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9. ANALYTICAL GEOMETRY, Part II., on the General Theory of Curves and Surfaces of the Second Order.

2d Edit. 7s. 6d.

10. ELEMENTS of the DIFFERENTIAL CALCULUS; comprehending the General Theory of Curve Surfaces and of Curves of Double Curvature. Second Edition. 12mo. 9s. 8vo. 12s.

"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 general theory of curve surfaces and of curves of double curvature. In the first, the author introduces the most valuable theorems and formula of the celebrated analysts, Euler, Lagrange, Demoivre, and Cotes. In the second, he has given a correct explanation 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 rendered much more simple. The chapter on maxima and minima presents considerable improvements in various parts of the investigation. In surveying the cases in which Taylor's theorem fails, Mr. Young has shown that it does not fail where the coeffi cients 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 false 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 that is most valuable in the large works of the most celebrated Analysts, are contained in a duode- | cimo 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."-Presbyterian Review.

11. ELEMENTS of the INTEGRAL CALCULUS; with its Applications to Geometry, to the Summation of Infinite Series, &c. 9s. "The volume before us forms the third of an Aualytical 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 auxiliaries will, of itself, we hope, prove an inducement to the cultivation of Analytical Science; for, to the want of such Elementary 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 intelligent student, and, in so doing, has contributed to the advancement of Mathematical Learning in Great Britain."-Presbyterian Review.

12. 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. 10s. 6d.

"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 considerably to his reputation as the author of elementary works of science.-Presbyterian Review. 13. LECTURE on the STUDY of MATHEMATICS, 2s. 6d. 14. A CATECHISM of ALGEBRA; Part I. Being an easy Introduction to the first Principles of Analytical Calculation.




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