Constructio Aequationum Quarundam Differentialium Quae by Euler Leonhard (1 results)

Hardcover. Condition: Very Good. No Jacket. 1st Edition. First Edition. 5 leaves, 560 pp, 15 leaves; 6 copper engravings. Contemporary 3/4-calf and marbled boards. 21.5 x 16.8 cm. Binding a little rubbed and some wear to corners. Minor rubbing to corners, edges and spine, with a little staining to binding. Very Good. Also includes papers by Heister, Hoffmann, Lavagnoli, Castroni, Clairalti, Gaubil, Leichner, Scheuchzer, et al. The title of Euler's paper, written only eight years after his first (1725) and the first of five (all mathematical) he wrote in 1733, translates as 'The transformation of certain differential equations, which do not permit the separation of variables'; it concerns the Ricatti equation. The 11th published paper in his lifetime, it is reprinted in Euler, Opera Omnia, I.22, 15-18. 'In the present article, Euler seems to be using the Nova acta eruditorum to make a kind of research announcement, probably to protect his priority on the results in [two other papers] that would not actually be published for another five years. It is hard to tell whether this article had much impact. The results, as presented here, are too sketchy for anybody else to make sense of them, and Euler's correspondence only mentions this article twice, once in a letter to D. Bernoulli in 1734 and again in a letter to the Italian mathematician and astronomer G. Poleni in 1735. In the 1730s, the word 'Constructio' in the title of this article had two close mathematical meanings when it was applied to equations. First, it meant the process of finding a formula or differential equation that describes a physical or geometrical situation. Second, it meant the process of 'constructing' or finding a solution to a differential equation. In this article, Euler uses the word in both senses' (Charles Edward Sandifer, The Early Mathematics of Leonhard Euler, 2007, p. 92). 'Euler used transcendental in his 1733 article in Nova Acta Eruditorum titled 'Constructio aequationum quarundam differentialium quae indeterminatarum separationem non admittunt': 'Now there are kinds of constructions, which can be called transcendental, which arise in solving differential equations and cannot be transformed into algebraic equations.' The above citation and translation were provided by Ed Sandifer' ('Earliest Known Uses of Some of the Words of Mathematics (T)' AOL Web page). For Euler, see A. P. Youschkevitch's article in D.S.B. IV: 467-484.