d G. Scheffers, _Geometrie der
Beruhrungstransformationen_, Bd. i. (Leipzig, 1896); Forsyth, _Theory
of Differential Equations, Part i., Exact Equations and Pfaff's
Problem_ (Cambridge, 1890); S. Lie, "Allgemeine Untersuchungen uber
Differentialgleichungen, die eine continuirliche endliche Gruppe
gestatten" (Memoir), _Mathem. Annal._xxv. (1885), pp. 71-151; S. Lie
und G. Scheffers, _Vorlesungen uber Differentialgleichungen mit
bekannten infinitesimalen Transformationen_ (Leipzig, 1891). A very
full bibliography is given in the book of E. v. Weber referred to;
those here named are perhaps sufficiently representative of modern
works. Of classical works may be named: Jacobi, _Vorlesungen uber
Dynamik_ (von A. Clebsch, Berlin, 1866); _Werke, Supplementband_; G
Monge, _Application de l'analyse a la geometrie_ (par M. Liouville,
Paris, 1850); J. L. Lagrange, _Lecons sur le calcul des fonctions_
(Paris, 1806), and _Theorie des fonctions analytiques_ (Paris,
Prairial, an V); G. Boole, _A Treatise on Differential Equations_
(London, 1859); and _Supplementary Volume_ (London, 1865); Darboux,
_Lecons sur la theorie generale des surfaces_, tt. i.-iv. (Paris,
1887-1896); S. Lie, _Theorie der transformationsgruppen_ ii. (on
Contact Transformations) (Leipzig, 1890).

([beta]) _Quantitative or Function Theories for Linear Equations_:--C.
Jordan, _Cours d'analyse_, t. iii. (Paris, 1896); E. Picard, _Traite
d'analyse_, tt. ii. and iii. (Paris, 1893, 1896); Fuchs, _Various
Memoirs, beginning with that in Crelle's Journal_, Bd. lxvi. p. 121;
Riemann, _Werke_, 2^r Aufl. (1892); Schlesinger, _Handbuch der Theorie
der linearen Differentialgleichungen_, Bde. i.-ii. (Leipzig,
1895-1898); Heffter, _Einleitung in die Theorie der linearen
Differentialgleichungen mit einer unabhangigen Variablen_ (Leipzig,
1894); Klein, _Vorlesungen uber lineare Differentialgleichungen der
zweiten Ordnung_ (Autographed, Gottingen, 1894); and _Vorlesungen uber
die hypergeometrische Function_ (Autographed, Gottingen, 1894);
Forsyth, _Theory of Differential Equations, Linear Equations_.

([gamma]) _Rationality Group (of Linear Differential
Equations)_:--Picard, _Traite d'Analyse_, as above, t. iii.; Vessiot,
_Annales de l'Ecole Normale_, serie III. t. ix. p. 199 (Memoir); S.
Lie, _Transformationsgruppen_, as above, iii. A connected account is
given in Schlesinger, as above, Bd. ii., erstes Theil.