We send this as a sample of Part Third, or the advanced course of Prof. Olney's "Special or Elementary Geometry." This book will be bound up with Parts First and Second, under the title of Olney's Elements of Geometry and Trigonometry-UNIVERSITY EDITION. SHELDON & COMPANY, New York. A TREATISE ON SPECIAL OR ELEMENTARY GEOMETRY. IN FOUR PARTS. UNIVERSITY EDITION. INCLUDING PLANE, SOLID, AND SPHERICAL GEOMETRY, AND PLANE AND PART III. WHICH DISTINGUISHES THE UNIVERSITY FROM THE SCHOOL EDITION, 160 PROPOSITIONS AND PROBLEMS FOR EXERCISE IN GEOMETRICAL AND AN INTRODUCTION TO THE MODERN GEOMETRY. BY EDWARD OLNEY, PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF MICHIGAN. NEW YORK: SHELDON & COMPANY, 677 BROADWAY. 1872. Stoddard's Mathematical Series. STODDARD'S JUVENILE MENTAL ARITHMETIC SHORT AND FULL COURSE FOR GRADED SCHOOLS. STODDARD'S PICTORIAL PRIMARY ARITHMETIC $ 25 40 50 1 00 30 75 1 25 The Combination School Arithmetic being Mental and Written Arithmetic in one book, will alone serve for District Schools. For Academies a full high course is obtained by the Complete Arithmetic and Intellectual Arithmetic. HIGHER MATHEMATICS OF THE SERIES, BY EDWARD OLNEY, PROFESSOr of maTHEMATICS IN THE UNIVERSITY OF MICHIGAN. A COMPLETE SCHOOL ALGEBRA, in one vol., 410 pages, $1.50. Designed for Elementary and higher classes in Schools and Academies. Price $2.50 A GEOMETRY AND TRIGONOMETRY, in one vol., 8vo, A GEOMETRY AND TRIGONOMETRY, UNIVERSITY EDITION, in one vol., 8vo, Price $3.00 The other books of this Series will be published as rapidly as possible. Entered according to Act of Congress, in the year 1872, by SHELDON & COMPANY, In the Office of the Librarian of Congress, at Washington. PART III. AN ADVANCED COURSE IN GEOMETRY. CHAPTER I. EXERCISES IN GEOMETRICAL INVENTION. SECTION I THEOREMS IN SPECIAL OR ELEMENTARY GEOMETRY. 623. This chapter will afford a review of Parts I. and II., while it will greatly extend the student's knowledge of geometrical facts. Great pains should be taken to secure good habits as to neatness of execution in the construction of figures, orderly and proper arrangement of thought, and in style of expression. The practice of constructing every figure upon geometrical principles-guessing at nothing cannot be too strongly commended. As to the form of a geometrical argument, observe the following order: 1st. The enunciation of the theorem or problem in general terms. 2d. The elucidation of the general statement, by reference to the particular figure which it is proposed to use. 3d. A description of the figure, with reference to any auxiliary construction which is used in the demonstration or solution. 4th. The demonstration proper. 624. If two adjacent sides of a quadrilateral are equal each to each, and the other two adjacent sides equal each to each, the diagonals intersect at right angles. SUG's.-1st, Draw a quadrilateral having such sides as the data require, and draw its diagonals. 2d. State the proposition with reference to the figure. |