92 Correspondence of J. Nickiés. 
produced two remarkable memoirs in transcendental analysis; 
in 1815, he published his memoir on the theory of numbers, in 
the course of which he demonstrated in full a theorem an- 
nounced by Fermat, a theorem which had hitherto been demon- 
strated only in some of its particulars by mathematicians most 
skilled in these departments, as Gauss and Legendre. The 
Academy proposed this year, as a subject for the great mathe: 
a prize,—To establish the theory of the propagation of 
waves on the surface of a heavy fluid, and of indefinite depth. 
Cede resolved the question completely. His memoir was 
crowned in 1816, and bore this epigram ‘from Virgil, ‘ Nosse 
quot lonii veniant ad littora “mao (Georgics II,) a very happy 
selection, as the line contains a complete and altogether exact 
announcement of the proposed. orbit 
uccesses so rapid and fertile for a young man of 27 years, 
assured him the first place that should become vacant in the 
ee emstical Section of the Institute. A circumstance which 
Acai rimitive designations, ‘of Académie Fran- 
aise i gabe des scriptions et Belles-Lettres, Soa. Beatie 
Arts; and carried out the new organization. In the Academy — 
ence, two celebrated names, those of Carnot and Monge, — 
of Sci 
were replaced by two new names, those of Breguet and Cauchy. 
Towards the end of 1813, Cauchy was named Adjunct Pro 
fessor of Analysis at the Polytechnic School. He became’ fall — 
Professor in 1816. He was eminently a man of duty. Call 
to instruct, he turned all his thoughts to instruction. From — 
1816 to 18 26, he published his course of Algebraic analysis, — 
Analysis _ 
Differential Caleulus, and Application of Infinitesimal 
to ee el of Curv es,—three excellent: works, well arranged, — 
with demonstrations that are both vigorous and 
in new defile, In this period he also published a memoir on : 
the Integrals taken between imaginary limits—a subject ‘ 
has ee rise to several important works among our young . 
geomet 
In 1826, he undertook the publication and authorship of aS 
iodical review, styled “Exercises Mathematiques,” in whi 
all departments of mathematics, elementary as well as transceD’ — 
ental, were treated with so much generality, fertility and i 
ventive power, that Abel, one of the profoundest analysts | 
our times, after reading one of these publications, wrote to 
friend, “Cauchy is the geometer who best understands how 
mathematics should be studied.” In fact the inventions of neW — 
methods and devices scattered through these ‘“ Exercises,” he 
been not only for the author, but also for many other geometers a 
. a 
GaN NM rsy BRE PO RS RET ate an ys 
