MENSURATION FOR BEGINNERS. Plane and Solid. ADAPTED TO THE SPECIFIC SUBJECT, PUPIL TEACHER, BY WILLIAM DODDS, Author of "Algebra for Beginners," "Algebraic Test Cards," "Inspectors' THOMAS MURBY, 32, BOUVERIE STREET, FLEET STREET, E.C. 183. AND ALL BOOKSELLERS. 151. PART ALGEBRA FOR BEGINNERS. NEW EDITION, ENLARGED And Improved. I.-Notation, Addition, Subtraction, Brackets. Price 2d. PART II.-Multiplication, Division, Factors, G.C.M., L.C.M., Involution, Evolution, Simple Equations of One Unknown not involving Fractions, and Problems producing them. Price 2d. PART III.-Algebraic_Fractions, Simple Equations of One Unknown involving Fractions, Simple Equations of Two and Three Unknowns, and Problems. Price 3d. PART IV.-Quadratic Equations, and Problems producing them Price 3d. PARTS I.-IV., cloth limp. Price 10d.; with Answers, Is. 4d. Answers, 6d. The attention of Teachers and Students is directed to the following alterations which have been made in this Edition, to adapt it to the requirements of the under-mentioned examining bodies:-In PART I., a large number of new Exercises are given in Addition, Subtraction, and the use of Brackets. In PART II., Simple Equations of One Unknown not involving Fractions, with several additional Problems, have been included, to adapt it to Standard V. of the Government Code. PART III. has been almost entirely re-written. The whole of the Answers have been verified. Many of the examples have been taken from the Examination Papers of the Education Department (New Code, Schedule IV., Pupil Teachers', Scholarship and Certificate) London University (Matriculation and first B.A.); Royal College of Preceptors; Civil Service; Royal College of Surgeons (Preliminary); and Oxford and Cambridge Locals. PRACTICAL OPINION OF THE WORK. "I have often thought I would drop you a line to express my high opinion of your' Dodds' Algebra.' As a specimen of careful and sensible graduation, I have never seen its equal, the chapter on Quadratics being quite perfect. This part of Algebra is generally considered very difficult by learners; but the author has succeeded in making the way so plain that the merest tyro in mathematics will advance with ease and pleasure. The secret of the success in graduation lies in the plan pursued by the Author throughout, of presenting only one difficulty at a time. Just the book to give a young P.T. a love of Algebra."-G. HAMLETT, St. Jude's Schools, Leeds. ALGEBRAIC TEST CARDS. IN FOUR PACKETS, EACH CONTAINING 26 CARDS, WITH TWO COPIES OF ANSWERS. PRICE Is. PER PACKET, IN SET CLOTH CASE. I.-Notation, Addition, Subtraction, and Brackets. SET II.-Multiplication, Division, Factors, G.C.M., L.C. M., Involution, Evolution. SET III.-Fractions, Simple Equations, Problems. SET IV.-Quadratic Equations, Problems. Many of the questions contained in these Cards have been selected with great care from the published Examination Papers of the Education Department, the Universities, the Royal College of Preceptors, and other public examining bodies, and may be used with great advantage by those who adopt the Author's Algebra for Beginners. PREFACE. The following are the characteristic features of the 1. The rules are subdivided, so that one difficulty only is presented to the learner at a time. 2. Simple demonstrations, explanations, and illustra- tions are given, requiring no previous knowledge of Euclid or Algebra, or of Arithmetic beyond Vulgar and 3. Every variety of example is given under each subdivision; the published Examination Papers of the London University (Matriculation), the Education De- partment (Pupil Teachers', Queen's Scholarship and Certificate), the College of Preceptors, and the Oxford and Cambridge Local Examination Board, having ali been laid under contribution. The rest are original, and have been expressly constructed with reference to the most important points and to the usual difficulties of 4. In framing the questions, great care has been taken (for which the Author justly claims special credit) to avoid wearying the pupil with unnecessarily long and tedious arithmetical calculations. By a happy use of the Diophantine Analysis, he has been able to give examples on the Right-angled Triangle, and that bête noire of pupils, the Area of a Triangle when the three sides are given, every one of which "comes out without a remainder." This has not been done without great labour, but it will be appreciated by teachers, and render the work more popular with their boys than anything else. No single figure has been put down at random. Many of the paragraphs have been written over several times, as some point or other seemed to require further 5. As in the "Algebra for Beginners," hints for the solution of the more difficult problems are added, which will enable pupils to work without the constant super- 6. Whilst going through the press, the answers have been repeatedly tested by the teachers and pupils of |