A COMPLETE COURSE OF PURE MATHEMATICS, BY MR. YOUNG,

Lately published by J. Souter, School Library, 73, St. Paul's Churchyard.

1. AN ELEMENTARY TREATISE ON ALGEBRA, Theoretical and Practical; with attempts to simplify some of the more difficult 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 Series, &c. 8vo. bds. 10s. 6d.

From Dr. Gregory's edition of Hutton's Mathematics, vol. i. p. 261. “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 practical 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."

Newcastle Magazine, November 1825.—"For the summation of infinite series the author gives a new and ingenious method, which is very easy and extensive in its application."

2. AN ELEMENTARY TREATISE ON THE COMPU TATION 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: particular reference is made to this little Work.

A duodecimo volume of Logarithmic and Trigonometrical Tables, to x company the preceding Essay, is in preparation.

3. ELEMENTS OF GEOMETRY; containing a new and universal Treatise on the Doctrine of Proportion, together with Notes, in which are pointed out and corrected several Importan Errors that have hitherto remained unnoticed in the writings Geometers. Also, an Examination of the various Theories Parallel Lines that have been proposed by Legendre, Bertrand Ivory, Leslie, and others. 8vo. 8s.

Philosophical Magazine, March 1828.-" His observations on the theory parallel lines, the labour he has bestowed on the doctrine of proportion, as we as his corrections of many errors of preceding Geometers, and supplying the defects, together with his minute attention to accuracy throughout, may be just considered as rendering his performance valuable, especially to the learner."

The Times, November 2, 1827.-" In the notes, which he has appended the volume, is much valuable matter, even for those who have advanced stil further in these studies. On the theory of parallel lines, which has not a lit perplexed geometers of all ages, there is a very able and elaborate commentary

Monthly Magazine, September 1827.-" In perspicuity Euclid has no riva except, perhaps, in that part of his work which treats of Geometical Proportio This is abstruse, and subtle, and intricate. The Doctrine of Proportion, as co nected with Geometry, must necessarily be so. Hence Legendre has exclude consideration of it from his Elements, leaving all knowledge of the subje acquired from Numerical Proportion. This is a defect which Mr. You

supplied. Indeed, we have never seen a work so free from pretensi

Books Published by J. Souter.

nd of such great merit. Various fallacies latent in the reasonings of some elebrated mathematicans, both of ancient and modern date, are pointed out nd discused in a tone of calm moderation, which we regret to say is not always mployed in the scientific world."

From the Weekly Times, Dec. 2, 1827.-" This is a work of valuable informaon, the conception of a most enlightened mind, and executed with a simplicity hich cannot but carry the important truths it speaks of, home to the convicon of every understanding. In the Notes appended to the work, Mr. Young deavours to point out, in his own words, 'some remarkable errors and inconstencies into which modern Geometers have fallen, particularly in reference to e Theory of Parallel Lines, and the Doctrine of Proportion.' This volume is at the first part of the work. The second is to be devoted to the Geometry of lanes and Solids, with Notes and an Appendix on the Symmetrical Polyedrons Lagendre. If Mr. Young acquits himself as successfully of the second underking as he has of the one before us, he will bestow an invaluable benefit upon e student."

Sunday Times, Feb. 10, 1828.-" Mr. J. R. Young, who has distinguished mself as the author of a useful elementary treatise on Algebra, has just pubshed a work of the same beneficial description Elements of Geometry,' with otes. The great advantage which students will derive from this work is, that e converse of every geometrical proposition (where demonstration is possible) is ven. This has never been systematically done before. Several other improveents are introduced (especially with regard to the Doctrine of Proportion), ■d many errors of former Geometers corrected."

4. THE ELEMENTS OF ANALYTICAL GEOMETRY; comehending the doctrine of the Conic Sections, and the general eory of Curves and Surfaces of the second order, with a variety · local Problems on Lines and Surfaces. Intended for the use Mathematical Students in Schools and Universities. 7s. cloth. The Atlas, July 25, 1830.—" If works like the present be introduced genely into our schools and colleges, the continent will not long boast of its imense superiority over the country of Newton, in every branch of modern anaical science.'

5. THE ELEMENTS OF THE DIFFERENTIAL CALCULUS; mprehending the GENERAL THEORY of CURVE SURFACES and CURVES of DOUBLE CURVATURE: intended for the use of udents in Schools and Universities, and forming a Sequel to e Analytical Geometry. 7s. cloth.

Presbyterian Review, Sept. 1831.-"The work is divided into three sections, 1 each section is subdivided into chapters of a moderate length. The first tion treats of the differentiation of functions in general; the second contains - application of the differential calculus to the theory of plane curves; and the rd unfolds the general theory of curve surfaces and of curves of double curure. In the first the author introduces the most valuable theorems and formulæ the celebrated analysts, Euler, Lagrange, Demoivre, and Cotes. In the second, has given a correct explanation of what the French have termed consecutive The third contains the most beautiful theorems of Euler, Monge, and pin, relative to the curvature of surfaces in general, together with a chapter on sted surfaces, a subject hitherto confined to foreign writers. The whole forms hore simple, consistent, and comprehensive view of the differential calculus, I its various applications, than any hitherto published.

ves.

But the work does not merit attention merely on account of arrangement,

Books Published by J. Souter.

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 rendered much more simple. The chapter on maxima and minima presents considerable improvements in various parts of the investigation. In survey. ing 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 coefficients becoming infinite. In one of the problems on this subject he has detected a fale solution by Lagrange, which has been transcribed by Garnier and several others merely on the faith of a great name.

"The whole Elements of the Differential Calculus, comprehending all the is most valuable in the large works of the most celebrated Analysts are containe 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 ca scarcely fail to be very generally adopted."

Philosophical Mag. Oct. 1831." There are no affected changes of method there is no parade of original plan or of novelty of principle; and yet there much original matter, much original reasoning, and what is of more va than all questions about originality in an elementary treatise, there is a p spicuity, a unity of method prevailing in all its parts that renders it more t any book we have seen peculiarly adapted to instruction.

"It is not, however, as an elegant and perspicuous development of the principles of the Calculus, merely, that we have admired, and therefore commended Mr. Young's little work: we have found much to commend in a more profound character; much that we look for in vain in larger works, indeed in all English books.

"The paralogisms of some other writers, distinguished ones too, are po put in the preface, and in the body of the work; and many steps which hitherto been deemed unquestionable have been shown by Mr. Young to altogether fallacious. We wonder, indeed, when we see them pointed out they did not occur to ourselves nor to anybody else till now; and we look the aptitude displayed in these detections to be highly characteristic of a which looks with a laudable anxiety to the purity of the fundamental princ of science."

4. THE ELEMENTS OF THE INTEGRAL CALCULE with its Applications to Geometry to the Summation of Intit Series, &c. &c., intended for the use of Mathematical Stude in Schools and Universities; and forming a sequel to the Di ential Calculus. 9s. cloth.

Spectator, Sept. 24, 1831.-"We remember the time when such a wo this would have been invaluable, and we do not think that any late public has superseded the necessity of it."

tt For other recommendations of Mr. Young's Works see the Newcastle zine for August; Monthly Magazine for September; and Ladies Diary 1831, p. 25.

Also may be had of the same Publisher,

A BRIEF TREATISE on the USE and CONSTRUCT of a CASE of MATHEMATICAL INSTRUMENTS; cont ing a copious Explanation of each; particularly the Sector, the lines of separately treated of, and their use shown in solving several cases of Tr The whole designed to give the young Student a knowledge in us ents, and constructing Geometrical Figures with accuracy. B. A. Queen's College, Cambridge. New Edition, 2s. 6d.

By G