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. XVii
ARTICLE PAGE
354. To find the greatest quadrilateral figure that can be formed
by four given straight lines taken in a given order........ 497
355. Of all spherical triangles upon the same base and having
equal perpendiculars, to find that which has the greatest
vertical angle................................. 498
356. To determine the greatest curvilineal figure of a given
species which can be described in, and the least which can
be described about, anothei given curvilineal figure....... 499
357. To draw a tangent to a curve defined by an equation
between two straight lines drawn to two given points. 502
358. To draw a tangent to a curve defined by an equation
between a rectilineal ordinate and a curvilineal abscissa... 503
359. To draw a common tangent to two curves defined by
given equations........................................ 504
360. To find the locus of the intersection of the tangent with
the perpendicular, drawn upon it from the origin, in any
curve................................ 506
363. To find the locus of the intersection of two tangents drawn
to a curve after some determinate law................... 508
364. To determine the nature of a curve which shall always
touch any number of straight lines drawn after a given law 510
365. To determine the nature of the curve which shall always
touch any number of curves of a given species, described
according to a given law............................ 513
366. To find the length of the evolute of any proposed part of
a curve whose equation is given...................... 514
367. In a polar curve to find the locus of the point of intersecsection of the tangent by the perpendicular, let fall upon it
from the pole.......................................... 515
371. To find the locus of the point of intersection of the polar
subtangent and tangent.................................518
372. To express the cosine of the multiple of an arc in descending powers of the cosine of the are itself................. 518
373. To find the content of the greatest parallelopiped that
can be inscribed in a given ellipsoid.................. 519
374. To find when the volume of the pyramid, formed by the
tangent plane to a curve surface, and the three co-ordinate
planes, is the least possible............................ 50
C