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Berlin, G. Reimer, 1844. 4to. As extracted from "Journal für die reine und angewandte Mathematik, 28 Band, 4. Heft, 1844". Without wrappers and backstrip. Fine and clean. [Eisenstein:] Pp. 289-374. [Entire issue: 289-380 + 2 folded plates]. First printing of German mathematics prodigy Eisenstein's paper on third degree equations with basis in a devided circle. Even though he died prematurely at the age of 29, he managed to prove biquadratic reciprocity, Quartic reciprocity, Cubic reciprocity, to be imprisoned by the Prussian army for revolutionary activities in Berlin and making Gauss state that: "There have been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein". Alexander von Humboldt, then 83, accompanied Eisenstein's remains to the cemetery. The papers presented in the present issue is among his most prominent and made him famous throughout the mathematical world. (James, Driven to innovate, P. 88). "The twenty-seventh and twenty-eighth volumes of Crelle's Journal, published in 1844, contained twenty-five contributions by Eisenstein. These testimonials to his almost unbelievable, explosively dynamic productivity rocketed him to fame throughout the mathematical world. They dealt primarily with quadratic and cubic forms, the reciprocity theorem for cubic residues, fundamental theorems for quadratic and biquadratic residues, cyclotomy and forms of the third degree, plus some notes on elliptic and Abelian transcendentals. Gauss, to whom he had sent some of his writings, praised them very highly and looked forward with pleasure to an announced visit. In June 1844, carrying a glowing letter of recommendation from Humboldt, Eisenstein went off to see Gauss. He stayed in Göttingen fourteen days. In the course of the visit he won the high respect of the "prince of mathematicians," whom he had revered all his life. The sojourn in Göttingen was important to Eisenstein for another reason: he became friends with Moritz A. Stern-the only lasting friendship he ever made. While the two were in continual correspondence on scientific matters, even Stern proved unable to dispel the melancholy that increasingly held Eisenstein in its grip. Even the sensational recognition that came to him while he was still only a third-semester student failed to brighten Eisenstein's spirits more than fleetingly. In February 1845, at the instance of Ernst E. Kummer, who was acting on a suggestion from Jacobi (possibly inspired by Humboldt), Eisenstein was awarded an honorary doctorate in philosophy by the School of Philosophy of the University of Breslau.Eisenstein soon became the subject of legend, and the early literature about him is full of errors. His treatises were written at a time when only Gauss, Cauchy, and Dirichlet had any conception of what a completely rigorous mathematical proof was. Even a man like Jacobi often admitted that his own work sometimes lacked the necessary rigor and self-evidence of methods and proofs." (DSB)

Leipzig, B. G. Teubner, 1889. 8vo. Bound in recent full black cloth with gilt lettering to spine. In "Mathematische Annalen", Volume 34., 1889. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Very fine and clean. Pp.57-122 [Entire volume: IV, 600 pp.]. First publication of Killing's important third paper (of a total of four) in which he laid the foundation of a structure theory for Lie algebras."In particular he classified all the simple Lie algebras. His method was to associate with each simple Lie algebra a geometric structure known as a root system. He used linear transformation, to study and classify root systems, and then derived the structure of the corresponding Lie algebra from that of the root system."(Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences)Unfortunately for Killing a myth arose that his work was riddled with error, which later has been proved untrue. "As a result, many key concepts that are actually due to Killing bear names of later mathematicians, including "Cartan subalgebra", "Cartan matrix" and "Weyl group". As mathematician A. J. Coleman says, "He exhibited the characteristic equation of the Weyl group when Weyl was 3 years old and listed the orders of the Coxeter transformation 19 years before Coxeter was born."The theory of Lie groups, after the Norwegian mathematician Sophus Lie, is a structure having both algebraic and topological properties, the two being related.

Kbhvn., Udgivet af Den danske Radeerforening, 1935. 4to. Orig. bogtrykt omslag, lidt plettet. VII, 21 pp. Oplag: 500 ekspl.

New York, E. Dexter & Son, 1865. Large 4to. Contemp. hcalf. Spine gilt, but somewhat worn. Top edge gilt.Frontcover detached from spine. Engraved portrait of Washington as frontispiece. VIII,399 pp. + List of Subscribers. No. 15 of 50 copies in 4to., signed E. Dexter. (In all printed in 150 copies, 50 in 4to and 100 in 8vo.). With huge margins.

4to. Wrappers with tears and loss of back. Block loose. 803 pp. Richly illustr. Small hole in inner margin of the first 3 leaves. Internally fine and clean, unopened.

Kbhvn., 1971-74. 12 orig. hfableabd. m. smudsomslag.

London, W.Nicol, 1826. 4to. No wrappers as extracted from "Philosophical Transactions" 1826 - Part III. With titlepage to Part III.Pp. 423-482 and 3 engraved plates, of which 2 are larger and folded. A faint dampstain to margins of plates. James South " fitted up an observatory attached to his house in Blackman Street, Borough, with two equatoreals of respectively five and seven feet focal length, besides a first-rate transit instrument by Troughton Here he observed, jointly with John Frederick William Herschel, 380 double stars. In presenting him with the gold medal of the Astronomical Society in 1826, Francis Baily spoke of his ‘princely collection of instruments, such as have never yet fallen to the lot of a private individual’. In 1835 South removed his five-foot telescope to Passy, near Paris, where he came to know Humboldt and Arago, and convinced Laplace of the reality of revolving stars by ocular demonstration in the case of 70 Ophiuchi. He executed there in a few months what Herschel called ‘a noble series of measures’ on 458 compound stars, of which 160 were new ; and for these labours, together with his paper ‘On the Discordances between the Sun's observed and computed Right Ascensions,’ presented to the Royal Society on 8 June 1826 (the paper offered), was awarded the Copley medal in 1826. He was elected a member of the Royal Society in 1821.

Amsterdam, North-Holland Publ. Comp., 1967 8vo. Without wrappers (as issued). Offprint from "Nuclear Structure", 1967. Very fine and clean. 10 pp. Offprint of Aage Bohr and Mottelson's paper on Fermi Beta-decay. In 1975 the were both awarded The Nobel Prize in Physics "for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection".

Paris, L'Imprimerie Royale, 1832. Clothbacked contemp. blue boards. IX,85 pp.

Berlin, G. Reimer, 1848. 4to. Bound in contemporary shirt. "Journal für die reine und angewandte Mathematik, entire 37 Band, 1848". Fine and clean. [Neumann:] Pp. 21- [Entire issue: IV, 372 + 2 plates.]. First printing of Neumann's important exposition on reciprocal coordinates. The volume contain several other important papers by influential contemporary mathematicians such as C. G. J. Jacobi, Stern and Eisenstein.

Kiöbenhavn, Brünnich, 1812. Lille 4to. Senere hshirtbd. VIII,24 pp. samt en dobbeltsidet kobberstukket planche gengivende talrige skrifttyper. Trykt på svært skrivepapir.

Kiøbenhavn, Simon Poulsen, 1800. Smujkt nyere hldrbd. Rygforgyldning og forgyldt skindtitel på ryg. X,218,(2)pp.

Berlin, G. Reimer, 1838. 4to. In "Journal für die reine und angewandte Mathematik, 18. Band, 4 Heft, 1838". In the original printed wrappers, without backstrip. Fine and clean. [Minding:] Pp. 297-302. [Entire issue: Pp. 281-376, (2) + 1 folded plate.]. First printing of Minding's first work on the deformation of general ruled surfaces into ruled surfaces and showed that any ruled surface can be developed on another whose direction vectors form a circular cone. This was subject in which he was to make his most important discoveries. "Minding's most important discoveries were in the dilierential geometry of surfaces; in these works he brilliantly continued the researches of Gauss, which had been published in 1828. In his first paper (1830), which dealt with the isoperimetric problem of determining on a given surface the shortest closed curve surrounding a given area (on the plane it is the circumference of a circle), he introduced the concept of geodesic curvature. It was independently discovered in 1848 by O. Bonnet, and it was he who named it geodesic curvature. Minding soon proved, as did Bonnet after him, the invariance of the geodesic curvature under bending of the surface. Neither of them knew that the same results had been presented in an earlier, unpublished paper of Gauss's (1825)." (DSB).

Kjøbenhavn, P.G. Philipsen, (1840). Samtidigt hldrbd. med overdådig rygforgyldning. XIV,206,398 pp. Spredte brunpletter. Nogle læg lettere brunede.

Lancaster, American Institute of Physics, 1953. Lex8vo. Volume 89, January 15, No. 2, 1953 of "The Physical Review", Second Series. Entire volume offered in the original blue wrappers with previous owner´s stamps to front wrapper. A fine and clean copy. Pp. 472-73. [Entire issue: Pp. 343-530]. First publication of Dicke's influential paper in which the "Dicke Effect" is presented for the first time."He [Dicke] contributed also notably to the field of Spectroscopy and Radiative Transfer by means of predicting the phenomenon called Dicke narrowing [The Dicke Effect](aka. Collision narrowing): When the mean free path of an atom is much smaller than the wavelength of one of its radiation transitions, the atom changes velocity and direction many times during the emission or absorption of a photon. This causes an averaging over different Doppler states and results in an atomic linewidth that is much narrower than the Doppler width." (Basu, Encyclopaedic Dictionary of Astrophysics, 2007, p. 91.)

Berlin, Kiepenheuer, 1930. Both vols. in orig. printed wrappers. Wrappers a bit frayed in outer margins. A small cornerpiece lost on Heft 1. - 36 pp. a. (45-) 148 pp. (complete). First edition. (Brecht Versuche 1-3 u. 4-7 = Heft 1-2).

Coloniæ Agrippinæ, 1702. 12mo. Cont.full vellum. Engr.title, 410 pp. + Index.

(København), A.P. Liunge, 1838. Lille 8vo. Orig. papbd. med permer af rosafarvet glanspapir. Den forgyldte rygtitel bevaret, dog med små tab. Helt guldsnit. Halvtitelbladet: Nytaarsgave for 1838. X,216 pp. Spredte brunplatter. Originaludgaven af Carit Etlars romandebut.

Breslau, 1824. 2 cont.hcalf. VIII, 400, 380 pp. St.o.t.

Paris, Valenciennes, Labady, ca. 1760. Uncut in original marbled stiff wrappers. Stamp on title-page. (4),228,(2) pp. Clean and fine.

Amsterdam, Barthelemy Foppens, 1700. 8vo. In contemporary floral printed wrappers. Extremities with wear. Internally very nice and clean. Printed on good paper. Copperplate vignettes to each of the six chapters. (22), 322, (2) 325-556, (28) pp. Wanting the frontispiece.

Leipzig, B. G. Teubner, 1886. 8vo. Bound in recent full black cloth with gilt lettering to spine. In "Mathematische Annalen", Volume 26., 1886. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. With a marginal tear affecting pp. 275-282 and 2 cm of the text, otherwise very fine and clean. Pp. 275-299. [Entire volume: IV, 606 pp.]. First printing of Bacharach's paper which gave the final solution to what later was to be known as the Cayley-Bacharach Theorem: That when a plane curve of degree r is drawn through the mn points common to two curves of degrees m and n (both less than r), these do not count for mn conditions in the determination of the curve but for mn reduced by (m + n - r - 1) (m + n - r - 2)."Cayley wrote copiously on analytical geometry, touching on almost every topic then under discussion. Although, as explained elsewhere, he never wrote a textbook on the subject, substantial parts of Salmon’s Higher Plane Curves are due to him; and without his work many texts of the period, such as those by Clebsch and Frost, would have been considerably reduced in size. One of Cayley’s earliest papers contains evidence of his great talent for the analytical geometry of curves and surfaces, in the form of what was often known as Cayley’s intersection theorem (C. M. P., I, no. 5 [1843], 25-27). There Cayley gave an almost complete proof (to be supplemented by Bacharach, in Mathematische Annalen, 26 [1886], 275-299)" (DSB).

(Berlin, Georg Reimer, 1830) 4to. As extracted, without backstip. In ""Journal für die reine und angewandte Mathematik", 5 band. Fine and clean. Pp. 113-32. First printing. In the 1820s, yet another pupil of Gauss, August Ferdinand Mobius (1790-1868), also developed an interest in geometrical optics, but the papers that he devoted to the subject were also very much part of the eighteenth-century tradition of dioptrics and catoptrics. Taking the basics of this kind of optics for granted, he concentrated on the simplification of the calculations involved [The present paper]. (Atzema "ALL PHENOMENA OF LIGHT THAT DEPEND ON MATHEMATICS").

Stuttgart, W. Kohlhammer, 1907-09. Lex8vo. Contemp. full cloth. Titlelabel in leather with gilt lettering. VIII,220;(6),242 pp. Internally clean and fine.

Uddevalla, 1972-86. Ialt 15 bind.