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.

400

Index.

linearly discontinuous function, 247; c.
296, 307-8, 311.
Liouville, 349 n*.
Lipschitz, 14 n.
logarithm, 13, 83, 119, 136, 334.
differentiated, 54, 63, 145.
logarithmic branching point, 372, c.
136-7, 346-7.,, differentiation, 55.,, integral, 234, 262, 287n.,, operation, 151-2, 157.
series, 81, 139n, 346.
logarithmically infinite, 207, 307, 355.
loop, 350-1.
Machin, 84n.
Mac Laurin, 69n*, 99, 292.
many-valued function, 19, 22, 128, 131,
145; n-valued, 154,363.,, point, 163.
many-elementary point, 379, k-, 378-9.
Mascheroni, 293 n*.
mass of points, 244-6, 296.
maxima and minima, 35, 244-7, 254-6,
309, c. oscillate.
maximum value, 31, 80.
mean value, 33, 263, 282, 286-7, 319.,,,, [theorem of the
meaning, 3, 92, 105, 111, 257, 259, 298.
measure of change of function, 33, 40.
measurement of surface, 179n, 296n.
mechanical, 42-3, 60.
Mercator, N., 81n*.
Meyer, 93 n*.
Minding, 235 n.
minima, 89, 159, 184,.361-2'
mixed differential coefficients, 94, 320.
Mobius, 128 n*.
mod [] = modulus of complex, 129,-=abs.
modulus of complex, 113-30,166,322,328.,, elliptic integral, 216, 230.
Moigno, 272 n*.
monotropic, 128.
motion, 1, 15, 42-3, 46.
multipartite boundary, 366-7.
multiple, 2, 20, 113.,, integrals, 296n, 304.,, point, 105, 364, 379-80.,, root, 156-7, 188-93, 348, 363,
380, 385.
multiplication, 2, 67-n, 115.,, of infinite series, 124,
230.
multiplicity, 244, 311, 386-7.
multiply connected, 318n, 320, 327-9,
352.
mutually unique relation, 184.
natural logarithms, 53, 55, 83.,, series of numbers, 1.
nature, 1, 3, 4, 16, 46, s. physical.
negative circuit, 338-9, 342.,, numbers, 3, 6, 21, 49.,, sign, 6.

neighbourhood of a branching point,
364-73.
~,,,,, line, 308, c. 331.
7,,,,, point, 26, 87, 129,
158, 244, 348.
neighbouring points or values, 31, 93,
106, 248, 358.
net, 86, 294, 297, 303.
Newton, 11, 15, 43W-i*, 71n, 80in,
180n, 380-n*.
Nicolai, 293 n*.
non-essential infinity point, 155-6.,, singular point, 130-1,148 n,
156,331-3,354.,,,,,, and branching
point, 340,372.
singularity, 130, 168, 342.
norm, 116.
normal elliptic integrals, 212-8, 232.,, to boundary curve, 313.
not convergent, 69, 80-2, 138, 222, 234,
345, s. divergent.,, integrable, 227, 247, 258, 262, 277,
309.
notation, 39, 42, 58, 176, 349.
Nother, 378n*, 380n1.
nullitude, 149, 151, 153, 261-2, 309.
nullity, 149, 261.
number as a limiting value, 9, 16, 118.,, [complex,, in a closed form, 8, c. 16.,, in the abstract, 3, 111.,, [irrational, of a given logarithm, 13,22,288., [pure
numbers, [real
numerical conception, 2, 4, 16, 120.,, equations, 153.,, values, 8, 22.
numerically greatest, 75, 79, 219.
odd functions, 85.
Oldenburg, 380n.
one-valued, 19, 25, 29, 87, 128, 139,
s. unique.
operation, [logarithmic
operations, [algebraic
-,, [arithmetical,, of the calculus, 23.
order, 2, 73, 121-3, c. arrangement,
succession.,, of algebraic expression, form,
function, 151, 15t, 375, c.
degree.,,,, becoming infinite, 130, 257-8,
269, 369.,,,,,, infinitely small, 34 n,
59, 279, 285, 309.,,,, branching point, 378.,,,, contact, 377-8.,,,, derivates, 85, 369.,,, differentiations, 95-6.,,,, integrations, 270, 300.,,, multiple point, 379.