The Liverpool Standard and General Commercial Advertiser.
Liverpool, Merseyside, England, 1833-08-27 00:00:00

" We have to notice these excellent productions, as clear
guides to the higher branches of science. They do infinity
credit to Mr. Young; and no works of the same class can be
ore ti: to be put into the hands of students."--Literary Ga-
its, May 28, -1831. -
VII. 14.:LEMENTS OF THE DIFFERENTIAL CAL-
CULUS; comprehending the General Theory of Curve Sur-
faces and of Curves of Double CurVature. Bs. in cloth.

The work is divided into three sections, and each section
is subdivided into chapters of a moderate length. The first
section treats of the differentiation of functions in general;
the second contains the application of the differential calculus
to the theory of plane curves ; and the third unfolds the gene-
ral theory of curve surfaces and of curves of double curvature.
In the first the author introduces the most valuable theorems
and formulw of the celebrated analysts, Euler, Lagrange, De-
moivre, and Cotes. In the second, he have given a correct ex-
planation 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 pub-
lished.

" But the work does not merit attention merely on account
of arrangement, and the judicious selection which it contains
frdiu the writings of others. It has also claims to originality.
What the author has adopted from' other writers, he has ren-
dered much more simple. The chapter on maxima and minima
presents considerable improvements in various parts of the in-
vestigation. In surveying the cases in which Taylor's theorem
fails, Mr. Young has shown that it does not fail where the
coelEcients become imaginary, as is asserted by Lacroix
and his folloWers, but that these failing cases are always indi-
cated by the co-efficients becoming infinite. In one of the pro•
blenis on this subject he has detected a false solution by La-
grange, which has been transcribed by Gamier' and severa
others, merely on the faith of a great name. * * *
" The whole Elements of the Differential Calculus, com-
preliending alt that is most valuable in the large works of the
most celebrated Analysts are contained in a duodecimo volume,
beautifully printed on a tine paper and neatly bound in cloth.
It aupears to be in every respect well fitted for a Class Book,
and-eau scarcely fail to be very generally adopted."—Presby-
terian 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
au elementary treatise, there is a perspicuity, a unity of me-
thod prevailing in all its parts, that renders it more than any
book we have seen peculiary adapted to instruction.
It is not, however, as an elegant and perspicuous develope-
ment of the first principles of the Calculus, merely, that we have
win-fired, and therefore recommended Mr. Young's lithe work;
we have alio found much to commend in it of a more profound
character; much that we look for iu vain in larger works, and
indeed in all English books. '
"The paralogisms of some other writers, distinguished ones
too, are pointed out in the preface, and in the body of the 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 anybody else till now ; and we look
upon the aptitude displayed in these detections to be highly
characteristic of a mind which looks with a laudable anxiety to
the purity of the fundarnentat pinicipies of scieuce."—l'hiioso-
phical,bagazine, October, leGi.
VIII. ELEMENTS OF THE INTEGRAL CALCULUS;
with its applications to Geornetiy, and to the Summation of In-
finite Series, &c.. 9s. in cloth.
" The voiume before us forms the third of an Analytical
Course, which commences with the 'ELEMENTS OF AN A L Y.FICAL •
GEOMETRY.' More eiegant 'Text-books do pot exist in the
English Language, and we trust they will speedily be adopted
in our Mathematical Seminaries. The existence of such auxi-
liaries will, of itself, we hope, prove au inducement to the culti-
vation of Analytical Science; for, to the want of such Elemen-
tary Works, the indifference hitherto manifested in this country
on 'the subject is, we apprehend, chiefly to be ascribed. Mr.
Young has brought the science within the reach of every intelli-
gent student, and, in so doing, has contributed to the advance-
ment of Mathematical Learnaig in Great Britaiu."—Presiry-
terian Review, January, 1832.
" We remember the time when such a work as this would
have been invaluable, and we do not think that any late publi-
cation has superseded the necessity of it."—Spectatar, Septem-
ber, 21, 1831.
ELEMENTS OF I\l ECHANICS; comprehending the
Theory of Equilibrium and of Motion, and the rirst Principles
of Physical ilstronomv, together with a variety of Statical and
Dynamical Problems, illustrated by numerous Engravings; by
J. R. Young. Ills. 6s. iu cloth.
" Young is already favourably known to the public by
his writings; and the Treatise on 11Iechanics,"•which we now
propose, briefly to notice, wilfadd Considerably to his reputation
as tire author of elementary works of science.
"TO"- tead'the works of Laplace, Ivory, Somerville, &c. a
kncwiedge of the methods employed by these writers is previ-
ously required, and renders such preparatory works as those
of Mr. Voting. absolutely ueeessary.''—Presoyterian
Jul Y-1832-
Published by J. Souter, 73, St. Paul's Church-yard, London;
sold. by Parker and Co.; Oxford ; F. Johnson, Cambridge ;
White and Co., EdinL:l:-.:17 W. Jackson. New 1 ork ; Mid
by ail other booksellers.