Koenig (Kōnig), Johann Samuel

(b. Büdinge, Germany, July 1712; d. Zuilenstein, near Amerongen, Netherlands, 21 August 1757)

mathematics, physics.

Koenig was the son of the theologian, philologist, and mathematician Samuel Koeing (1671–1750), who after a very active existence spent his last twenty years as a professor of oriental studies in his native city of Bern. Koenig received his first instruction in science from his father, whose enthusiasm he shared. After studying for a short time in Bern, in 1729 he attended the lectures of Frèdéric de Treytorrens in Lausanne. In 1730 he left for Basel to study under Johann l Bernoulli and, beginning in 1733, under the latter’s son Daniel as well—thus receiving the best mathematical training possible. Durng his stay of more than four years in Basel, Koenig, along with Clairaut and Maupertuis, studied the whole of mathematics, particularly Newton’s principia mathematica. Koenig was introduced to Leibniz’ philosophical system by Jakob Hermann, who returned from St. “Petersburg in 1731. He was so impressed by it that in 1735 he went to Marburg” to further his knowledge of philosophy and law under the guidance of Leibniz’ disciple Christian von Wolff.

Koenig’s first mathematical publications appeared in 1735. In 1737 he returned to Bern to compete for the chair at Lausanne left vacant by the depth of Treytorrens (the position went to Crousaz). Koenig then began to practice law in Bern and was so successful that he seriously intended to give up mathematics, which he had found something less than lucrative. First, however, he wanted to write on dynamics; two articles appeared in 1738. Before the start of the new year Koenig was in Paris, where in March 1739 Maupertuis introduced him to the marquise du Chêtelet, Voltaire’ learned friend. During the following months Koenig instructed te marquise du Chatelet in mathematics and Leibnizian philosophy. He also went to Charenton with Voltaire and the marquise to visit Réaumur, who inspired koenig to write his paper on the structure of honeycombs. On the bais of this work Koenig was named a corresponding member of the Paris Academy of Sciences. Following the break with the marquise—the result, according to René Taton, of a disagreement about money—Koenig remained in Paris for a year and a half and then settled in Bern. By this time, after repeated unsuccessful attempts, he had give up hope of obtaining a chair in Lausanne. Besides conducting his legal practice, he studied the works of Clairaut and Maupertuis, whose influence is evident in his book on the shape of the earth (1747, 1761).

In 1744 Koenig was exiled from Bern for ten years for having signed a political petition that was considered too liberal, although it was in fact very courteously written. Through the intervention of Albrecht von Haller, Koenig finally obtained a suitable position as professor of philosophy and mathematics at the University of Franeker, in the Netherlands, and had considerable success there. Under the patronage of Prince William IV of Orange he moved to The Hague in 1749 as privy councillor and librarian. He became a member of the Prussian Academy on Maupertuis’s nomination.

While still in Franeker, Koenig wrote the draft of his important essay on the principle of least action, which was directed against Maupertuis. The controversy touched off by this work, which was published in March 1751, resulted in perhaps the ugliest of all the famous scientific disputes.¹ Its principal figures were Koenig, Maupertuis, Euler, Frederick II, and Voltaire; and, as is well known, it left an unseemly stain on Euler’s otherwise untarnished escutcheon. The quarrel occupied Koenig’s last years almost completely; moreover, he had been ill for several years before it started. Koenig emerged the moral victor from this affair, in which all the great scientists of Europe—except Maupertuis and Euler—were on his side. The later finding of Kabitz² testifies to Koenig’s irreproachable character.

Koenig never married. A candid and amiable man, he was distinguished by erudition of unusual breadth even for his time. He was a member of the Paris Academy of Sciences, the Royal Prussian Academy, the Royal Society, and the Royal British Society of Sciences in Göttingen. The opinion is occasionally voiced that were it not for the controversy over the principle of least action, Koenig would be completely forgotten in the history of science. His formulation of the law (named for him) of the kinetic energy of the motion of a mass point system relative to its center of gravity³ is sufficient in itself to refute this view. According to Charles Hutton, koenig “had the character of being one of the best mathematicians of the age”. It is most regrettable that Koenig never accomplished his favorite project, publication of the correspondence between Leibniz and Johann Bernoulli.

NOTES

1. See Dictionary of Scientific Biography, IV, 471.

2. Willy Kabitz, “Ueber eine in Gotha aufgefundene Abschrift des von S. Koeing in seinem Streite mit Maupertuis und der Akademie veröffentllichten, seiner Zeit für unecht erklärten Leibnizbriefes”, in Sitzungsberichte der K. Preusischen Akademie der Wissenschaften zu Berlin,2 (1913), 632-638.

3. The law states that the kinetic energy of a system of mass points is equal to the sum of the kinetic energy of the motion of the system relative to the center of gravity and of the kinetic energy of the total mass of the system considered as a whole, which moves as the center of gravity of the system; therefore

See A. Masotti, “Sul teorema di Koenig”, in Atti dell’ Accademia pontificia dei Nuovi Lincei,85 (1932), 37-42. Koenig’s original formulation of the law can be found in “De universali principio aequilibrii et motus....”

BIBLIOGRAPHY

I. Original Works. Koenig’s writngs include Animadversinem rhetoricarum specimen subitum quod cessante Professoris rhetorices honore Academico d. 17 . Nov. 1733 propon. Ant Birrius respondente lectissimo juvene j. Sam. Koenigio, J. Sam. Bernate, philos. imprimisque mathesi sublimiori studioso (Basel, 1733); “Epistola ad geometras”, in Nova acta eruditorum (Aug. 1735), 369-373; “De nova quadam facili delineatu trajectoria, et de methodis, hue spectantibus, dissertatiuncula”, ibid. (Sept.1735), 400-411; “De centro inertiae atque gravitatis meditatiuncula prima”, ibid. (Jan. 1738), 34-48; “Demonstratio brevis theorematis Cartesiani”, ibid., p. 33; “Lettre de Paris a Berne le 29 novembre 1739 sur la constrction des alveoles des abeilles, avec quelques partifularites ltteraires”, in Journal helvetique (Apr. 1740), 353-363; and Figur der Erden bestimmt durech die Beobachtugen des Herrn von maupertuis... (Zurich, 1741; 2nd ed., 1761).

Subsequent works are De optimis Wolfianae et Newtonianae philosophiae methodis earumque consensu (Franeker, 1749; Zurich, 1752); the MS of the 2nd pt. of this history of philosophy must have been in existence at Koenig’s death but appears to have been lost; “Mémoire sur la véritable raison du défaut de la régle de Cardan dans le cas irréducible des équations du trosiéme degré et de sa bonté dans les autres”, in Histoire de I’ Académie Royale de Berlin (1749), pp. 180-192, on which see M. Cantor, Geschichte der Mathematik, 2nd ed. (Leipzig, 1901), III, 599ff.; “De universali principio aequilibrii et motus, in vi viva reperto, deque nexu inter vim vivam et actionem, utriusque minimo dissertatio”, in Nova acta eruditorum (Mar. 1751), 125-135, 162-176; Appel au publique du jugement de I’Academie royale de Berlin sur un fragment de lettre de Monsieur de Leibnitz cité par Monsieur Koenig (Leiden, 1752); Défese de I’Appel au publique (Leiden, 1752); Recueil d’écrits sur la question de la moindre action (Leiden, 1752); Maupertuisiana (Hamburg, 1753), published anonymously (see mitteilungen der Naturforschenden Gesellschaft in Bern [1850], 138); and Élémens de géométrie contenant les six premiers livres d’Euclide mis dans un nouvel ordre et á la portée de la jeunesse sous les derections de M.le prof. Koenig et revus par M. A. Kuypers (The Hague, 1758).

Miscellaneous mathematical works can be found in Feriis Groningianis. Correspondence with Haller was published by R. Wolf in Mitteilungen der Naturforschenden Gesellschaft in Bern, nos. 14 , 20, 21, 23, 29, 34, and 44 (1842-1853). A portait of Koenig by Robert Gardelle (1742) is in the possession of Dr. Emil Koenig, Reinach, Switzerland; it is reproduced in the works by E. Koenig and I. Szabò (see below). MSS and unpuplished letters are scattered in the libraries of Basel, Bern, Franeker, The Hague, Leiden, Paris, and Zurich . Two unpublished MSS, “De moribus gysatoriis”, appear to have been lost.

II. Secondary Literature. See Frieslands Hoogeschool und das Rijksathenaem zu Franeker, II, 487-491; J. H. Graf, Geschichte der Mathemtik und der Naturwissen– schaften in Bernischen landen, no. 3, pt. 1 (Bern–Basel, 1889), pp. 23-62; E. Koenig, 400 Jahre Bernburgerfamilie Koenig (Bern, 1968), pp.31-35, and Gestalten und Geschichten der Bernburger Koenig (Bern, 1972), pp. 6-8; O. Spiess, Leonhard Euler (Frauenfeld–Leipzig, 1929), pp.126 ff.; and R. Wolf, Biographien zur Kulturgeschichte der Schweiz, II (Zurich, 1858-1862), pp. 147-182.

On the principle of least action, see P. Brunet, Étude historique sur le principe de la moindre action, Actualités Scientifiques, no. 693 (Paris, 1938), with bibliography; Leonhardi Euleri opera omnia, J. O. Fleckenstein, ed., 2nd ser., V, intor. (Zurich, 1957), pp. vii-xlvi, including a bibliography by P. Brunet; and I. Szabó, “Prioritätsstreitum das Prinzip der kleinsten Aktion an der Berliner Akademie im XVIII. Jahrhundert,” in Humanismus und Technik,12 no. 3 (Oct. 1968), 115-134.

E. A. Fellmann