623182 1. FIRST LESSONS IN NUMBERS : An illustrated Arithmetic for Beginners. 16mo, pp. 118. 2. INTERMEDIATE ARITHMETIC : Mental and Written, containing a simple treatment of the elementary principles and common applications of Arithmetic, with numerous practical examples. 16mo, pp. 256. 3. PRACTICAL ARITHMETIC : In which operations on abstract and denomi nate numbers and their various applications, are thoroughly explained and illustrated by numerous examples adapted to the business of practi. cal life. A complete treatise, rendering higher book unnecessary for ordinary arithmetical studies. 12mo, pp. 348. 4. MENTAL ARITHMETIC: After the inductive method of Pestallozzi ; con taining numerous oral exercises for arithmetical training 160. 16mo, pp. 5. ELEMENTARY ALGEBRA : A plain, progressive introduction to Algebra 12mo, pp. 317. 6. ELEMENTS OF GEOMETRY: A complete translation and adaptation of the latest edition of the standard work of Legendre, with many exercises in Geometrical Analysis and hints for their solution. Crown 8vo, pp. 366. 7. A KEY to the Mental and Practical Arithmetics. 12mo. 8. A KEY to the Elementary Algebra. 12mo. Entered according to Act of Congress, in the year 1875, by the UNIVERSITY PUBLISHING COMPANY, *** 539. PREFACE. The Geometry of Legendre has held its high place among works on Elementary Geometry for more than sixty years. During this period a number of modifications have been suggested by various editors and commentators in the methods of treating particular subjects, but the great body of his work has stood the test of time as the most successful modification of Euclid which has ver appeared. It forms the basis of all the later text-books on Elementary Geometry which have appeared in France, and of all the recent works designed to modernize the Euclidian Geometry for the schools and colleges of England, and of nearly all the geometrical instruction in America, for thirty or forty years. In the preparation of the present edition a careful analysis has been made of such works as Planche (Cahiers de Géométrie pour servir de complement au traité de Legendre), Blanchet's Legendre, Bobillier, Amiot, and of the very complete work of Rouchè and De Comberousse, and the editor has adopted such additions and changes as he considered improvements on the original. These changes consist mainly in the discussion of parallels ; in the treatment of tangencies (in Book II.); in the addition of some theorems and the omission of a few; in the substitution of the method of limits for the method of the reductio ad absurdum in the treatment of the measure of the circle and of the “three round bodies ;” and in the fuller treatment of the plane and the triedral in Book V. While this edition is made from a completely new translation of the French edition of Legendre of 1865, yet the translation has been carefully compared with that of Sir David Brewster, and his words adopted where they seemed fittest. Brewster's example has also bee followed in making the “Doctrine of Proportion" introducto |