THE INTRODUCTION OF THE NOTATION F(x)

EULER, LEONHARD & LAGRANGE, JOSEPH LOUIS.

Einleitung in die Analysis des Unendlichen. Aus dem Lateinischen übersetzt und mit Anmerkungen und Zusätzen begleitet von Johann Andreas Christian Michelsen. Erstes- (Drittes Buch). 3 Bde. (Bd. 3 auch mit eigenen Titel: Die Theorie der Gleichungen. Aus den Schriften der Herren Euler und de la Grange.).

Berlin, Carl Matzdorff, 1788-91. Bound in 3 nice uniform contemp. calf. Spinesgilt. Tome-and titlelabels withgiltlettering. A paperlabel pasted on top of spines. Stampson title-pages. XXIV,626,(3);VIII,578;(8),530 pp., 2 tables (one folded) and 9 double-page folded engraved plates (8+1). A bit of soiling and browning to title-page in volume 1. Volume 3 has a rather faint dampstain to the lower third of leaves, causing a bit of yellowing to some leaves in the middle of the volume. A few scattered brownspots,but clean.

Scarce first German edition of his "Introductio in analysin infinitorum" from 1748, a work by which Euler lays the foundation of modern mathematical analysis, by summarizing his numerous discoveries in infinite series, infinite products, and continued fractions, and it is here he introduces the CONCEPT OF FUNCTION by the notation F(x), and defines it as any analytical expression formed in any manner from a variable quantity and constants. He includes polynomials, power series, and logarithmic and trigonometric expressions. He also defines a function of several variables. - "Euler's book is one of the few books on mathematics that is mentioned by John Carter and Percy H. Muir in their Printing and the Mind of Man. There Euler is compared with Euclid: what Euclid did with his "Elements" for geometry, Euler did with his "Introductio" for analysis. It was by means of this textbook that analysis became an independent discipline within mathematics." (Karin Reich in "Landmark Writings in Western Mathematics").

Enestrom (Euler Archive): E 101-02 (Introductio) - Volume 3 is not listed by Enestrom, and it comprises 7 memoirs on equations, 2 by Euler and 5 by Lagrange. All 7 are first German translations as the memoirs originally appeared in Latin and French in St. Petersbourg Akad. der Wissenschaften and in Königl. Akademie der Wissenschaften zu Berlin. (Euler: translation of Enestrom E 30 (1738) and E 282 (1764)).

The 5 memoirs by Lagrange consist of his famous contributions to the theory of algebraic equations originally published in French in Königl. Akademie der Wissenschaften zu Berlin 1769-73, here in the first German translations, and among these his groundbreaking "Von der Auflösung der numerischen Gleichungen" (Sur la Résolution des Équations Numèriques 1769), where he provides methods, by examining the roots of algebraic equations, of separating the real and imaginary roots of approximating the real roots with continued fractions.
Enestrom E 101-102 (1. ed., not listing vol. 3) - PMM: 196 (Introductio).

Order-nr.: 51419