| Properties of the Triangle | p. 1 |
| Methods of solution | p. 1 |
| Circumcentre, incentre, orthocentre, nine-point centre, polar circle | p. 4 |
| Centroid | p. 10 |
| Distance between special points | p. 15 |
| Errors | p. 20 |
| Properties of the Quadrilateral | p. 24 |
| Cyclic quadrilateral | p. 24 |
| General quadrilateral | p. 27 |
| Circumscribable quadrilateral | p. 27 |
| Equations, Sub-Multiple Angles, Inverse Functions | p. 33 |
| General solutions | p. 34 |
| Sub-multiple angles | p. 41 |
| Inverse functions | p. 46 |
| A Hyperbolic Function and Logarithmic and Exponential Functions | p. 52 |
| Area-function for rect. hyperbola | p. 52 |
| Differentiation | p. 57 |
| Addition theorem | p. 60 |
| Properties of log x and e[superscript x] | p. 63 |
| Useful inequalities | p. 67 |
| Euler's constant | p. 69 |
| Expansions in Power-Series | p. 77 |
| Convergence | p. 77 |
| Expansions of sin x and cos x | p. 79 |
| Expansion of log (1 + x) | p. 84 |
| Expansion of tan[superscript -1]x | p. 88 |
| Evaluation of [pi] | p. 89 |
| Expansion of e[superscript x] | p. 90 |
| [characters not reproducible](1 + x/n)[superscript n] | p. 93 |
| The Special Hyperbolic Functions | p. 104 |
| Definitions, sh x, ch x, th x | p. 104 |
| Formulae | p. 105 |
| Calculus applications | p. 107 |
| sh[superscript -1]x, ch[superscript -1]x, th[superscript -1]x | p. 110 |
| Projection and Finite Series | p. 118 |
| Projections and general angles | p. 118 |
| cos(A + B), sin(A + B) | p. 123 |
| [Sigma]cos[alpha + (r - 1) beta], etc. | p. 125 |
| Difference series | p. 130 |
| Complex Numbers | p. 137 |
| Definitions | p. 138 |
| Notation and manipulation | p. 140 |
| Modulus and amplitude | p. 145 |
| Use of Argand Diagram | p. 148 |
| Products and quotients | p. 150 |
| Principal values | p. 155 |
| De Moivre's Theorem and Applications | p. 162 |
| De Moivre's theorem | p. 162 |
| Principal values | p. 164 |
| Values of z[superscript p / q] | p. 165 |
| Powers and roots in Argand Diagram | p. 165 |
| Expansions of cos[superscript n theta], sin[superscript n theta] | p. 169 |
| Expansions of cos n[theta], sin n[theta], tan n[theta] | p. 172 |
| [Sigma]x[superscript r] cos r[theta], etc. | p. 174 |
| Cos n[theta], sin n[theta] / sin [theta] as polynomials in cos [theta], etc. | p. 178 |
| One-Valued Functions of a Complex Variable | p. 189 |
| Absolute convergence | p. 189 |
| Series of complex terms | p. 190 |
| Exponential series and exponential function | p. 191 |
| Modulus and amplitude of exp (z) | p. 194 |
| sin z, cos z, tan z | p. 197 |
| sh z, ch z, th z | p. 198 |
| Roots of Equations | p. 204 |
| Formation of equations | p. 204 |
| Symmetric functions of the roots | p. 206 |
| Essentially distinct roots | p. 212 |
| Factors | p. 219 |
| Algebraic functions | p. 219 |
| Trigonometric functions, sin n[theta], etc. | p. 222 |
| x[superscript 2n] - 2x[superscript n] cos n[alpha] + 1 | p. 226 |
| Comparison of series and products | p. 228 |
| Partial fractions | p. 231 |
| Many-Valued Functions of a Complex Variable | p. 241 |
| Log w | p. 241 |
| Expansion of log(1 + w) | p. 245 |
| Circle of convergence | p. 247 |
| z[superscript w] | p. 252 |
| Binomial series | p. 253 |
| Logarithms to any base | p. 253 |
| Inverse functions | p. 256 |
| Miscellaneous Relations | p. 263 |
| General identities | p. 263 |
| Conditional identities | p. 265 |
| Miscellaneous transformations | p. 268 |
| Elimination | p. 270 |
| Inequalities | p. 274 |
| Miscellaneous Examples on Chapters I-XIV | p. 278 |
| Answers | p. 285 |
| Index | p. 333 |
| Symbols | p. 336 |
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