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.

392

Index.

Bombelli, 111n.
Bonnet, 254n*.
boundary between values, 60.,, curve, 125, 297,305, 311,328.,, of a curve, 331.,,,, domain or region, 87, 150,
294, 318n, 342, 366-7.,, point, 157, 329, 352.
bounding circle or curve, 138, 367.
branch (limb) of curve, 104,309,379,380., of function, 131-5,154-63,348,364.
branched element (expansion), 380, 388.
branches connected, 364.,, [cycle of
branching, 364, 379, s. ramification.
point, 132, 162, 207,351,359.,,,, at infinity, 163, 372,,,, at a singular point,
329, 372.,,, [logarithmic,,,, [neighbourhood of a,,,, of integral, 339-40.,,,,,, logarithm, 136,
152, 346.,, section, 134, 329, 364, 375.,,,, of binomial, 347.,,,,,, logarithm, 334.
breaches of continuity, 247.
break, 16, 43, s. discontinuous.,, off, 103.
Briot and Bouquet, 141 n, 154n*, 374 n1*,
380n.
calculation, 10, 67, 288.,, by infinite series, 99, 341,
350, 352.,, of a number, 8, 51, 83-4.,,, functions, 23, 129, 321.,, with variables, 17, 43.
calculus, 23, 179n.,, [differential,, [integral
Cantor, G., 14n*, 221 n, 244 n, 246 n,, 296.
carried on continuously, 103, 375.
Cartesian, 24, 35, 86, 112-3, 206, s.
Descartes.
casual, 19.
Cauchy, 44n11, 46', 60n, 6711n, 11n,
113, 121n, 122n, 124n*, 133,
153n*-, 154n*, 258n, 272n*,
322 n*, 342.
Cauchy's theorem, 152, 342.
central conics, 217.
centre of expansion, 147, 150, 345-8.
change of values in ramification, 162-3,
363, s. interchange.,, [sudden
changed arrangement or order of terms,
73, 121-3.
changes discontinuously, 43, 128.
character of a discrete mass of points,
246.,,,,, rational function, 74n,
160.

character of an analytic function, 333,
341.,,,,, infinity point, 155,340.
circle in integration, 323, 333, 352., of convergence, 138, 145, 152,337,
346, s. convergency.,, surrounding infinity, 163, s. curve.
circles in the process of extension of
functions, 150, 159, 345-7.
circuit of branching point, 136-7, 162-4,
c. 335, 359-60, 364-5, 372.,,,, loop, 350.,, positive or negative, 314-5, c.151.
circular functions, 22-3, 54, 63, 83-5, 228.
ring, 126, 294.,, sectors, 21, 365.
circumference of circle, 126, 337, 360.
classification of functions, 19, 86, L28,
141n, 148n, 210n, 357, 373.
Clebsch, 207*.
closed at infinity, 127,,, circuit, 372.,, curve, 134-7, 161, 311, 329, 364-6.,, domain, 346.,, form, 8, 16, 153.
coefficient, [binomial,, [differential
coincident infinity points, 155, 260, 374.
combination in a complex, 112, 143.
of partitions, 175,243,295.
common logarithms, 83.
complete circuit, 364-5, 372.,, elliptic integral, 229.,, group of complex numbers,
114, 120.
completely (quite) indeterminate, 5, 30,
37, 120, 222, 238, 258-9, 262, 273, 355.
complex argument, 125, 282, 337, 345.,, domain, 129, 321, 341., function, 141, 321, 326.
integral, 323, 326.,, limiting value, 158, 322, 359.,, number, 14, 110-21.,, plane, 321.,, points, 206-7.,, quantity, 114,126,140,189,194.,, roots of equations, 153, 167,
189-93, 212-3.,,,,,, numbers, 117, 347., series, 121-5.,,,, of powers, 138-40,
145-53, 336-51.,, solutions, 104, 153.,, value, 126, 135, 167, 282.,, variable, 125-6, 333.,, [function of a
complexes, [conjugate
concentration in a point, 127, 245-6.
conception extended, 110-ln, 244.,, introduced, 4, 7, 15-7, 121n.
of infinite number of points,
244.,,,, integral, 176, 239, 258n.,, number, 9, 111.