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MENSURATION

FOR BEGINNERS.

Plane and Solid.

ADAPTED TO THE SPECIFIC SUBJECT, PUPIL TEAcier,

AND OTHER EXAMINATIONS.

BY

WILLIAM DODDS,

Author of “ Algebra for Beginners," " Algebraic Test Cards," " Inspectors'
Recent Examination Cards (Arithmetic)," • An Easy Elementary Latin

Series,” “A Complete Guide to Matriculation,” etc., etc.

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London:

THOMAS MURBY,
32, BOUVERIE STREET, FLEET STREET, E.C.

AND ALL BOOKSELLERS.

183.

1511

ALGEBRA FOR BEGINNERS.

NEW EDITION, ENLARGED AND IMPROVED.

PART 1.-Notation, Addition, Subtraction, Brackets. Price 2d.

U _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 Un

known 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 iod. ; 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 ls. PER PACKET, IN

CLOTH CASE. SET 1.-Notation, Addition, Subtraction, and Brackets. SET II.-Multiplication, Division, Factors, G.C.M., L.C.M., In

volution, Evolution. SET III.-Fractions, Simple Equations, Problems. SET IV.-Quadratic Equations, Problems.

Mapy 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

work :-

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

Decimal Fractions.

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 all

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

beginners.

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 tedions 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

elucidation.

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-

vision of a teacher.

6. Whilst going through the press, the answers have

been repeatedly tested by the teachers and pupils of
several Middle Class Schools, and are guaranteed correct.

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