The Sun.
London, England, 1834-11-27 00:00:00

conceive, consists in its unity of purpose, the continuity of its plan,
and the very close attention paid to the student's power of com-
pleting the whole series of processes which are involved in the
solution of the problem under consideration. Though a suffi-
cient number of examples is always a desideratum in every
elementary book, the clear development of the whole pro-
icess is greatly more important ; but in Trigonometry examples
are so easily formed, and the results so easily verified, that
we think there is less necessity for this kind of amplifica-
tion than in any other branch of elementary mathematics. We
therefore think Mr. Young has donejudiciously in rather giving ex-
amples of completely-worked questions under each head, than in
Adding a great number of unwrought questions, merely as an exer-
cise for the student in performing operations for which has no model,
nor, to him, an intelligible rule. Having done this, we think the
number of exercises given in the present work will furnish ample
practice for the most unapt of his readers.
" Mr. Young has added a set of logarithmic and other tables :
* • we feel it proper to state that we have lately dipped into them,
at hazard, and with others of established reputation on our desk for
comparison, about Iwo hundred times, and in no one of these cases
did we detect an error.
" We hope, therefore, that the account we have been able to
offer of this unpretending work, will have the effect of calling the
attention of younger students (and still more of professional tutors)
to it, as a book eminently calculated to ensure an early intimacy
with the, practice as well as the principles of trigonometry, and of
attracting the notice of geometers generally to the curious results
that appear in the supplemental chapters, and inducing them to at-
tempt the extension of a branch of science, which apparently ad-
mits of almost unlimited cultivation."—London and Edinburgh
philosophical Magazine, November, 1833.
*" The design of this work,' as Mr. Young observes, is to
establish the theory of plane and spherical trigonometry analyti-
cally, and to present that theory in a form fitted for elementary
instruction.' * * Were nothing required in trigonometry but an
elementary knowledge of the properties of plane and spherical
triangles, then we should say, that the beautiful geometrical eluci-
dations by Dr. Simson would be sufficient to engage attention.
Butt he smote, to be generally or extensively useful, must be car-
ried furtliftnd recourse be had to analytical methods of investi-
gation, from which, in most cases, results are obtained more con-
venient for turning into actual numbers. In these respects Mr.
Young appears to have left nothing to be wished for ; having fur-
nished numerous analytical formula, and numerous examples of
their arithmetical results. The great recommendation of the work
is. its being a sure and plain guide in almost every species of trigo-
nometrical calculation. " * Mr. Young has now nearly com-
pleted a course of mathematics, which is certainly the best we pos-
sess."—The Tyne Mercury, August 27, 1833.
MATHEMATICAL TABLES; comprehending the Logarithms
of all Numbers from 1 to 36,000; also the Natural and Logarith-
mic Sines and Tangents ; computed to seven places of Decimals,
and arranged on an improved plan ; with several other Tables,
useful in Navigation and Nautical Astronomy, and in other De-
partments of Practical Mathematics. Second edition, cloth, 6s. 6d.
AN ELEMENTARY TREATISE on the COMPUTATION
of LOGARITIAMS. Intended as a Supplement to the various
Books on Algebra, 12mo. New edition, with important Addi-
tions. In the press.
See Dr. Gregory's edition of Hatton's Mathematics, vol. i. p.
157, where a particular referenee is made to this little work.
ELEMEMENTS of ANALYTICAL GEOMETRY; compre-
hending the Doctrine of the Conic Sections, and the general
Theory of Curves and Surfaces of the second Order, with a
variety of local Problems on Lines and Surfaces. Intended for
the use of Mathematical Students in Schools and Universities :
cloth, Os.
"If works like the present be introduced generally into our
schools and colleges, the Continent will not long boast of its immense
superiority over the country of Newton in every branch of modern
analytical science.—The Atlas, July 25, 1830."
" We have to notice these excellent productions, as clear guides
to the higher branches of science. They do infinite credit to Mr.
Young ; and no works of the same class can be more fit to be put
into the hands of students."—Literary Gazette, May 28, 1831.

ELEMENTS of the DIFFERENTIAL CALC FLUS ; compre-
hendinc, the General Theory of Curve Surfaces, and of Curves
of Double Curvature ; in cloth, Bs. .

" 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 function :in general; the second
contains the application of the differential calculus to the theory of
plane curves; and the third unfolds the general theory of curve
surfaces and of curves of double curvature. In the first the author
introduces the most valuable theorems and formulae of the cele-
brated analysts, Euler, Lagrange, Demoivre, and Cotes. In the
second, he has given a correct explanation of what the French have
termed consecutive curves. The third contains the most beautiful
theorems of Euler, Menge, 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 sokition by Lagrange, which hasbeen transeribeclby Gamier Ind
several others, merely on the faith of a great name. ,* *
" The whole Elements of the Differential Cale.:;,us, 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 find 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 orignsal 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 fir in 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 wo 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.