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ON THE

Geometry and Measurement

OF

PLANE FIGURES.

BEING

Solutions of the Theorems, Problems and Questions,

in Wormell's Modern Geometry.”

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

183.

152

g

EDUCATIONAL WORKS PUBLISHED BY THOMAS MURBY.

MATHEMATICAL WORKS, .

By RICHARD WORMELL, M.A., B.Sc.

I.-Wormell's Modern Geometry: A New Course

of Plane Geometry, in which the Theory of the Science and its Practical Applications are treated simultaneously.

Crown Svo, 256 pp. Price

35. 6d.

The explanations and illustrations of the leading problems of Geometry here treated, and the logical demonstrations of their principles, place this work amongst the very best of the kind, and its easy and graduated method makes it at once the best that has hitherto appeared. Evening Standard.

II.-An Elementary Course of Plane Geometry.

Third Edition. Revised and Enlarged. Price 35.

III.-An Elementary Course of Solid Geometry.

Second Edition. Price 2s. 6d. *** These works (II. & III.) arc adopted by the New Brunswick Council on Education as Text-books for use in schools throughout that province.

Iỹ.- Solutions to Exercises in Solid Geometry.

Price 2s. 6d.

V.-Solutions to Exercises in the Author's

Modern Geometry. Price 25. 6d. *** These Solutions are also adapted to the Elementary Course of Plane Geometry, (II. above, the Exercises being the same both in that work and in the Modern Geometry.

VI.-Arithmetic for Schools and Colleges.

Revised Edition. Price 25., with answers, 35.

VII.-Graduated Arithmetic. A Selection from the

preceding work. Price 9d. VIII.- Answers to Arithmetic for Schools and

Colleges. Price is.

THOMAS MURBY, 32, Bouverie Street, Fleet Street, London, E.C.

PART I.

THEOREMS AND PROBLEMS.

CHAPTERS 1. AND II.

LINES AND ANGLES.

THEOREMS ON ANGLES.

E

F

A

B

1. The bisectors of the two adjacent angles formed when one straight line meets another are perpendicular to one another.

Let ACD and B C D be the adjacent angles and let C E bisect the angle A C D and CF bisect the angle BCD; then shall the angle ECF be a right angle.

Because ECD is half 2 ACD,

and FC D is half _ BCD; :. The sum of LECD and LFC D is half the sum of 2 ACD and LBCD;

But we know the sum of ACD and BCD to be two right angles.

:: LECF, which is the sum of LECD and LFCD, is one right angle.

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