Equations of more than one dimension in dry Differential equations of the second order Total differential equations of several variables Partial differential equations of the first order Partial differential equations of superior orders. Integration of partial differential equations by series. 261 252 . 255 . ib. Reduction of functional equations to equations of 341 The following symbols, although not original, may perhaps LIST OF WORKS WHICH HAVE BEEN REFERRED TO BY INITIAL LETTERS.. W. E. E. Add. F. Bour. L. L. C. B. Leg. G. G. A. E. M. Leg. W. L. Wood, Algebra. Euler, Algebra. Additions in the second edition of Euler's Algebra. Francœur, Cours complète de Mathematiques pures. Lacroix, Eléments d' Algèbre. Lacroix, Compléments d' Algèbre. Garnier, Eléments d' Algèbre. Garnier, Analyse Algèbrique. Encyclopedia Metropolitana. (In Trigonometry.) Legendre, Trigonométrie. Woodhouse, Trigonometry. Lardner, Trigonometry. L. A. G. L. C. D. L. D. C. Tr. L. Lardner, Algebraic Geometry. Lacroix, Traitè du Calcul Differentiel, &c. Lardner, Differential Calculus. Translation of Lacroix, Differential Calculus. L. Mec. Cel. Laplace, Mécanique Céleste. ALGEBRA. Art. (1.) Definitions and Axioms. (2.) Rules for addition, and subtraction. a + (b−c)=a+b—c. a-(b-c)=a-b+c. a+(-c)=a-c. a− (−c)=a+c. (3.) Rules for multiplication and division. (a-b)c=ac-bc. (ab) (c-d)=ac-bc-ad+bd. (ab)(d)=-ad+bd. (-b)(d)=bd. (W. 47-72; &c.) (F. 94-7.) The general rule for the signs both in multiplication, and division is, that like signs give a positive, and unlike, a negative result. (4.) an=a.a.a...... to n factors. am× an=am+n. (1) (am)n = amn. If n is not a positive integer, the signification of a" is conventional, being merely such as to satisfy equation (1). - n =aman. am a = |