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`.l,_3oorto PribitObcb,

ANALYTICABYL COURSE OF MA.T.
kiYIATICS,
I.
MR. J. SE
YOUN
tiILEMENTS OF GEOMETY ; containing a New and,
_EA Universal Treatise on the Doc ne of Proportion, together
with Notes, in which are pointed o t and corrected several im-
ertant-Errors that have hitherto remained unnoticed in the
ritirigs of Geometers. Bvo. Bs.
" His observations on the theory of parallel lines, the labour
he has bestowed on the doctrine of proportion, as well as his
corructiong 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
zinc, March, 1828. •
"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 all ages, there is a very able and
elaborate commentary."— The Times,. November 2, 1827.
" 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 propor-
tion, as connected with geometry, must necessarily be so.—
Hence Legendre has excluded the considerationnf 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 out and discusied
in a tone of calm moderation, which we regret to say is not al-
ways employed in the scientific world."—Monaly Magazine,
September, 1827.
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 of 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. If Mr.
Young acquits himself as successfully of the second undertaking
as he has of the one before us, he will bestow an- invaluable be-
nefit on the student."—Weekly Times, December, 1827.
" A new and ingenious general method of solving Equations
has 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 opr coidial recommendatiou."—Dr.
Gregory's edition ofillaton's Mathemattcs, vol. i. p. 261.
" For the
." Summation of Infinite Series," the author gives
a new and ingenious method, which.-;s very easy and extensive
in its application."—Netocastle ._,ovember,lBlth.
111. ELEMI-3,FfB-, PL.I.-N114... _ _P.I4.£IIICAI
TRIGONOMETRY, with its Applications to the Principles of
Navigation and Nautical-Astronomy, with the necessary Lo-
garithmic and Trigonometrical Tables; by J. R. Young, 7s.
cloth. To which is added, - some .Original Researches in
Spherical Geometry; by T. S. Davies, Esq., F.R.S.E.,
F.R.A.S. &c.
IV. MATHEMATICAL TABLES, comprehending the
Logarithms of all Numbers from 1 to 3000; also the Natural
and Lo.garithmic 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 ELEMENT AO( TEATISE ON THE COM-
PUTATION OF LOGA THM S. Intended-as a Supplement
to the various Books on Algebra. 12mo. 2s. 6d.
See Dr. Gregory's edition -of Hutton's Ma.theinatics, vol. i.
p. 157, where a particular reference is made to this little work.
VI. ELEMENTS OF ANALYTICAL GEOMET Y ;
comprehending the Doctrine of the Conic Sections, and the ge-
neral Theory of Carves and Surfaces of the Second order, with
a variety of local roblems 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, J1y25,1830.
" We have to notice these excellent productions, as clear
guides to the higher branches of. science. They do infinita
credit to Mr. Young; and no works of the same class can be
more 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. 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 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 containSWeicost-laeautiful 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
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 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
coefficteuts become imaginary, as is asserted by Lacroix
and his followers, but that these. failing cases are always indi-
cated by the coefficients becoming infinite. -In one of the pro-
blems on this subject he 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 whole Elements of the Differential Calculus, com-
prehending all that is most valuable in the large works of the
most celebrated Analysts are contained in a duodechno 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 fail to be very, generally adopted."—Presby-
terian Review, Sept. 1831.
" Theie 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 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
admired, and therefore recommended Mr. Young's little ivork;
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 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 putity of the fundamental principles of science."—Philoso-
phical Magazine,' Octobr, 1831.
VIII. ELEMENTS OF THE INTEGRAL CALCULUS ;
with its application's to Geometry, and to the Summation of In-
finite Series, &c. Os. 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 Analytical .Science; for, to the want of such Elemen-
tary Works, the indifference hitherto manifested in this country
on the subject is, we appFehend, 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, 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."—Spectator, Septem-
ber, 21, 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, illustrated by numerous Engravings; by
J. R. Young. 10s. 6s. in cloth.
" Mr. Yonng 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
knowledge of the methods employed by these writers is previ-
ously required, and renders such preparatory works as those
of Mr. -Young absolutely necessary."—Presbyterian Review,
July 1832.
Published by J. Souter, 73, St. Paul's Church-yard, London;
sold by Parker and Co., Oxford ; E. Johnson, Cambridge ;
White and Co., Edinburgh; W. Jackson: New York; and
by all other booksellers.

In 3 vols. post Bvo. •
THE ABBESS ; a Romance. By Mrs. TROLLOPE.
" 'The Abbess' is really and effectively what the Author
calls it, and what we have much wanted of late, a romance. The
proper elements of romance abound in its pages: monasteries
and convents, dark, intriguing monks and suffering nuns, the
dungeon-grave, the inquisition; the stake, poison, and various
crimes stir the blood in quick success n, and bind us fixedly to
the progress of the story."—Sir d Herald.
" ' The Abbess' is a very ex ordinary book, and will am-
ply repay the readers."—Junii ult.
"In almost every page we recognise the same sharp and in-
trepid spirit, the same leaning to the picturesque side of every
thing, the same love of heightening the effect of all, and not a
little- of the same liking for warm delineations which we per-
ceived in her ' Domestic Manners of the Americans.' Un-
questionably some of the chapters equal any thing in the lan-
guage for liveliness and theh."—A,n„
By same Author
The DOMESTIC MANNERS of the AMERICANS.
Fourth Edition. 2 vols. post Bvo. with 24 Plates, 21s.
is exactly the title-page we have long wished to see,
and we rejoice to say that, now that the subject has been taken
up, it is handled by an English lady of sense and acuteness,
who possesses very considerable power of expression, and en-
joyed unusually favourable opportunities for observation."—
Quarterly Review.
" Lively, pleasant gossiping."—Literary Gazette.
Whittaker, Treacher, and Co., Ave Maria-lane.
Of whom may be had,
SKETCHES of PORTUGUESE LIFE, MANNERS, COS-
TUMES; and CHARACTER. With 2i) coloured plates,
Bvo., 16s. •
" Mr..l. R. Young, who has distinguished himself as the
author of a useful elementary treatise ou 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, that the converse of every geome-
trical proposition (where demonstration is possible) is given.—
This has never been systematically done before. Several other
improvements are introduced (especially with. regard to the
doctrine of Proportion), and many errors of former geometers
corrected."—Sunday Times' February 10, 1828.
11. An ELEMENTARY TREATISE ON ALGEBRA,
Theoretical and Practical, with attempts to simplify. some of
the more difficult Parts ofthe Science, particularly the Demon-
stration of the Binomial Theorem, in its most general form;
the Solution of Equatiops of the higher orders ; the ....,i.unmation.
• of Infinite Series, &c., Bvo. boards, 10s. Gd.