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.

401

order of set of points, 245-6.,,,summation, 297.,, vanishing, 149, 261, 309, 373.,, winding surface, 162-3, 364.
origin or point zero, 15, 334, 338.
oscillate, 17, arbitrarily (infinitely) often
in region of a point, 30, 34-7, 69,
135, 257, 259, 261, 309, 322. c. indeterminate, infinitely many, maxima etc..
overleap, 26-7, 174, 252, 254.
parabola, 206, 208, 308, 338.
parabolic curves, 180n.
parameter, 19, 86, 321.,, of elliptic integral, 217-8.,, uunder integral sign, 264,
274,300; in the limits, 267.
part, 121, 141, 157, s. constituent.
partial derivate, 91, 314, 327, 351, 380., derived function, 90, 93, 141,
315, 317, 376., differential coefficients, 327, 3-18.,,,, quotient, 93, 143.
differentials, 92, 99.
fractions, 186, 333., integration, 233, 251., intervals, 173-4,184,242, 247,253.
partition of linear intervals, 174-5,
241-3, 247, 249, 257.,,,, superficial elements, 295,
297, 303.
parts of a domain, 149, 294.
path of complex argument, 158-62, 375.,, integration, 322-9, 332-5, 338-9.
peculiarity, 93, 155, c. irregular, singular, special.
perforated plane leaf, 133, 136, 144-5,
162, 334.
period of exponential function, 119, 136.,,,trigonometric function, 21-2,
78, 84.
periodic decimals, 8, 52.,, functions, 21, 136.
periods of algebraic integrals, 168.
physical quantities, 3, 19, 111.
n a definite number, 20, 78.,, expressed by infinite product, 278.,~,,,,,, series, 83-4.
Picard, 148n.
place in a product, 289.,,,,, series, 9-11, 16, 18,.68-9, 72,
84n, 138, 220, 242.
places, 250, 296, c. positions.
of decimals, 84n, 293-n.
plane, 86, 93-4, 112, 127, 321., leaves, 133-4.,, set of points, 296.
planes, 60, 128, 143, 161, 360.
Pliicker, 349n*.
point (or points) at infinity, 206-7., corresponds to system of values,
15, 24, 86, c. 112, 376.,, infinity, or, at infinity, 127, 130-1,
135, 156, 161-5, 332-4, 356, 374.
HARNACK, Calculus.

point [infinity,, [irregular,, [singular,, zero or origin, 85, 245, 333-4, 367.
points infinitely numerous, 24, s. set
of points.,, of discontinuity, 28-9.,,,, division, 31, 177, s. dividing
points.
polar coordinates, 113, 143, 303.
pole, 148n.
polygon, 20, 383-7.,, represents a function, 24,
35-6, 46, 86, 179-80.
polynomial, 20, 47, 153.,, theorem, 377, s. binomial.
positions, 245-6.
positive circuit, 314-5, 328, 343.,, numbers, 3, 11.
sign, 6.
positively or negatively infinite, 16,
29, 39, 50.
possible, 2-4, 6, 8, 350, 369.
power, 6, 130.,, differentiated, 49, 55, 61, 144.
power-series = infinite series of ascending positive integer powers.
prime numbers, 2, 247-8.
principle of Dirichlet, 343n.,,,, Riemanna, 296n.
problem of calculation, 23, 47, 168.,,,, integral calculus, 172, 239.
~,,,, tangents, 42, 180n.
process of continuation, 150, c. 159, 345,
351.,,,, evolution, 8.,,,, subdivision (partition) of
intervals, 26-7, 31, 174-5,
243, 295.
product, 2-6, 17, 32, 110, 115.,, [infinite,, of infinite series, 118, 124-5.,,, integrable functions,259-60,
296.,,,, simple integrals, 310-1.,, [rule of the
progressive and regressive, 34, 37-43,
55-7, 92, 103, 108, 141,
172, 323.
differential quotient, 37,
39n, 77, 169-71,224, 255.
projective geometry, 127, 206.
property of analytic function, 143, 346,
s. analytic property.,, essential point, 136, 354-5.
proper fractional rational function, 186,
355.
Puiseux, 154ln:, 380-n.
pure number, 20.
purely arithmetical, 15, 78, 244.,, imaginary, 118, 141.
quadrant, 195, 307, 313, 335-6.
quadratic equations, 104, ll0n, 388.
226