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It has been the intention, in this course, to unite the analytical methods of the French, with the prac, tical methods of the English School. These works embrace the entire course of Mathematics pursued at the United States Military Academy. They have also been adopted by many of the Colleges as regular Text Books, and are likewise extensively used in Select chools and Academies. Numerous testimonials in favor of these works have been received from professional men, in all parts of the United States. They are respectfully recommended to the attention of 'Instructers and all others interested in education.

DAVIES' MENTAL AND PRACTICAL ARITHMETIC, It is the object of this work to explain in a brief and clear manner, the properties of nuinbers, and the best rales for their various applications. The subjects are arranged throughout in a natural and scientific order, each depending on those which have gone before it. All the terms, or technical words, are defined. In each subject the most elementary idea is first presented, generally under the form of a question, then follow illustrations or examples, and lastly the general rule.

KEY to Davies' Mental and Practical Arithmetic, for the use of Teachers only. This work has each gum in the Arithmetic carefully and fully wiought out. It also contains additional examples in each rule, which are not found in the Arithmetic--so that the Teacher will be enabled to ex, ercise his pupils, if he wishes, by questions which are not in their books.

Davies' First Lessons in Algebra-Being an introduction to the Science. It has been the intention, in this work, to form a connecting link between Arithmetic and Algebra, lo nnite and blend, as far as possible, the reasoning in mumbers, with the more abstruse method of Analysis. It is designed to follow the Mental and Practical Arithmetic, and to serve as an introduction to Bourdon's Algebra. This work is an abridgemeut of the work of M. Bourdon, with the ad.

dition of practical Examples. The treatise on Algebra, by Bourdon, is a work of singular excellence and merit. In France, it is one of the leading text books, and shortly after its publication had passed through several editions. It has been translated, in part by Professor De Morgan, of the London University, and it is now used in the University of Cambridge. Davies' Legendre's Geometry and Trigonometry. Being an abridgment of the work of

M. Legendre, with the addition of a Treatise on Mensuration of Planes and Solids, and a

Table of Logarithms and Logarithmic Sines. This work has passed through several editions since its publication in 1834, and is becoming a general text book in the institutions of the country, Davies' Surveying ; with a description, and Plates of the Theodolite, Compass, Plane-Table and

Level; also, Maps of the Topographical Signs adopted by the Engineer Department, and an

Explanation of the method of Surveying the public lands. It has been the intention in this work to begin with the very elements of the subject, and to combine those elewents in the simplest maoner, so as to repder the higher branches of plane surveying comparatively easy. All the instruments needed for plotting have been carefully described ; and the uses of those renröred for the measurement of angles are fully explained. Davies' Analytical Geometry ;-Embracing the equations of the point and straight line, a

system of Conic Sections ;-the Equations of the line and plane in Space--also, the discus

sion of the general Equation of the Second degree, and of surfaces of the Second order. For about sixteen years the subject or Analytical Geometry has made a part of the course of Mathematics pursued at the Military Academy, and the methods which have adopted in the present work, are ihoxe which hve been taught with the greatest succese.

Davies' Descriptive Gcometry-With its application to Spherical Projections. The intimate connection which this subject has with civil engineering and architecture, renders its ac, quisition desirable to those who devote themselves to these pursuits. Dav es' Differe til and Integral Calculus-Embracing the Rectification and Quadratura

of Curves, llic Mensuration of Surfaces, and the Cubature of Solids. This branch is justly considered the most difficult of the pure Mathematics ; it has been the intention however to render the subject a& plain as the nature of it would admit, but still, it cannot be mastered without patience and severe study,

Davies' Shades and shadows and Linear Perspective. The subjects treated of in this work are certainly useful to the Architect and Draftsman a knowledge of them is indispensable.

The above works are for sale by booksellers generally throughout the United Stater,

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JUNE, 1839.




AFTER the childe hath learned perfectlie the eight parts of speach, let him then learne the right joyning together of substantives with adjectives, the nowne with the verbe, the relative with the antecedent. And, in learning further his syntaxis, by my advice, he shall not use the common order in common scholes, for making of Latines: whereby the childe commonly learneth, first, an evill choice of wordes, (and “Right choice of wordes, saith Cæsar, is the foundation of eloquence;'') then a wrong placing of wordes ; and, lastlie, an ill framing of the sentence, with a perverse judgment, both of words and sentences. These faultes, taking once roote in youth, be never, or hardlie, plucked away in age. There is a waie, touched in the first booke of Cicero de Oratore, which, wiselie brought into scholes, truly taught, and constantly used, would not only take wholly away this butcherlie feare of making of Latines, but would also with ease and pleasure, and in short time, as I know by good experience, worke a true choice and placing of wordes, a right ordering of sentences, an easy understanding of the tonge, a readiness to speake, a facilitie to write, a true judgment,

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