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The plan and scope of this work may be indicated briefly by the following characteristic features :

Directed lines and Cartesian coordinates are introduced as a working basis.

Each subject, when first introduced, is treated in a general manner and is presented as fully as the character of the work demands. This avoids the necessity of treating the same subjects several times for the purpose of modifying and extending certain conceptions.

Statements in the form of theorems and problems are used freely to indicate the aim of various articles and to define the data clearly.

Inverse functions are treated more fully than is customary.

The general principles governing the solution of triangles, the solution of trigonometric equations, and the proof of identities are carefully presented.

Special attention is given to the arrangement of computations.

The sine and cosine series are obtained from De Moivre's Theorem, thus completing the line of development which leads to the calculation of the trigonometric functions.

The work on spherical trigonometry contains the development of all the formulas that are generally used in practical astronomy.

The right spherical triangle is treated from two points of view: as a special case of the oblique triangle, and directly


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