ON THE RECENT PROGRESS OF ANALYSIS. 319 



quarr6s. 0. in. 191. The demonstration referred to is founded 

 on elliptic functions. 



- Note sur les Fonctions Elliptiques. G. in. 192. 



- Suite des Notices sur les Fonctions Elliptiques. C. in. 303. 



- Suite des Notices, etc. C. in. 403. 



- Suite des Notices, etc. C. iv. 185. These notes contain theo- 

 rems stated for the most part without demonstration. Y. R 

 p. 271. 



- TJeber die Anwendung der elliptischen Transcendenten auf 

 ein bekanutes Problem der Elementar-geometrie, u. s. w. C. ill. 

 376. This paper contains a geometrical construction for the 

 addition and multiplication of elliptic integrals of the first kind. 

 A translation of the most important part appears in Liouville's 

 Journal, x. 435. V. R p. 272. 



- De Functionibus Ellipticis Commentatio. C. iv. 371. Trans- 

 formations of integrals of the second and third kinds, &c. Y. R 

 p. 288. 



- De Functionibus Ellipticis Commentatio altera. C. iv. 397. 

 We find here an elementary demonstration ofM. Jacobi's theo- 

 rem. Y. R. p. 288. 



- Note sur une nouvelle application de 1'Analyse des Fonctions 

 Elliptiques a 1'Algebre. C. vii. 41. It relates to the develop- 

 ment in continued fractions of a function of the fourth degree. 



- Notiz zu Theorie des Fonctions Elliptiques de Legendre, Troi- 

 sieme Supplement. C. vm. 413. Y. R. p. 288. 



- De Theoremate Abeliano C. ix. 99. Y. R p. 249. 



- Considerationes Generales de Transcendentibus Abelianis. 

 C. ix. 394 [1832]. This memoir lays the foundation of the 

 theory of the higher transcendents. Y. R p. 301. 



- De Functionibus Duarum Yariabilium quadrupliciter Periodi- 

 cis, &c. C. xin. 55. M. Jacobi here proves the impossibility of 

 a function of one variable being triply periodic. Y. R. p. 303. 



- De usu Theorise Integralium Ellipticorum et Integralium 

 Abelianorum in Analysi Diophantea. C. xin. 353. It is here 

 pointed out that a problem of indeterminate analysis, discussed 

 by Euler in the posthumous memoirs recently published by the 

 Academy of St Petersburg, is in effect that of the multipli- 

 cation and addition of elliptic integrals. Suggestions are made 

 as to the corresponding application that might be made of the 

 Abelian integrals. 



- Formulae novae in Theoria Transcendentium Fundamentales. 

 C. xv. 199. Elegant elementary formulae. 



