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. xi
ARTICLE PAGIK
du
112. To determine whether all the roots of the equation d- = 0,
necessarily render the function u either a maximum or
a minimum........................................ 157
CHAP. VIII.
Tangents, 8yc. to Curves referred to rectangular Co-ordinates.
126. General Introduction to the subject............... 180
128. To find the angles which a right line, cutting a curve in
two points, makes with the co-ordinate axes.............. 182
129. To find the angles which a right line, touching a curve at
any point, makes with the co-ordinate axes.............. 183
133. To find the angles in which a curve intersects the co-ordinate axes................................ 187
134. To find the rectilineal angle in which two given curves
intersect each other................................... 189
135. To determine the points in which the tangent to a curve
intersects the co-ordinate axes.................... 191
140. To find the equation to the tangent at any point of a proposed curve........................................ 200
143. To find the equation to the tangent of a proposed curve,
which shall make given angles with the axes.......... 202
144. To find the equation to the tangent of a proposed curve,
which shall pass through a given point.................. 203
145. To find the points in which the normal to a proposed curve
intersects the co-ordinate axes........................... 204
148. To find the equation to the normal at any point of a proposed curve......................................... 208
151. To find whether a proposed curve admits of a rectilineal
asymptote, and to determine its position........... 210
152. To find the equation to the rectilineal asymptote of a curve 215
155. To find the position of a curve at any point with respect
to its rectilineal tangent.................. 219
159. Definitions, &c. of the Orders of Contact................. 224
162. To determine the nature and conditions of the contact subsisting between a straight line and any proposed curve.... 226