The Sun.
London, England, 1834-07-31 00:00:00

(No. 13,070

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PUBLICATIONS.

(Lisz 1.)
PROFESSOR YOUNG'S WORKS
ON THE MATHEMATICS, NAVIGATION, MENSU-
RATION, GEOMETRY, TRIGONOMETRY,
Published by J. SOUTER, School Library, 73, St. Paul's Church..
Yard, London; and sold by most respectable Booksellers.
ANALYTICAL COURSE of MATHEMATICS,
by J. R. YOUNG, Professor of Mathematics in Belfast
College.
ELEMENTS of GEOMETRY : containing a New and Univer-
sal Treatise on the Doctrine of Proportion ; together with Notes,
in which are pointed out and corrected several important Errors
that have hitherto remained unnoticed in the Writings of Geo-
meters. Bvo. Bs.
%* The following brief notices have been selected from various
Criticisms too numerous for insertion here, all speaking of Mr.
Young's Works in high terms of approbation :
" Mr. Young's Observations on the theory of parallel lines, the
labour he has bestowed on the doctrine of Proportion, as well as
his corrections of many errors of preceding geometers, and supply-
ing their defects, together with his minute attention to accuracy
throughout, may be justly considered as rendering his performance
valuable, especially to the learner.—Philosophical Magazine.
" In perspicuity, Euclid has no rival, except, perhaps, in that
part of his work which treats of Geometrical Proportion. This is
abstruse, and subtle, and intricate. The doctrine of proportion,
as connected with geometry, must necessarily be so. Hence Le-
gendre has excluded the consideration of it from his Elements,
leaving all knowledge of the subject to be acquired from numerical
proportion. This is a defect which Mr. Young has ably supplied.
Indeed, we have never seen a work so free from pretension, and of
such great merit. Various fallacies latent in the reasonings of
some celebrated mathematicians, both of ancient and modern date,
are pointed but and discussed in a tone of calm moderation, which,
we regret to say, is not always employed in the scientific world."—
'
Monthly Magazine.
" Mr. J. R. Young, who has distinguished himself as the author
of a useful elementary treatise on Algebra, has just published a
work of the same beneficial description, Elements of Geometry,'
with Notes. The great advantage which students will derive from
this work is, that the converse of every geometrical proposition
(where demonstration is possible) is given. This has never been
systematically done before. Several other improvements are intro-
duced (especially with regard to the doctrine of Proportion), and
many errors of former geometers corrected,"—Sunday Times.
AN ELEMENTARY TREATISE on ALGEBRA; Theoretical
and Practical ; with Attempts to simplify some of the more diffi-
cult Parts of the Science, particularly the Demonstration of the
Binomial Theorem, in its most general form ; the Solution of
Equations of the higher Orders; the Summation of Infinite Se-
ries, B‘c. A new Edition, greatly improved, in one vol., duode--
cimo. Price ss. 6d.
%* " A new and ingenious general method of solving Equa-
tions has been recently discovered by Messrs. H. Atkinson, Hol-
dred, and Horner, independently of each other. For the best prac-
tical view of this new method and its applications, consult the Ele-
mentary Treatise on Algebra, by Mr. J. H. Young, a work which
deserves our cordial recommendation. "—Dr. Gregory's Edition of
Hutton's Mathematics, vol. 1, p. 261.
" For the summation of infinite series the author gives a new and
ingenious method, which is very easy and extensive in its applica-
tion. "—Newcastle Magazine, November, 1825.
A TREATISE on the GENERAL THEORY and SOLUTION
of ALGEBRAICAL EQUATIONS, intended as a Supple-
mentary Volume to the Treatise on Algebra, 12m0., 7s.
*** In this volume the recently discovered method of solving
Numerical Equations by Continuous Approximation is reduced to
the utmost simplicity of form of which that method appears sus-
ceptible.
ELEMENTS of PLANE and SPHERICAL TRIGONO-
METRY, with its Application to the Principles of Navigation
and Nautical Astronomy, with the necessary Logarithmic and
Trigonometrical Tables. By J. R. YOUNG. Duodecimo.
6s. cloth, or, with the Mathematical Tables, I2s.
"* * * * These reflections have originated in a comparison
of Mr. Young's excellent treatise on Trigonometry, with some
other works that have made their appearance within the last ten or
twelve years, and a comparison of all these with the standard
works that preceded them. We have more than once taken occa-
sion to express the opinion we were led to form of this gentleman's
course of analytical mathematics ; and, though in some respects the
nature of the work itself affords less scope for the exercise of that
happy faculty which Mr. Young possesses for exposing the paralo-
gisms and supplying satisfactory solutions for the elementary diffi-
culties of science—yet in many parts we see traces of that same
peculiar attention to logical and philosophical accuracy which dis-
tinguished his former writings. The great value of this work, we
conceive, consists in its unity of p►►rpose, 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-
cess 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 brands of elementary mathematics. We
therefore think Mr. Young has done judiciously 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 two 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.
But the science, to be generally or extensively useful, must be car-
ried further, and 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 formulae, 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 LOGARITHMS. 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 Huiton's Mathematics, vol. i. p.
157, where a particular reference 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, 9s.
"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 CALCULUS ; compre-
hending 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

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THE COURT of DIRECTORS of the EAST
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