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NOTE TO REVISED EDITION.

THE first edition of this Geometry was issued about nine years ag The book was received with such general favor that it has been nece sary to print very large editions every year since, so that the plate are practically worn out. Taking advantage of the necessity for ne plates, the author has re-written the whole work; but has retaine all the distinguishing characteristics of the former edition. A fe changes in the order of the subject-matter have been made, some the demonstrations have been given in a more concise and simp form than before, and the treatment of Limits and of Loci has bee made as easy of comprehension as possible.

More than seven hundred exercises have been introduced into th edition. These exercises consist of theorems, loci, problems of co struction, and problems of computation, carefully graded and special adapted to beginners. No geometry can now receive favor unless provides exercises for independent investigation, which must be of suc a kind as to interest the student as soon as he becomes acquainte with the methods and the spirit of geometrical reasoning. The auth has observed with the greatest satisfaction the rapid growth of th demand for original exercises, and he invites particular attention the systematic and progressive series of exercises in this edition.

The part on Solid Geometry has been treated with much great freedom than before, and the formal statement of the reasons for th separate steps has been in general omitted, for the purpose of giving more elegant form to the demonstrations.

A brief treatise on Conic Sections (Book IX) has been prepare and is issued in pamphlet form, at a very low price. It will also bound with the Geometry if that arrangement is found to be ge

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ciation of the generous reception given to the Geometry heret the great body of teachers throughout the country, and he co anticipates the same generous judgment of his efforts to bring up to the standard required by the great advance of late in ence and method of teaching.

The author is indebted to many correspondents for valua gestions; and a special acknowledgment is due, for critici careful reading of proofs, to Messrs. C. H. Judson, of Greenvi Samuel Hart, of Hartford, Conn.; J. M. Taylor, of Hamilto W. Le Conte Stevens, of Brooklyn, N.Y.; E. R. Offutt, of S Mo.; J. L. Patterson, of Lawrenceville, N.J.; G. A. Hill, bridge, Mass.; T. M. Blakslee, Des Moines, Ia.; and G. W of Cambridge, Mass.

Corrections or suggestions will be thankfully received.

PHILLIPS EXETER ACADEMY,

1888.

G. A. WENTWO

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GEOMETRY.

DEFINITIONS.

1. If a block of wood or stone be cut in the shape repre sented in Fig. 1, it will have six flat faces.

Each face of the block is called a surface; and if these faces are made D smooth by polishing, so that, when a straight-edge is applied to any one of them, the straight edge in every part will touch the surface, the faces are called plane surfaces, or planes.

C

FIG. 1. B

2. The edge in which any two of these surfaces meet is called a line.

3. The corner at which any three of these lines meet is called a point.

4. For computing its volume, the block is measured in three principal directions:

From left to right, A to B.

From front to back, A to C.

From bottom to top, A to D.

These three measurements are called the dimensions of the block, and are named length, breadth (or width), thickness (height or depth).

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