The Liverpool Standard and General Commercial Advertiser.
Liverpool, Merseyside, England, 1833-07-23 00:00:00

ANALYTICAL COURSE OF :I.I.I.THEMATICS,
BY MR. J. R. YOUNG.

I.
TTLEMENTS OF GEOMETRY ; containing a New and
B.". 1 Universal Treatise on the Doctrine of Proportion, together
with Notes, in which are pointed out and corrected several hn-
poetant Errors that have hitherto remained unnoticed in the
Writings of Geometers. Bvo. Bs.
His observations on the theory of parallel lines, the labour
he has bestowed ou 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 perform-
ance valuable, especially to the learner."—Philosophical &sena-
engine, March, 18e8.
" In the notes, which he has appended to the volume, is much
valuable matter, even for those who have advanced still further
in these studies. On the theory of parallel lines, which has not
a little perplexed geometers of alt ages, there is a very able and
elaborate commentary."—The Times, November 2, 1327.
" In perspicuity Eliclid 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 propor-
tion, es connected with f.eometry, must necessarily be so.—
Hence Legendre has excluded the consideration of it from his
,Elemcnts, leaving all knowledge of the subject to he acquired
from numerical proportion. I. his 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. yarious fallacies
latent in the reasonings of some celebrated mathematicians,
both of ancient and modern dateeare pointe out and discussed
in a tone of calm moderation, which we re et to say is not al-
ways employed in the 'smeatifie world. Monthly Magazine,
September, 15.7..
" This is a work of valuable information, the conception of a
most enlightened mind, and executed with a simplicity 'which
cannot but carry the important truths it speaks of home to the
conviction of every understanding. In the notes appended to
the work, Mr. Young endeavours to point out, in his own words,
'some remarkable errors and inconsistencies into which modern
geometers have fallen, particularly in reference to the theory of
parallel lines, and the doctrine or proportion.' This volume is
but the first part of the work. The second is to be devoted to
the Geometry of Planes and Solids, with Notes, and an Appen-
dix on the 'Symmetrical Polyedrons of Legendre. It' Mr.
Young acquits himself as successfully of the second und.ertakiug,
as he has of the one before us, he wid bestow an invaluable he.
nefit on the student."—Weekly Times, December, 1827.
" Mr. J. 11, Young, who has distinguished himself es the
author of a useful elementary treatise on Algebra, has just pub-
lished a work of the same beneficial description, Elements of
Geometry,' with Notes. The great advantage which students
will derive from this work is, thatl the converse of every geome-
trical proposition (where demonstration is possible) is given.—
This has never been systematically den:: before. Several other
improvements are introduced (especially with regard to the
doctrine of Proportion), and many errors of former geometers
corrected."—Sanday Tires.', February 10, 1828.
11. An ELEMENTARY TREATISE ON ALGEBRA,
Theoretical and Practical, with attempts to simplify some of
the more difficult Parts of the Science, particularly the Denten-
etration of the Binomial theorem, in its most general form;
the Solution of Equations of the higiier orders ; the Summation
of Infinite Series; &c., Svo. boards, 10s. 6d.
" A new and ingenious general method of solving Equations
bag been recently discovered by Messrs. H. Atkinson, Holdred,
and Horner, independently of each other. For the best prac-
tical view of this new method and its applications, consult
the. ' Elementary Treatise on Algebra,' by Mr. J. R. Young, a
work which deserves our cordial recommendation."--Dr.
Gregory's edition of 14 utton's Mathematics, vol. i. p. 261.
" For the " Summation of Infinite Series," the author gives
a new and ingenious method, which is very easy and extensive
in its applicatiou."—Newcastle Magazine, November, 1825.
111. ELEMENTS OF PLANE AND SPHERICAL
TRIGONOMETRY, with its Applications to the Principles of
Navigation and Nautical Astronomy, with the necessary Lo-
garithmic and Trigonometrical Tables; by J. It. Young:7s.
cloth. To which is added, some Original Researches in
Spherical Geometry ; by 'l'. S. Davies, Esq., F.R.S.E.,
F.R.A.S. &c.
IV. MATHEMATICAL TABLES, comprehending the
Logarithms of all Numbers from 1 to 36,000 ; also the Natural
and Logarithmic 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 departments of Practical Mathematics; by J. R.
Young; 6s. cloth.
V. AN ELEMENTARY TREATISE ON THE COM-
PUTATION OF LOGARITHMS. Intended as a Supplement
to the various Books on Algebra. 12mo. 2s. 6d.
See Dr. Gregory's edition of Hutton's Mathematics, vol. i.
p. 157, where a particular reference is made to this little work.
VI. ELEMENTS OF ANALYTICAL GEOMETRY ;
comprehending the Doctrine of the Conic Sections, and the ge-
neral 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 Universi-
ties. 9s. cloth.
" 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, July2,s, 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
snore fit to be put into the hands of students."—Literary Ga-
zette, May 28, 1831.
VII. ELEMENTS OF THE DIFFERENTIAL CAL-
CULUS; comprehending the General Theory of Curve Sur-
faces and of Curves of Double Curvature. Ss. 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 formulae 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 surfacer, 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
from 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 improverhents 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
coefficients become imaginary, as is asserted by Lacroix
and his followers, but that these fel:lug, cases are always indi-
cated by the co-efficients becoming infinite. In one of the pro •
blems on this subject be has detected a false solution by La-
grange, which has been transcribed by Gamier and several
others, merely on the faith of a great name. * * *
" The whose Elements of the Differential Calculus, com-
prehending all that is roost valuable in the large works of the
most celebrated Analysts are contained in a duodecimo volume,
beautifully printed on a fine paper and neatly bound in cloth.
It appears to be in every respect well fitted for a Class Book,
and can scarcely fad 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
an elementary treatise, there is a perspicuity, a unity of me-
thod prevailing in all its parts, that reuders 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
admired, and therefore recommended 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.
"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 he altogether fallacious. We
wonder, indeed, when we see them pointed out, why they did
not occur to ourserves 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 fundamental principles of science."—Philoso-
phical Maciazine, October, 1831.
VIII. ELEMENTS OF THE INTEGRAL CALCULUS;
with its applications to Geometry, and to the Summatiou of In-
finite Series, &c. 9s: in cloth.
" The volume before us forms the third of an Analytical
Course, which commences with the 'ELEMENTS OF ANALYTICAL
GEOMETRY! More elegant Text-books do not 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 an inducement to the culti-
vation of Arialvtical 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 -Learning in Great Britain."—Presby-
terian Review., January, IEO2,
" We remember the tone 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."—Spectator, Septem-
ber, 24, 1831.
IX. 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,. illustrates' by numerous Engravings ; by
J. R. Young. 10s. 63. in- cloth.
" Mr. Young is already favourably known to the public by
his writings e and the " Treatise on Mechanics," which we now
propose briefly to, notice, will add considerably to his reputation
as the author of esementary works of science.
"To read the works of Laplace, Ivory, Somerville, &c. a
knowledge of the methods employed by these writers is previ-
ously required, and renders such preparatory works as those
of Mr. Young absoletely necessary."—Presbyterian Review,
July 1832.
Pubdihed by J. 'Sauter, 73, St. Paul's Church-yard, London;
sold by Piirk.er and Co., Oxford ; E, Johnson, Cambsidge;
White and CO.. Ediaburgh ; W. Jackson, New York; and
by all other booksellers.