The Sun.
London, England, 1834-11-03 00:00:00

second, he has given a correct explanation of what the French have '
termed consecutive curves. The third contains the most beautiful
theorems of Euler, Monge, and Dupin, relative to the curvature of
surfaces in general, together with a chapter on twisted surfaces;
a subject hitherto confined to foreign writers. The whole forms a
more simple, consistent, and comprehensive view of the differential
calculus, and its various applications, than any hitherto published.
" But the work does not merit attention merely on account of
arrangement, and the judicious selections which it contains from
the writings of others. It has also claims to originality. What
the author has adopted from other writers he has rendered much
more simple. The chapter on Maxima and Minima presents con-
siderable improvements in various parts of the investigation. In
surveying the cases in which Taylor's theorem fails, Mr. Young
has shown that it does not fail where the coefficients become ima-
ginary, as is asserted by Lacroix and his followers, but that these
failing cases are always indicated by the coefficients becoming in-
finite. In one of the problems on this subject he has detected a
false solution by Lagrange, which has been transcribedby Gamier and
several others, merely on the faith of a great name. *
" The whole Elements of the Differential Calculus, comprehend-
ing all that is most valuable, in the large works of the most cele-
brated analysts, are contained in a duodecimo volume, beautifully
printed on a fine paper, and neatly bound in cloth. It appeared to
be in every respect well fitted for a class-book, and can scarcely fail
to be very generally adopted.—Presbyterian Review, Sept. 1831.
" There are no affected changes of method ; there is no parade
of original plan or of novelty of principle ; and yet there is much
original matter, much original reasoning, and, what is of more
value than all questions about originality in an elementary treatise,
there is a perspicuity, a unity of method, prevailing in all its
parts, that renders it more than any book we have seen peculiarly
adapted to instruction.
" It is not, however, as an elegant and perspicuous development
of the first principles of the Calculus merely that we have admired,
and therefore recommend Mr. Young's little work; we have also
found much to commend in it of a more profound character ; much
that we look for in vain in larger works, and indeed in all English
books.
bb4The paralogisms of some other writers (distinguished ones too,)
tmeilliNthe berly-of-thfr work ; and
many steps which have hitherto been deemed unquestionable have
been shown by Mr. Young to be altogether fallacious. We wonder
indeed, when we see them pointed out, why they did not occur to
ourselves, nor to any body else, till now ; and we look upon the
aptitude displayed in these detections to be highly characteristic of
a mind which looks with laudable anxiety to the purity of the fun-
damental principles of science. "—Philosophical Magazine, Oct. 1831.
ELEMENTS of the INTEGRAL CALCULUS ; with its Ap-
plications to Geometry, and to the Summation of Infinite Se-
ries, &c., in cloth, 9s.
" The volume before us forms the third of an Analytical Course,
which commences with the ELEMENTS OF ANALYTICAL GEO-
METRY.' More elegant text-books do not exist in the English
language, and we trust they will speedily be adopted in our Mathe-
matical Seminaries. The existence of such auxiliaries will of it-
self, we hope, prove an inducement to the cultivation of Analytical
science ; for, to the want of such elementary works, the indiffe-
rence hitherto manifested in this country on the subject is, we ap-
prehend, chiefly to be ascribed. Mr. Young has' brought the
science within the reach of every intelligent student, and, in so do-
ing, has contributed to the advancement of Mathematical Learning
in Great Britain."—Presbyterian Review.
ELEMENTS of MECHANICS ; comprehending the Theory
of Equilibrium and of Motion, and the first Principles of Physical
Astronomy ; together with a variety of Statical and Dynamical
Problems. Illustrated by numerous engravings ; cloth... 0 10 6
" Mr. Young is already favourably known to the public by his
writings ; and the Treatise on Mechanics, which we now propose
briefly to notice, will add considerably to his reputation as the
author of elementary works of science.
" To read the works of Laplace, Ivory, Somerville, &c., a know-
ledge of the methods employed by these writers is previously re-
quired, and renders such preparatory works as those of Mr. Young
absolutely necessary."—Pres. Review, July, 1832.
AN INTRODUCTORY LECTURE, delivered at the open-
ing of the Mathematical Classes, in Belfast College, by Professor
Young, price 2s.