An introduction to the study of the elements of the differential and integral calculus. From the German of the late Axel Harnack, With the permission of the author.

402

Index.

quadrature, 179n, 296n.
quotients, 2, 17-8, 32-3, 115.,, [differential, indeterminate, 5, 21-2, 28,
105-9.,, of differences, 33-8, 60, 140,
158, 169, 222-4.
radical, 8, 214, 365, 369, s. root.
radius of convergency, 138,146,150,361-2.
ramification, 379., (branching point) 132,
363-4, 369, 371.
ramify, 388.
range, 6, 125, 194.
rapid convergence, 84.
ratio of two complexes, 158.,,.,, infinitesimals, 59, 258n.
rational algebraic functions, 49, 67,
186, 341-2, 373.,, approximations, 12, 67, c. 118.,, form, 8, 197, 209.,, functions, 129-31, 148n, 154,
355-7.,, integer function, 74n, c. 357 n.,, integral, 196, 206, 233.,, numbers, 5-15, 216, 383.,,,, used to express irrational, 12, 118, 153.
rationalisation, 196, 200.
real integral, 182, 322, 326.,, linear substitution, 212.,, numbers, 14, 19, 111, 125.
reality, 111.
reciprocal, 22, 118, 128, 354, s. inversion, substitution.
rectangle, 86-7, 294, 297, 299, 306-8,
310-1, 316-8.
rectangular coordinates, 24, 35, 86,
112, 128, 291, 382.
rectification of conics, 209n, 217.
recurring formulas, 63, 85, 231, 349,
361.,,,, of integration, 193,
200-5, 210, 236.
reducible form, 154, 351, 376.
reduction-of double integral to simple
along the boundary, 311.,,,, simple integrals, 183-5,
196, 198-217.
region, 25-7, 87, 90, 99, 149, 182, 297,
308, 328, 358, 361.
regressive, 76, s. progressive.
regular domain, 350, 364, 366.,, [function,, points, 130-1, 156, 158, 161,
163, 348-51, 376, 380.
relation, s. connexion between functions.
relatively prime, 2, 6, 116-7, 197.
remainder, 2.,, of series, 51, 69, 85, 219-27.,.,, Taylor's series, 70, 100.
remarkable points of a function, 33.
representation, 1, 24, 111, 127, 161.

representative point, 156.
resolution, 294, s. partition.,, into factors, 151, 351, 375.,,,, partial fractions, 187.
restrictedly continuous variable, 126.
resultant, 154n, 156.
Riemann, B., 46, 124n*, 128n11, 133,
141n, 161, 239-n*, 248-n*, 258n*-n,
311n*, 3221n*, 326, 374n*.
Riemann's surface, 134-5, 163, 364,,, theorem, 247, 296n.
right line, 15, 24, 36, 125, 206, s. line.
ring surface, 126, 294, 306, 329, 342.
Rolle, 41n.
root of a number, 6-8, 11, 110, 116-7.,,,,,, variable, 55, 347, s. radical.,,,, an algebraic equation, 52n, 153,
186, s. vanishing point or
value.,,,,,, algebraic equation, s. implicit algebraic function.
Rouquet, 108 n*.
rotation, 21, 42, 113, 313, 383.
rule of the product, 62-3.
rules of differentiation, 47-9, 54-5.,,,, integration, 183.,, signs, 4.
Salomon, 280n1, 2811*.
Schellbach, 217 n*.
Schl6milch, 63 n*, 67n.
section, s. branching section, perforated.
sector of circle, 21, 365.
segments, 241, 246, 313.
semiconvergence, 138.
semiconvergent, 73, 123, 139-n, 228.
sense, 3, 21, 34, 39, 111-3.
separate, s. discrete, isolated.,, lines, 296.
points, 24, 172, 227, 244-n,
296, 351, 358, 375.
separation of branches, 154, 350.,,,, factors, 151.
sequence, 1, 16, 34, 289, c. succession.
series, 1, 7, s infinite series.,, [binomial,, [continuous,, [convergent,, defining a number, point or
value, 8-13, 15, 27, 31, 118.,, [lerived, = of derivates,, [divergent,, [exponential,, Llogarithmic,, not defining a number, 16, 30., of continuous functions, 74 n, 219.,,,, ffunctions, 46, c. 225, 249.,,, omoduli or absolute values,
122, 138, 336, 339.,,,, numbers, [continuous,,,,,, [discontinuous,,,,, having a limiting
value, 40, 242.,,,, points, 42, 247.