. Equations of more than one dimension in dzy Differential equations of the second order Linear equations of the mothe order Approximate integration of differential equations 248 Comparison of elliptic transcendents . Total differential equations of several variables 251 Partial differential equations of the first order Partial differential equations of superior orders . 255 Integration of partial differential equations by series . 261 Singular solutions of partial differential equations ib. . . 4, 5. APPLICATION OF THE DIFFERENTIAL AND INTEGRAL 9-11. Curves referred to polar co-ordinates . 16, 17. The contact of curves of double curvature . 28. Transformation of co-ordinates Conditions which render a curve quadrable 30. Conditions which render a curve rectifiable 32-38. Remarkable algebraical curves 4. Differences of functions of two or more variables 295 Differences of the trigonometrical lines The construction of logarithmic and trigonometrical Inverse method of differences. Integration of algebraic functions Integration of exponential functions Equations of mixed differences 23, 24. Reduction of functional equations to equations of General solution of functional equations obtained from 10, 11. The following symbols, although not original, may perhaps require explanation, as they have not yet been generally a $b is read a is not greater than b, acob . a is divisible by b, a is of the same form as b. LIST OF WORKS WHICH HAVE BEEN REFERRED TO BY INITIAL LETTERS, Leg. W. Wood, Algebra. E. Euler, Algebra. E. Add. Additions in the second edition of Euler's Algebra. F. Francour, Cours complète de Mathematiques pures. Bour. Bourdon, Algèbre. L. Lacroix, Eléments d'Algèbre. L. C. Lacroix, Compléments d'Algèbre. B. Barlow, Theory of Numbers. Leg. Legendre, Théorie des Nombres. G. Garnier, Eléments d'Algèbre. G. A. Garnier, Analyse Algèbrique. E. M. Encyclopedia Metropolitana. (In Trigonometry.) Legendre, Trigonométrie. W. Woodhouse, Trigonometry. L. Lardner, Trigonometry. Cagnoli, Trigonométrie. Hustler, Conic Sections. 36 15 52 6 98 14 119 tuo last 131 13 14 154 15 ef 195 13 21 196 1, Note 198 5, 6, Note 1995 203 11 210 5 230 14 231 3 232 6 from the bottom 244 4 after same insert time read sin B sin inscribed B, C, + B,C, COS a (sec x)2 (1-x)2 (1-x2) m in the denominator m dr-): d." 0: insert , if u = 0, read ait beach constants C2 y des=sdir rp up (72 - p2) (u?— p2) I(SER d" u. ...., not 267 last 274 6 from the bottom 288 4. 346 last ALGEBRA. Art. (1.) Definitions and Axioms. (W.47—72; &c.) (2.) Rules for addition, and subtraction. a +(6c)=a+b-c. (3.) Rules for multiplication and division, (a−b)c=ac-bc. (F.947.) The general rule for the signs both in multiplication, and division is, that like signs give a positive, and unlike, a negative, result. (4.) a"=a.a.a...... to n factors. am xa" =am+n. (1) If n is not a positive integer, the signification of an is conventional, being merely such as to satisfy equation (1). am-n=ama". 1 |