HARVARD Entered, according to Act of Congress, in the year 1888, by in the Office of the Librarian of Congress, at Washington COPYRIGHT, 1899 BY &. A. WENTWORTH ALL RIGHTS RESERVED 614.7 The Athenæum Press PREFACE. A SUFFICIENTLY full treatment of the theorems of limits is given in the Plane Geometry to lay the foundation for rigorous proofs of the theorems in Solid Geometry that involve limits. Theorems not found in previous editions are introduced in this edition wherever deemed necessary for satisfactory proofs of propositions that follow. In Book VII Theorem XVI, for example, is necessary for a logical proof of the important theorem that follows it, and Theorems XXII and XXVIII are likewise necessary for the proofs that follow on Cylinders and Cones, respectively. While rigorous proofs have claimed first attention, still every effort has been made to bring the proofs within the comprehension of students who read the subject for the first time. Woodcuts are employed to illustrate the definitions, and are placed by the side of the ordinary figures used in demonstrations. It is expected that these woodcuts will be of great value in helping the student to gain clear conceptions of the figures, and to cultivate a correct geometrical imagination. Book IX, Conic Sections, has been carefully revised, and new figures have been substituted for the old ones. The excellent cuts of the Solid Geometry are largely due to Miss M. Gertrude Cross, of Boston, Mass. |