CHEAP SCHOOL-BOOKS. 



PRINCIPLES OF GEOMETRY. 



FAMILIARLY ILLUSTRATED, AND APPLIED TO A VARIETY OF 

 USEFUL PURPOSES. 



By WILLIAM RITCHIE, LL.D. 



12mo. 1*. 6d. cloth. 



This book is intended to conduct the student through the elements of plane and 

 solid geometry, in a method uniting theory with practice, each illustrating the 

 other. As the fundamental properties of the science are communicated, they are 

 applied, in examples, to the mixed sciences and the mechanical arts. By this 

 means, the two principal advantages of mathematical learning are combined: 

 1st. The discipline of the reasoning powers by the habit of rigorous demonstration : 

 and 2nd. The possession and employment of a key to many of the most important 

 arts of life. To the young engineer this book is particularly adapted, as it not 

 only shows the construction and use of the instruments employed in surveying 

 such as the diagonal scale, theodolite, and cross-staffbut gives a variety of 

 problems in surveying and levelling, the determination of heights and distances, 

 mensuration of surfaces and solids, and the elements of trigonometry. The nature 

 of geometrical analysis is also explained, and the pupil is introduced to the most 

 important principles of optics and astronomy. The work is interspersed with 

 numerous exercises, carefully adapted to the state of the learner's knowledge at 

 each step of his progress. 



4. 



A FIEST BOOK OF PLANE TRIGONOMETRY, 



GEOMETEICAL TRIGONOMETRY, AND ITS AP- 

 PLICATION TO SURVEYING. 



ByGK W. HEMMING, M.A. 



12mo. 1*. 6d. cloth. 



This book is intended to supply to the student and the engineer, within a small 

 compass and in a lucid form, sufficient knowledge of Geometrical Trigonometry, to 

 enable him to effect the practical object of measuring heights, distances, and 

 areas. In treating the subject, the aim of the author has been to give full deve- 

 lopment to the essentials, but to avoid embarrassing the learner by introducing 

 complications and extensions which, however useful they might be at a subsequent 

 stage of his studies, are beside his present purpose. The work is especially 

 adapted to schools, as there is nothing in it which does not come fairly within the 

 capacity of an average school-boy who has mastered the first elements of Algebra 

 and Geometry. 



TABLESIOF LOGARITHMS, COMMON AND TRIGO- 

 NOMETRICAL, TO FIVE PLACES. 



Foolscap 8vo. It. 6d. cloth. 



This book is a reprint of Lalande's Tables of Logarithms, with some additions. 

 The first part contains the Logarithms of the numbers from 1 to 10,000, calculated 

 to five places of decimals, with a column of differences with this variation from 

 Lalande, that the index or characteristic of the Logarithm is omitted as a worse 

 than useless incumbrance ; the decimal point, however, being retained before the 

 mantissa (contrary to the usual practice), in order to make the distinction more 

 marked between the column of Logarithms and that of numbers. The second part 

 contains the Logarithms of the Trigonometrical ratios to every minute of the 

 quadrant ; the characteristic, whether positive or negative, being always increased 

 by ten for the sake of uniformity, whereas the Logarithms are so augmented in 

 Lalande's Tables only in case of negative indices. At the close of the book is a 

 Table of the most useful Constants relating to mensuration, trigonometry, 

 astronomy, etc., including the numbers necessary for the exact reduction of the 

 modern French decimal system of weights, measures, and degrees, to the English 

 equivalents, and vice vertd, 



V Tills Series vill be continued. 



