GAUSS, CARL FRIEDRICH & NIELS HENRIK ABEL - ANNOUNCING "THE PRINCIPLE OF LEAST CONSTRAINT".

Über ein neues allgemeines Grundgesetz der Mechanik (Gauss) + (Abel:) Précis d'une théorie des fonctions elliptiques + Précis dúne théorie des fonctions elliptiques. (Suite du mémoire 19. cah. dern.). 3 Memoirs.

(Berlin, G. Reimer, 1829). 4to. No wrappers. Extracted from "Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle", Bd. 4. - Gauss' paper: pp. 232-35. - Abel's papers: pp. 236-278 and pp. 309-348.

First printing of probably Gauss' most importent work in physics by presenting his "Principle of Least Action" , which states that the motion of a system of points which are influenced both by each other and by outside conditions is such as to maximize the agreement with free motion, given the existent constraint. The work is based on his Potential Theory.
"In it (the present paper) Gauss stated that the law of least constraint: the motion of a system departs a little as possible from free motion, where departure, or constraint, is measured by the sum of products of masses times the squares of their deviations from the path of free motion. He presented it merely as a new formulation equivalent to the well-known principle of d'Alembert. This work seems obviously related to the old meditations on least aquares, but Gauss wrote to Olbers on 31 January 1829 thai it was inspired by studies of capillarity and other physical problems." (Kenneth O. May in DSB).

The two papers (first printings) by Abel (book-lenghts memoirs) are his last works - he died 1829 and they were published after his death - on the theory of "elliptic functions", the discovery of which he shared with Jacobi. In these papers he mentions also the great discoveries published in his memoir 1826 (Memoire sur une proprieté générale d'un classe très-etendu de fonctions transcendentes), which was not published until 1841.

Together with these 3 memoirs is found a paper by Alexander von Humboldt: "Über die bei verschiedenen Völkern üblichen Systeme von Zahlzeichen und über den Ursprung des Stellenwerthes in den indischen Zahlen", 1829. Pp. 205-231.

Order-nr.: 41607