An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of, by the Rev. M. O'Brien.

SUMMARY. Xiii
ARTICLE PAGE
201. To determine the position of a spiral with respect to its
pole or radius vector............................... 272
202. Definitions, &c. of the Orders of Contact................ 274
203. To find the conditions necessary that a circle may have
contact of the second order with a proposed spiral..... 276
205. To find expressions for determining the magnitude and
position of the circle of curvature to any point of a spiral,
and also the chord passing through the pole.............. 277
206. To find the equation to the evolute of a polar curve..... 278
CHAP. X.
Singular Points of Curves referred to rectangular and polar
Co-ordinates.
214. Points corresponding to evanescent ordinates............. 286
215. Points corresponding to infinite ordinates......... 288
216. Points corresponding to equal ordinates................. 290
217. Points corresponding to maximum and minimum ordinates 292
218. Points of Inflexion or Contrary Flexure............. 295
226. Isolated or Conjugate Points.......................... 308
229. Points of maximum and minimum curvature............. 312
231. Points in which two or more branches intersect each other 316
234, To determine the multiple points of a curve formed by the
intersections of its different branches..................... 320
235. Points in which two or more branches touch each other... 325
236. To determine the multiple points of a curve formed by the
contacts of its different branches........................ 326
238. Points of Reflexion, commonly called Cusps............. 327
243. To determine the nature of any proposed point of a curve
whose equation is given............................ 336
251. To find whether a polar curve has a point of Inflexion,
and to determine its position.......................... 342
CHAP. XI.
Tracing or Describing of Curves referred to rectangular and polar
Co-ordinates.
252. A variety of Curves traced or described...................0. 344