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Liverpool, Merseyside, England, 1833-10-04 00:00:00

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ANALYTICAL COURSE OF MATHEMATICS,
15Y AIR. J. R. YOUNG.
I.
ELEMENTS OF GEOMETRY; containing a New and
Universal Treatise on the Doctrine of Proportion, toge-
ther with Notes, in which are pointed out-and corrected several
important 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 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 ha justly considered as rendering his perform-
nnce valuable, especially to the learner."—Phileseprical Maga-
zine, 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."— Th e Timex, November 2, 18:27.
" In perspicuity Euclid has no rival, except, perhaps, in that
part of his work which treats of geometrical proportion. This
is ahstruse, and subtle, and intricate. The doctrine of propor.
tion, as connected with geometry, must necessarily be so.—
Hence Legendre 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
froin 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 discussed
in a tone of calm moderation, which we regret to say is not
always employed in the scientific world."—Monthly 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 el 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
nut-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 at 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 11r. J. R. Young, a
work which deserves our cordial recommendation."—Dr.
Gregory's edition of Huttou'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 application."—Netrectstte Maga!ine-finvember 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. 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 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 otherdepartinents of Practical Mathematics; by .1. R.
Young; 6s. clod'.
V. AN ELM:MN-TARN Tr EATI'Sr, GX" THE CGm-
PUTATION OF LOGARITHMS. Intended as a Supple-
ment to the various Books on Algebra. 12mo. 2s. 6d.
See Dr. Gregory's edition of Button's Mathematics, vol. i.
p. 137, 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 or 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 college's, the Continent will not long boast of its
immense superiority over the country of Newton in 'every
.branch of modern analytical science."--- The Atlas, July2s, 1830.
"We have to notice these excellent productions, as clear
guides to the higher branches of science. They do infinite cre-
dit to Mr. Young; and-no works of the sanie•ciass can be-more
fit to be put into the hands of students."—Literary Gazette, May
28, 1831.
VII. ELEMENTS OF THE DIFFERENTIAL CAL-
CULUS; comprehending the General Theory at' Curve Sur-
faces and of Carves 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 has 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 published.
"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 ten-
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
coefficients become imaginary, as is asserted by Lacroix and
his followers, but that these failing cases are always indicated
by the co-efficients becoming infinite. In one of the problems
on this subject he has detected a false solution by Lagrange,
which has been transcribed by Gamier and several others,
* *
merely on the faith ofa 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 duodecimo volume,
beautifully printed on a fine paper and neatly bound in cloth.
I' appears to be in every respect well fitted for a Class Book,
and can scarcely fail to be very generally adopted."—Presby-
terian Review, S'ept., 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
origival matter, much original reasoning, and, what is of more
value than all questions about originality in an elementary trea-
tise, there is a perspicuity, a unity of method prevailing in all
its parts, that renders it inure than any book we have seen pe-
culiary adopted to instruction.
It is not, however, as au •elegant and perspicuous develope-
ment of the first principles of the Calculus merely that we have
admired, and therefore recommended Mr. Younti's little work
we have also found touch 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. . .
"'Pile paralogisms of sonic 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, wheu 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 witli'a laudible anxiety to
the purity of the fundamental principles of science."—Philoso-
phical Magazine, October, 1831.
VIII. ELEMENTS OF THE INTEGRAL CALCULUS.:
with its applications to Geometry, and to the Summation of In-
finite Serie, &c. 9s. in cloth.
" The volume before us forms the third of an Analytical
Course, which commences with the ELEMENTS OF ANALYTICAL
GROMETRY'.' More elegant Text-books do,pot exist in--the
English Language, and we trust they will speedily be adopted
in our Mathematical Seminaries. Tfie 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 apprehend, chiefly to he ascribed.
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 2-1, 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
Dvrminical Problems, illustrated by numerous 'Engravings.; -by
J.R. Young. 10s. 6d. in cloth.
" 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 considerately to his reputation
as the author of elementary works of 'science.
" To read the works or Lapliee, ivory, Somerville, Sze. 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. JohniOn, Cambridge;
White and Co., Edinburgh ; W. Jackson, New York ; and by
all other booksellers.