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

SUMMARtY.

XV

ARTICLE PAGE
301. To differentiate the volume and surface of a solid, bounded
by the co-ordinate planes and a curve surface whose equation is z =f(x, y).................................. 439
303. To investigate the analytical circumstances of the contacts
and osculations which may exist between two surfaces
defined by given equations........................... 443
307. To determine the radius of curvature of the section of a
curve surface made by a plane passing through the normal at any point..................................... 449
310. To determine the normal sections of greatest and least
curvature at any proposed point of a curve surface.... 451
312. To express the radius of curvature of any normal section,
in terms of those of the normal sections of greatest and
least curvature..4.................................. 452
315. To express the radius of curvature of the section of a
surface, made by any plane, in terms of the greatest and
least radii of curvature belonging to the same point... 454
317. To find the equation of a normal plane to a curve surface, through a point whose co-ordinates are x, y, z, the
section of the surface by this plane having dy=mdx..... 456
319. To determine a paraboloid which at its vertex shall
osculate with a proposed surface at a given point...... 458
321. To find the directions on a curve surface in which the
consecutive normals may intersect each other....... 459
323. Conical Surfaces and their equations...........461
327. To find the equation to the conical surface which shall
envelope another given surface...................... 465
328. Cylindrical Surfaces and their equations.............. 470
330. To find the equation to the cylindrical surface which
shall envelope a given ellipsoid....................... 473
331. Surfaces of Revolution and their equations............... 475
333. Annular Surfaces and their equations.................. 477
335. Developable Surfaces and their equation............ 480
336. Curves of Double Curvature........................... 482
337. To find the equations to the tangent at any point of a
curve of double curvature.......................... 483