ON THE RECENT PROGRESS OF ANALYSIS. 87 
_ Jacosi. Suite des Notices sur Jes Fonctions Elliptiques.—C. iii. 303. 
_ —. Suite des Notices, &c.—C. iii. 403. 
——. Suite des Notices, ete—C. iv. 185. These notes contain theorems 
stated for the most part without demonstration. V.R. p. 56. 
-——. Ueber die Anwendung der elliptischen Transcendenten auf ein 
bekanntes Problem der Elementar-geometric, u.s. w.—C. iii. 3°76. 
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. 
» 73. 
aay De Functionibus Ellipticis Commentatio.—C. iv,371. Transforma- 
tions of integrals of the second and third kinds, &c. V. R. p. 66, 
——-. De Functionibus Ellipticis Commentatio altera.—C. vi. 397. We 
find here an elementary demonstration of M. Jacobi’s theorem. V. R. 
. 66. 
eg Note sur une nouvelle application de l’Analyse des Fonctions Ellip- 
tiques a l’Algébre.—C. vii. 41. It relates to the development in con- 
tinued fractions of a function of the fourth degree. 
--—. Notiz zu Théorie des Fonctions Elliptiques de Legendre, Troisiéme 
Supplément.—C. viii. 413. V. R. p. 67. 
——. De Theoremate Abeliano—C, ix.99. V.R.p.41. 
——. Considerationes Generales de Transcendentibus Abelianis——C. ix. 
394 [1832]. This memoir lays the foundation of the theory of the 
higher transcendents. V. R. p. 75. 
—. De Functionibus Duarum Variabilium quadrupliciter Periodicis, &c. 
—C. xiii. 55. M. Jacobi here proves the impossibility of a function of 
one yariable being triply periodic. V. R. p. 76. 
——. De usu Theorie Integralium Ellipticorum et Integralium Abeliano- 
rum in Analysi Diophantea.—C. xiii. 353. It is here pointed out that 
a problem of indeterminate analysis, discussed by Euler in the posthu- 
mous memoirs recently published by the Academy of St. Petersburg, 
is in effect that of the multiplication and addition of elliptic integrals. 
Suggestions are made as to the corresponding application that might be 
made of the Abelian integrals. 
——. Formule nove in Theorid Transcendentium Fundamentales.—C. xv. 
199. Elegant elementary formule. 
_ =. Note von der Geoditischen Linie auf einem Ellipsoid, u. s. w.— 
C. xix. 309. M. Jacobi has here announced the important discovery 
that the equation to the shortest line on an ellipsoid is expressible by 
means of Abelian integrals of the first class. As this is perhaps the first 
application made of Abelian integrals since their recognition as elements 
of analysis, I have thought it well to mention it in this place. A trans- 
} lation of the note is found in Liouville’s Journal, vi. 267. 
_-——. Demonstratio nova Theorematis Abelianii—C. xxiv. 28. V. R. 
p- 80. 
_—- Zur Theorie der elliptischen Functionen.—C. xxvi. 93. This paper 
contains series for the calculation of elliptic functions, and a table of 
the function q. 
_ -—-. Ueber die Additions-theoreme der Abelschen Integrale zweiter und 
x, ie Gattung.—C. xxx. 121. We find here some remarkable formule. 
q » R. p. 81. 
_ ——. Note sur les Fonctions Abéliennes.—C. xxx. 183. This note relates 
f principally to the fact announced in M. Jacobi’s letter to M. Hermite. 
V. L. viii. 505. 
