226-229 Curve in general on opposite sides of the Asymptote

230

at opposite extremities. Exceptions,

Curvilinear Asymptotes,

231-233 Linear Asymptote obtained by Expansion,

234-235 Polar Equation to Asymptote,

236

Circular Asymptotes,

PAGES.

214

215

215-216

216-218

219

219-221

221-224

224

254-257 To examine the Nature of a specified point on a Curve, 242-248

258-259 To discriminate the Species of a Cusp,

248-253

260-261

Singularities of Transcendental Curves,

254-256

264

262-263 Maclaurin's Theorem with regard to Cubics,

Points of Inflexion on a Cubic are Collinear,

256-257

257-258

CHAPTER X.

CURVATURE.

265-266 Angle of Contingence. Average Curvature,

267-268 Curvature of a Circle. Radius of Curvature,

269-271 Formula for Intrinsic Equations,

272-275 Formulae for Cartesian Equations,

276-279 Curvature at the Origin, .

280 Formula for Pedal Equations,

281-282 Formulae for Polar Curves,

301

Tangent and Normal as Axes; x and y in terms of s,

CHAPTER XI.

ENVELOPES.

PAGES.

288-293

293-294

294-297

297-298

302-303 Families of Curves; Parameter; Envelope,

The Envelope touches each of the Intersecting Mem-

bers of the Family,

304

305

General Investigation of Equation to Envelope,

306-307 Envelope of AX2+2Bλ + C = 0, .

311

311-312

312-313

313-314

315-318

308-311 Several Parameters. Indeterminate Multipliers,

Converse Problem. Given the Family and the Enve-

lope to find the Relation between the Parameters, 318-320

315-317 Nature of the Problem; Order of Procedure in

Order of Procedure for Polar Curves,

323-325 Curves of the Classes r a sin ne, r sin noa,

326 Curves of the Class = an cos no. Spirals,

APPLICATION TO THE EVALUATION OF

SINGULAR FORMS AND MAXIMA

AND MINIMA VALUES.

MAXIMA AND MINIMA-ONE INDEPENDENT VARIABLE.

343-344 Elementary Methods,

345-347 The General Problem. Definition,

348-349 Properties of Maxima and Minima Values. Criteria

for Discovery and Discrimination,

PAGES.

369-373

373

374

374

375

381-383

384-386

386-392

356-366 On the Properties of the Cycloid,

417-424

PRINCIPLES AND PROCESSES OF THE

DIFFERENTIAL CALCULUS.