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

xii SUMMARY.
ARTICLE PAGI
163. To investigate the nature and circumstances of the contact
subsisting between a circle and a given curve............. 227
165. To find the nature and circumstances of the contact subsisting between a proposed curve and a parabolic curve of
any order......2.................................... 229
167. To ascertain generally the nature and circumstances of
the contact subsisting between any proposed curve, and
a curve of the second order............................ 231
170. If the contact between two curves be of an odd order,
they have only contact at the point of concourse, but
if it be of an even order, they have both contact and intersection.......................................... 233
176. To find expressions for determining the radius of curvature
of any proposed curve, and also the chords of curvature
parallel to the co-ordinate axes........................ 236
184. To find the equation to the curve which is the locus of the
centres of the osculating circles at the different points of a
curve............................. 2
185. The radius of the osculating circle at any point of a curve
is a tangent at the corresponding point of its evolute..... 255
186. The radius of the osculating circle of a curve varies by the
same differences as the corresponding arc of its evolute.. 257
CHAP. IX.
Tangents, 8-c. to Curves referred to polar Co-ordinates.
190. General Introduction to the subject..................... 262
191. To find the angle which a straight line, cutting a spiral in
two points, makes with the radius vector................. 263
192. To find the angle in which a straight line, touching a spiral,
cuts the radius vector................................. 264
196. To find the magnitude of the subtangent, and to draw
a tangent to a spiral.......................... 267
199. To find the magnitude of the subnormal, and to draw
a normal to a spiral................................ 269
200. To find whether a spiral admits of a rectilineal asymptote,
and to determine its position..................... 270