310 Proceedings of the Royal Society of Edinburgh. [Sess. 
Catalan, E. (1857). 
[Note sur la question 350 (Wronski). Nouv. Annales de Math., xvi. 
pp. 416-417.] 
Catalan, under the anagrammatic signature of “ M. Ange le Tauneac,” 
points out a simplification. Having got as far as 
n \7i \ \ = 1 ^ U + + • • • 
(1 -aq«)(l -x 2 z) ... (1 -x n z) 
he merely draws attention to the fact that the denominator on the left being 
1 
= (a 0 + a-fi + a 9 z 2 + .... + a n z n )- 
there results 
«o = ( 1 + ^i 2 +X 2 22+ • • • • )(a 0 + a 1 z + a 2 z 2 + . . . +a n z n ), 
whence Wronski’s set of relations follow at once. 
This, of course, is much preferable to Brioschi’s procedure. It has to be 
noted, however, that by taking a roundabout way Brioschi came across the 
equations connecting the tf’s and the s’s.* 
LIST OF AUTHORS 
whose writings are herein dealt with. 
1853. Spottiswoode, W. . 
PAGE 
. 304 
1856. Bruno, F. F. di 
PAGE 
. 308 
1854-5. Brioschi, Fr. 
. 305 
1857. Allegret, A. . 
. 308 
1855. Faure, 
. 306 
1857. Brioschi, Fr. . 
. 308 
1855. Bruno, F. F. di 
. 307 
1857. Catalan, E. 
. 310 
* After all, it is this set of equations and the two other similar sets that are worth 
knowing, namely, 
Newton’s, a Q s r + <x 1 s r _ 1 + a 2 s r _ 2 + ... + a r -is l +ra r = 0. 
Wronski’s, Gr + Xi ft r-1 + fc$2 a r-2+ • •• +H ra 0 = 0* 
Brioschi’s, sr + «l»r-l + K2»r-a+ • • ■ Nr-lSi = T$ r . 
( Issued separately March 27, 1911.) 
