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.

INDEX.

Abel, 72 *, 74n*, 140, 253.
abs I = absolute amount, 10, = mod.
absolute amount, 9, 113.,, convergence, 73, 121, 138, 290.
addition, 1, 10.,, [fundamental proposition of,, of infinite series, 73, 121.,,. [theorem of
additive constant, 48, 172, c. 256-7, 317.
algebraic curve, 103, 207, 377.,, equation, 153, 374-5.,, expression, 155, 375.,, Ifunction, 20,102,154, 350, 363.,, integrals, 168, 207., operations, 153.
sum, 10, 32, 73, c. 67.
algebraically, 30, 75., infinite, 257, 312.,, [vanish
along a curve or path, [analytic,,,, [continuous,,,, [given,,,, integral, [singular
altered values of integrable function,
244, 257, 314.
alternate signs in series, 80,122, 220,263.
alternation of increase and decrease,
40, 170, 184, 322.
ambiguity, 18,113, 144, s. many-valued.
ambiguous function, 19, 363.,, integral, 329, 372.
amount, [absolute
amplitude, 113.
analytic along a curve, 158.,, functions, 141, 145-8n, 321,327., [generally, property, 141, 143, 329-31.,, without exception, 141n, 327,
329, 341-3.
analytical expression of unique function, 343, 366.,, investigation, 23, 127, 304,
364.
angles in curves, 43, 144, 323.
angular quantity or magnitude, 20.
applicability of Taylor's theorem, 85,
341, 363.
applications of arithmetic, 111.
approximate discontinuously, 17.,, infinitely, 16.

approximation, [arbitrarily close, rational,, to a figure, 24, 86.,,,,,, number, 7, 153.,,,,, position, 42.,,,, value, 52, 67.
arbitrarily close approximation, 9, 20,
(= quam proxime, 11, 248)., great or large, 12, 17, 29,44.,, many, 9, 181, 239.,, small or little, 8, 9, 34, 149.
arc taken positively, 313, c. circuit.
area, 21, 128, 179, 297, 303, 313.
Argand, 112n*, 113, 153n*.
argument, 19, 125, 129.,, Cauchy's usage of term, 113.
arithmetical operations, 1, 8, 67, 111,
128, 143, 321, 350.
Aronhold, 207*, 208.
arrangement of factors, 67, 290.,,,, summands, 123, 146.
ascending positive integer powers, 145.,, powers, 84, 381.,, series, 368.
assignable, 10, 22, 30, 258.
assigned, 8, 9, 27, 97.
assumes a value, 30, 174, 239, 251, 297.
asymptotes, 107, 206.
at infinity, 127, 130, 148n, 206-8, 355-7,
374.
Atkinson, 391n.
ausserwesentlich, 148 n.
axes of conics, 206, 217.,,,, coordinates, 24, 87, 113, 294; 382.
Baltzer, 2n*.
bank, 134, 162, 334.
base of exponential or power, 6, 53, 118.,,,, logarithm, 13, 120.,,,, volume, 60, 296.
behaves regularly, 130, 355-6.
below any assignable limit, 27, 89, 170,
289.
Bernoulli, James, 18011.
Bernoulli, John, 19n1*, 180n1*, 186n*.
beyond all limits, 9, 96, 107, 127, 136.,, any finite amount, 39, 124, 126.
binomial coefficients, 50, 62, 99.,, integral, 197-9, 236, 284.,, series, 79, 139n, 347.,, theorem, 50, 377.