores of Lake Michigan, in the summer of the previous year. These test-flights, led to his introduction of the Pratt-trussed biplane configuration, the essential shape of the early airplane, which was later adopted by the Wright brothers, and which he described in the present article. "It was a pivotal moment in the history of aircraft design, ranking with Henson and Stringfellow's postulation of the Aerial Steam Carriage over half a century earlier and Cayley's even more distant derivation of the modern airplane shape. It ushered in an era of strong, light, straightforward, uncomplicated (and easily analysed) rectangular structures that quickly superseded the convoluted curves and framing of older attempts such as those by Adler and Lilienthal. Chanute, in short, had taken both glider experimentation and structural design to a new level, contributions of seminal importance" (Hallion, p. 177). "The Chanute glider, designed by Chanute but also incorporating the ideas of his young employee Herring with regard to automatic stability, was the most influential of all flying machines built before the Wright brothers began designing aircraft . Wilbur Wright, whom Chanute befriended, understood the importance of the 1896 biplane glider. 'The double-deck machine,' Wright remarked, 'represented a very great structural advance, as it was the first in which the principles of the modern truss bridge were fully applied to flying machine construction.' Chanute's rigid, lightweight structure provided the most basic model for all externally based biplanes. It was nothing less than the first modern aircraft structure" (Britannica). "The Wright brothers began their long association with Chanute in 1899, when they started serious work on their airplane. The Wrights corresponded with Chanute regularly, carefully detailing their thoughts to him. He served as their mentor, encouraging their efforts and offering advice. In 1901 he visited the brothers and encouraged them in their gliding experiments. Chanute also witnessed the early Wright flights, including the 1902 glider and the 1904 and 1905 powered flyer. He published the Wright brothers' writings in America and abroad, which did much to stimulate interest in aviation" (Octave Chanute and His Photos of the Wright Experiments at the Kill Devil Hills, www.memory.local.gov). OCLC locates eight known copies, including those at the Library of Congress and the Smithsonian. No copies on ABPC/RBH. Provenance: James Means (1853-1920), industrialist and aviation pioneer, inscribed on front wrapper to: Francis Blake Jr. (1850-1913), engineer and inventor who partnered with Alexander Graham Bell in the invention of the telephone (see below). "Born in 1832, the son of a history professor at the Collège de France, [Chanute] emigrated with his parents to the United States at age six, where his father assumed the vice presidency of Jefferson College in Louisiana. Though he considered himself American, young Chanute grew up in an intellectually oriented household so European in outlook that a pronounced Gallic accent would forever tinge his English. Gifted in mathematics, he chose a career in engineering while still a teenager, subsequently joining a railway survey crew and learning engineering first-hand. He eventually rose to the very top of his profession, earning a fortune while working with a series of railroad companies, as a noted bridge builder, and as the architect and chief engineer of the Union Stock Yards in Chicago and Kansas City . But Chanute harboured a dark secret, something he feared that if learned could hurt his reputation: he had accumulated a wealth of material on early flying attempts, paths taken, and configurations chosen. He was in fact a closet aerophile, had been since taking a trip to France with his wife and children in 1875 that had exposed him to the work of Pénaud, Wenham and others, and in a few more years, he hoped, he might be able to come out in the open . "Only when in his late 50s, so distinguished, accomplished, and professionally secure as to no longer fear ridicule for advocating and discussing aviation, did he now devote his full attention to flight. And he did so with the characteristic energy and enthusiasm he had brought to his career as a practicing engineer. He became a virtual one-man aeronautical information clearinghouse and also bankrolled a number of individuals studying aviation . Upon Chanute's death in 1910, Wilbur Wright would state: 'No one was too humble to receive a share of his time. In patience and goodness of heart he has rarely been surpassed. Few men were more universally respected and loved.' "In 1891 he wrote the first of a series of articles for American Engineer and Railroad Journal, which he would pull together and publish as a book three years later. He also sponsored professional meetings, most notably a four-day international Conference on Aerial Navigation held in Chicago on August 1-4, 1894, that drew together most of the major names in American aviation, and some international figures as well . "Chanute clearly enunciated his own thoughts on flight in his address at the opening of the conference. Flight to this point, he said, 'has hitherto been associated with failure,' its advocates viewed 'as eccentric - to speak plainly, as 'cranks''. But the record of ballooning and airship development, and now increasingly that of winged aviation, held great promise, even if the precise commercial and military promise of such craft could not yet be clearly seen. Most significant, Chanute emphasized the importance of seeking integrated solutions to the problems of flight. 'It is a mistake,' he wrote, 'to suppose t
Astronomiae Instauratae Progymnasmata

Astronomiae Instauratae Progymnasmata, quorum hunc cassel pars prima de restitutione motuum solis et lunae, stellarumque inerrantium tractat et praeterea de admiranda nova stella anno 1572 exorta luculenter agit. Frankfurt: Gottfried Tampach, 1610. [With:] De Mundi Aetherei recentioribus Phaenomenis. Liber Secundus. Excudi primun coeptius Uraniburgi Daniae, ast Pragae Bohemiae absolutus. Frankfurt: Gottfried Tampach, 1610 (Colophon: Pragae Bohemorum, Absolvebatur Typis Schumanianis, Anno Domini 1603). [With:] Epistolarum Astronomicarum Libro. Quorum primus hic Illustriss. et Laudatiss. Principis Gulielmi Hassiae Landtgravij ac ipsius Mathematici Literas, unaque Responsa ad singulas complectitur . Frankfurt: Gottfried Tampach, 1610 (Colophon: Uraniburgi, Ex officina Typographica Authoris, Anno Domini, 1596)

BRAHE, Tycho An extraordinary sammelband, uniting the three most important works of the great Danish astronomer, all in first edition, Frankfurt issues, in two volumes uniformly bound in contemporary vellum. "Tycho Brahe's contributions to astronomy were enormous . He revolutionized astronomical instrumentation. He also changed observational practice profoundly. Whereas earlier astronomers had been content to observe the positions of planets and the Moon at certain important points of their orbits, Tycho and his cast of assistants observed these bodies throughout their orbits. Without these complete series of observations of unprecedented accuracy, Kepler could not have discovered that planets move in elliptical orbits . Tycho's observations of the new star [now recognized to have been a supernova] of 1572 and comet of 1577, and his publications on these phenomena, were instrumental in establishing the fact that these bodies were above the Moon and that therefore the heavens were not immutable as Aristotle had argued and philosophers still believed . Further, if comets were in the heavens, they moved through the heavens. Up to now it had been believed that planets were carried on material spheres that fit tightly around each other. Tycho's observations showed that this arrangement was impossible because comets moved through these spheres" (Galileo Project). "Astronomiae instauratae progymnasmata was produced in 1602 by the author's own press at Uraniborg, and only a small number were printed for dedication purposes. It contains important investigations on the new star of 1572 which Brahe had discovered in Cassiopeia. This discovery led to far-reaching consequences in the history of astronomy as this work became the foundation on which Kepler, and later Newton, built their astronomical systems" (Sparrow). De mundi aetherei contains Brahe's observations of the great comet of 1577, the brightest of the century, and, most importantly, includes the first account of his geoheliocentric theory of the universe, according to which the inferior and superior planets of Mercury, Venus, Mars, Jupiter and Saturn revolved around the Sun, but the Sun and the Moon orbited the Earth. "There can be little doubt that Tycho regarded it [the geoheliocentric system] as his most significant achievement, and in the short term it surely was. As a geometrical equivalent of the Copernican system, it was capable of representing every aspect of the astronomical phenomena without demanding allegiance to a moving Earth, for which there would be no proof until much later" (Thoren, p. 8). The Astronomiae and De mundi were intended to form the first two parts of a trilogy, together with a work on the comets of 1582 and 1585, but this was never completed. The Epistolarum contains correspondence between Brahe and the Landgrave Wilhelm IV of Hesse-Cassel and his astronomer Christopher Rothmann, mostly concerning astronomical observations and the construction of astronomical instruments. "This correspondence covered all aspects of contemporary astronomy: instruments and methods of observing, the Copernican system (which Rothmann supported against Tycho's system), comets, and auroras" (DSB, under Rothmann). Brahe's description of Uraniborg contained here is one of the earliest descriptions of an astronomical observatory and its instruments. These three works were originally produced on Tycho's private press at Uraniborg, and were then reissued with minor textual changes at Prague and Frankfurt. The Astronomiae is present here in its second issue, the other two works in their third issue; the first issues of all three works are exceptionally rare as the few copies printed were intended for presentation only. "Tyge (Latinized as Tycho) Brahe was born on 14 December 1546 in Skane, then in Denmark, now in Sweden . He attended the universities of Copenhagen and Leipzig, and then traveled through the German region, studying further at the universities of Wittenberg, Rostock, and Basel. During this period his interest in alchemy and astronomy was aroused, and he bought several astronomical instruments . In 1572 Tycho observed the new star in Cassiopeia and published a brief tract about it the following year. In 1574 he gave a course of lectures on astronomy at the University of Copenhagen. He was now convinced that the improvement of astronomy hinged on accurate observations. After another tour of Germany, where he visited astronomers, Tycho accepted an offer from the King Frederick II to fund an observatory. He was given the little island of Hven in the Sont near Copenhagen, and there he built his observatory, Uraniburg, which became the finest observatory in Europe. Tycho designed and built new instruments, calibrated them, and instituted nightly observations. He also ran his own printing press. The observatory was visited by many scholars, and Tycho trained a generation of young astronomers there in the art of observing. After a falling out with King Christian IV, Tycho packed up his instruments and books in 1597 and left Denmark. After traveling several years, he settled in Prague in 1599 as the Imperial Mathematician at the court of Emperor Rudolph II. He died there in 1601" (Galileo Project). In 1600, Tycho met Kepler and asked him to be his assistant. This placed Kepler in a position not only to publish some of Brahe's works after his death, but also, after many trials and tribulations, to acquire Tycho's actual observations, from which he would deduce his laws of planetary motion. Although Tycho intended the Astronomiae to form the first work of his trilogy, "the corrected star places which were necessary for the reduction of the observations of 1572-73 involved researches on the motion of the sun, on refraction, precession, etc., the volume gradually assumed greater proportions than was originally contemplated, and was never quite finished in Tycho's lifetime" (Dreyer, pp. 162-3). The first to be completed, in 1588, was De mundi, Tycho's