18. Prove that, if n be either semi-axis of the curve represented by the equation ua® + vße + wy2 + 2u' By + 20' ya + 2w'aß= 0, the values of r will be the roots of the equation CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS, Cambridge Elementary Mathematical Series FOR COLLEGES AND SCHOOLS. I. ARITHMETIC AND ALGEBRA. ARITHMETIC. For the use of Schools. By BARNARD SMITH, M.A. New Edition (1861). 348 pp. Answers to all the KEY to the above. New Edition. Second Edition, containing Solutions to every Question in the latest Edition (1860). Crown 8vo. 88. 6. ARITHMETIC and ALGEBRA in their PRINCIPLES and APPLICATIONS. With numerous Examples, systematically arranged. Ios. 6d. ALGEBRA. For the use of COLLEGES and SCHOOLS. By I. TODHUNTER, M.A. Second Edition. Crown 8vo. 516 pp. (1860). 78. 6d. EXERCISES IN ARITHMETIC. By BARNARD SMITH, M.A. 104 pp. (1860). Cloth, limp. 28. Or with Answers. 28. 6d. Also sold in Two Separate Parts. 18. each. Cloth, limp. Answers. 6d. ARITHMETIC IN THEORY AND PRACTICE. For Ad vanced Pupils. By J. BROOK SMITH, M.A. Part First. 164 pp. (1860). Crown 8vo. 38. 6d. A SHORT MANUAL OF ARITHMETIC. By C. W. UNDERWOOD, M.A. 96 pp. (1860). Fcp. 8vo. 28. 6d. ELEMENTARY MATHEMATICAL SERIES. II. TRIGONOMETRY. PLANE TRIGONOMETRY. For Schools and Colleges. By I. TODHUNTER, M.A. Second Edition. 279 pp. (1860). Crown 8vo. 58. SPHERICAL TRIGONOMETRY. For COLLEGES and SCHOOLS. By I. TODHUNTER, M.A. 112 pp. (1859). Crown 8vo. 48. 6d. PLANE TRIGONOMETRY. With a numerous Collection of Examples. By R. D. BEASLEY, M.A. 106 pp. (1858). Crown 8vo. 38. 6d. PLANE and SPHERICAL TRIGONOMETRY. With the Construction and use of Tables of Logarithms. By J. C. SNOWBALL, III. MECHANICS AND HYDROSTATICS. ELEMENTARY TREATISE on MECHANICS. With a Collection of Examples. By S. PARKINSON, B.D. Second Edition, (1861). Crown 8vo. gs. 6d. ELEMENTARY HYDROSTATICS. With numerous Examples and Solutions. By J. B. PHEAR, M. A. Second Edition, 156 pp. (1857). Crown 8vo. 58. 6d. ELEMENTARY STATICS. For use in the Government Schools and Colleges in India. By G. RAWLINSON, M.A. Edited by E. STURGES, M.A. 150 pp. (1.860). Crown 8vo. 48. 6d. MACMILLAN AND Co., Cambridge and London. EGES Crown Crow $ The series of CAMBRIDGE CLASS-BOOKS FOR THE USE OF COLLEGES AND SCHOOLS, which have been issued at intervals during the last ten years by MACMILLAN AND Co., is intended to embrace all branches of Mathematics, from the most elementary to the most advanced, and to keep pace with the latest discoveries in mathematical science. Of those hitherto published the sale of many thousands is a sufficient in dication of the manner in which they have been appreciated by the public. A further series of a more simple character, adapted to the use of the lower classes in schools, is in course of preparation. 1. Arithmetic and Algebra in their Prin ciples and Applications. ARRANGED. Fellow of St. Peter's College, Cambridge. in cloth. The first edition of this work was published in 1854. It was primarily intended for the use of students in the Universities, and for Schools which prepare for the Universities. It has however been found to meet the requirements of a much larger class, and is now in use in a large number of Schools and Colleges both at home and in the Colonies. It has been found of great service for students preparing for the MIDDLE-Class and CIVIL AND MILITARY SERVICE EXAMINATIONS, from the care that has been taken to elucidate the principles of all the Rules. Testimony of its excellence has been borne by some of the highest practical and theoretical authorities; of which the following from the late DEAN PEACOCK may be taken as a specimen. “Mr. Smith's Work is a most useful publication. The Rules are stated with great clearness. The Examples are well selected and worked out with just sufficient detail without being encumbered by too minute explanations; and there prevails throughout it that just proportion of theory and practice, which is the crowning excellence of an elementary work." 16. 1. 62. 2. Arithmetic for the Use of Schools. By BARNARD SMITH, M.A. New Edition (1861), 348 pp. Crown 8vo. strongly bound in cloth. 48. 6d. Answers to all the Questions. KEY to the above, containing Solutions to all the Questions in the latest Edition. Crown 8vo. 392 pp. Second Edition. (1860). 88.6d. EXERCISES IN ARITHMETIC. 104 pp. Crown 8vo. (1860) 28. Or with Answers, 28. 6d. Also sold separately in 2 Parts price 18. each. ANSWERS, 6d. To meet a widely expressed wish, the ARITHMETIC was published separately from the larger work in 1854, with so much alteration as was necessary to make it quite independent of the ALGEBRA. It has now a large and increasing sale in all classes of Schools at home and in the Colonies. A very copious collection of Examples, under each rule, has been embodied in the work in a systematic order, and a Collection of Miscellaneous Papers in all branches of Arithmetic have been appended to the book. The EXERCISES have been published in order to give the pupil examples of every rule in Arithmetic, and a great number have been carefully compiled from the latest University and School Examination Papers. 3. Algebra. FOR THE USE OF COLLEGES AND SCHOOLS. By I. TODHUNTER, M.A. Fellow and Head Lecturer of St. John's College, Cambridge. Second Edition. 516 pp. (1860), strongly bound in cloth. 78. 6d. This work contains all the propositions which are usually included in elementary treatises on Algebra, and a large number .of Examples for Exercise. The author has sought to render the work easily intelligible to students without impairing the accuracy of the demonstrations, or contracting the limits of the subject. The examples have been selected with a view to illustrate every part of the subject, and as the number of them is about sixteen hundred and fifty, it is hoped they will supply ample exercise for the student. Each set of examples has been carefully arranged, commencing, with very simple exercises, and proceeding gradually to those which are less obvious. Macmillan and Co. |