determinatio attractionis quam punctum quodvis di gauss carl friedrich (3 risultati)

(23,5 x 19,5 cm). SS. 21-48. Moderner Halblederband. (Aus: Commentationes Societatis Regiae Scientiarum Gottingensis). Erste Ausgabe seiner fundamentalen Arbeit über die von einem Planeten ausgeübten Säkularstörungen der Planetenbahnen, "in dem sich u.a. die bekannte G(auss)sche Methode zur Berechnung elliptischer Integrale mit Hilfe des arithmetisch-geometrischen Mittels findet" (NDB 6, 105). - Titel mit gelöschtem Stempel und angesetztem rechten Rand (ohne Textverlust), sonst sauber und gut erhalten. - DSB 5, 302; Poggendorff I, 855; Merzbach 1820b.

Leatherbound. Condizione: NEW. Leather Binding on Spine and Corners with Golden leaf printing on spine. Bound in genuine leather with Satin ribbon page markers and Spine with raised gilt bands. A perfect gift for your loved ones. Reprinted from 1818 edition. NO changes have been made to the original text. This is NOT a retyped or an ocr'd reprint. Illustrations, Index, if any, are included in black and white. Each page is checked manually before printing. As this print on demand book is reprinted from a very old book, there could be some missing or flawed pages, but we always try to make the book as complete as possible. Fold-outs, if any, are not part of the book. If the original book was published in multiple volumes then this reprint is of only one volume, not the whole set and contains approximately 36 pages. IF YOU WISH TO ORDER PARTICULAR VOLUME OR ALL THE VOLUMES YOU CAN CONTACT US. Resized as per current standards. Sewing binding for longer life, where the book block is actually sewn (smythe sewn/section sewn) with thread before binding which results in a more durable type of binding. Language: Latin.

PLANETARY ORBITS AND ELLIPTIC FUNCTION THEORY. First edition, very rare separately-paginated offprint, preceding the journal appearance in Commentationes Societatis Regiae Scientiarum Gottingensis (vol. 4, pp. 21-48) by two years."In his first years at Göttingen, Gauss experienced a second upsurge of ideas and publications in various fields of mathematics. Among the latter were several notable papers inspired by his work on the tiny planet Pallas, perturbed by Jupiter [including] Determinatio attractionis quam in punctum quodvis positionis datae exerceret planeta si eius massa per totam orbitam ratione temporis quo singulae partes describuntur uniformiter esset dispertita (1818)" (DSB). In this paper, Gauss's last important contribution to theoretical astronomy, he showed "that the secular variations which the elements of the orbit of a planet would experience from another planet which disturbs it are the same as if the mass of the disturbing planet were distributed in an elliptic ring coincident with its orbit, in such a manner that equal masses of the ring would correspond to portions of the orbit described in equal times" (Dunnington, p. 111). (The 'secular variations' are those which occur over a period of time that is long compared to the orbital period of the planet; the 'elements' of the orbit are the parameters which determine it, such as its eccentricity the extent to which it differs from a circle and the inclination of the orbit to the plane of the ecliptic.) Gauss showed thatthe attraction caused by such a 'Gaussian ring' could be expressed in terms of elliptic integrals, and he related the evaluation of these integrals to the 'arithmetic-geometric mean' (see below). "In a letter, dated April 16, 1816, to a friend, H. C. Schumacher, Gauss confided that he discovered the arithmetic-geometric mean in 1791 at the age of 14. At about the age of 22 or 23, Gauss wrote a long paper describing his many discoveries on the arithmetic-geometric mean. However, this work, like many others by Gauss, was not published until after his death Gauss obviously attached considerable importance to his findings on the arithmetic-geometric mean, for several of the entries in his diary, in particular, from the years 1799 to 1800, pertain to the arithmetic-geometric mean" (Almkvist & Berndt, p. 586). Determinatio attractionis was the only work Gauss published on elliptic integrals, although much more remained in manuscript and was published after his death (this showed that he had anticipated some of the later work of Abel and Jacobi in this field). It perfectly illustrates the great breadth of Gauss's interests and expertise, combining as it does studies in both pure and applied mathematics: Gauss did not recognise the barrier between these two disciplines that exists today. "In 1813 on a single sheet appear notes relating to parallel lines, declinations of stars, number theory, imaginaries, the theory of colors, and prisms" (DSB). No copy of the offprint listed on ABPC/RBH. Already well known for contributions to algebra and number theory, Gauss (1777-1855) made his dramatic entry into the astronomical world at the age of 24. Having graduated from the University ofGöttingensome three years earlier, he had returned to his native city of Brunswick to continue the intense mathematical studies for which the Duke of Brunswick had been supporting the precocious youth since he had been in his mid-teens. "In January 1801 Giuseppe Piazzi had briefly observed and lost a new planet [the asteroid Ceres]. During the rest of that year the astronomers vainly tried to relocate it. In September, as his Disquisitiones arithmeticaewas coming off the press, Gauss decided to take up the challenge. To it he applied both a more accurate orbit theory (based on the ellipse rather than the usual circular approximation) and improved numerical methods (based on least squares). By December the task was done, and Ceres was soon found in the predicated position. This extraordinary feat of locating a tiny, distant heavenly body from seemingly insufficient information appeared to be almost superhuman, especially since Gauss did not reveal his methods. With the Disquisitiones it established his reputation as a mathematical and scientific genius of the first order" (DSB). Just one year after the discovery of Ceres, on March 28, 1802, another new planet (asteroid) was discovered serendipitously by Wilhelm Olbers; it was later named Pallas. "By now, Gauss was aware of the fact that his assumption that these celestial bodies move in elliptical orbits was not strictly true. This was revealed by the distribution of the errors between the new observational data being steadily accumulated, and by the theoretical predictions based on the best elements that he was able to compute from those data. He rightly interpreted these perturbations as being due to the gravitational attraction of other planets particularly Jupiter, the nearest and most massive pulling Ceres and Pallas out of their otherwise elliptical paths. His first efforts to develop a new theoretical approach, which made use of some of his early mathematical researches, had to be abandoned because it gave rise to an impossibly large computational burden. An alternative involving interpolation of the perturbation function, which he developed in 1805, proved to be more tractable and became the foundation of his logically coherent and mathematically elegant theory of the motion of the celestial bodies which was ultimately published in Latin four years later [Theoria motus corporum coelestium in sectionibus conicis solem ambientium, 1809) After completing that treatise, Gauss continued working on the general theory of Pallas's perturbations and delivered a disquisition on it to the Royal Society of Sciences in Göttingen on 25 November 1810. This research presented the greater challenge to his mathematical ingenuity because Pallas's orbit was more elliptical than that of Ce.