OLMSTED's School ASTRONOMY.-It is with peculiar pleasure we notice the appearance of this work, small in size, but containing more matter than many larger books. There is probably no instructor of much experience who has not felt serious inconvenience from the want of a proper text book in this department of science, as taught in our academies and higher schools. The treatise before us, however, is one which, after a careful perusal and the use of it as a text book, we can most cheerfully recommend as eminently adapted to supply the vacancy heretofore existing. Our author is particularly happy in the arrangement and division of the various subjects discussed; each occupying its appropriate place, involving no principle which has not been previously considered. He aims to fix in the mind the great principles of the science, first by stating them in the most concise and perspicuous terms, and then by lucid and familiar illustrations, without entering into an indiscriminate and detailed statement of a multiplicity of statistics, which only burden the memory and discourage the student. The learner is early made acquainted with the use of the globes, which greatly assists him in understanding the causes of various phenomena which otherwise would be wholly unintelligible. The student in his progress finds himself in possession of the keys of knowledge, and is highly pleased and encouraged in being able to anticipate effects and assign their true causes, which before seemed a mystery. Indeed, we feel assured, that this compendium need only be known to competent and judicious instructors, in order to secure its cheerful introduction into our schools and academies as an important auxiliary to science. Those who have had the misfortune to toil for many a tedious hour in treasuring up insulated facts in this science, without a knowledge of the principles upon which they depend, and consequently without any knowledge of the subject, will be fully convinced, after a patient perusal of the work under consideration, that the study of Astronomy is not necessarily dry and uninteresting, but that the difficulty arises in a great measure from an erroneous method of studying the subject. A. OLMSTED'S RUDIMENTS OF NATURAL PHILOSO. PHY AND ASTRONOMY: Designed for the Common Schools and younger classes in Academies, with numerous Wood Cuts. By Denison Olmsted. 18mo., half bound, cloth sides. Price 623 cents. ELEMENTARY AND HIGHER GEOMETRY, TRIGO. NOMETRY, AND MENSURATION: In Four Parts. By Nathan Scholfield. (Each Part sold separately.) The above is the title of a work just published, containing many valuable discoveries and improvements in mathematical science, especially in relation to the Quadrature of the Circle, and some other curves, as well as the cubature of certain curvilinear solids ; designed as a text book for Collegiate and Academic instruction, and as a practical compendium on mensuration. The first part consists of the Elements of PLANE GEOMETRY, and the mensuration of plane figures. The second part consists of the Elements of SOLID GEOMETRY, and the mensuration of elementary solids. The third part treats of SPHERICAL GEOMETRY, ANALYTICAL, PLANE, AND SPHERICAL TRIGONOMETRY, with their applications; the application of Algebra to Geometry; and on the Ellipse, Hyperbola and Parabola. The fourth part treats of the species and quadrature of the sections of a cone—the relations of cylindrical and conical segments and ungulas-a new class of curvilinear solids termed revoloids, and of such other solids as are subjects of the Higher GEOMETRY. Also, on some new curves termed the revoloidal curve, and curve of the circles quadrature; by the investigations of which, some important properties of the circle are developed, furnishing us with geometrical methods of approximating to the circles quadrature to any desirable extent; and by the same investigations are developed means of computing the area of any segment of a circle, when the arc of the segment and its sine are given, with as little labour as that of a triangle whose base and perpendicular are known. A new method of notation is also introduced, by which the relations of magnitudes, whose elements are a series of variable factors, may be intelligibly investigated; by means of which notation, is obtained a definite expression for the circle's quadrature, in positive and known functions of the diameter. The first principles of the differential and integral calculus are introduced, and the principles on which most of the operations of that science are performed, are rendered more intelligible by means of the notation above referred to. The series closes with the mensuration of such surfaces and solids as depend on the higher geometry The Elementary parts of the series, are based on Legendre's Elements, with various improvements and additions. This portion of the work, consisting of the first and second parts, is designed to be furnished separately from the whole series whenever it is required, in order to render it available in the primary institutions, or where the elements of the subject only are wanted. 1845 & 6. M-CURDY'S FIRST LESSONS IN GEOMETRY. Adapted, in connexion with The Charts of Geometry, to the use of Public Schools and Academies. By D. M'Curdy, of Washington, D. C. Price of the Book 25 cents. Two Charts $2 50 each. COFFIN'S SOLAR AND LUNAR ECLIPSES Familiarly illustrated and explained, with the method of calculating them, as taught in the New England Colleges, 8vo. cloth. Price $1 50. THE NORTH AMERICAN ARITHMETIC. Part 1st, for young learners. . PRESTON'S TREATISE ON BOOK-KEEPING: Comprising both Single and Double Entry; being a new, enlarged, and improved edition. Half bound, cloth sides. Price $1 00. 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