# Book:The Rev. Alfred Wrigley/Wrigley's Examples/Seventh Edition

## The Rev. Alfred Wrigley: *Examples and Problems in Pure and Mixed Mathematics: Seventh Edition. - Corrected.*

Published $\text {1865}$, **Longmans, Green, Reader, and Dyer**.

### Subject Matter

- Mathematical exercises

This book is often referred to as **Wrigley's Examples**.

### Contents

- PREFACE to THE FOURTH EDITION.

IN preparing this Edition, many additional Examples and Problems have been inserted in the Arithmetic, Theory of Equations, Geometry, Mensuration, Application of Algebra to Geometry and Conic Sections. The present arrangement, and order of questions, it is intended to retain in any future Edition.

It has been deemed expedient to omit examples in the elementary processes of the Differential and Integral Calculus, leaving those problems in Mixed Mathematics, which require the higher calculus, to suffice for that subject.

All the Examples and Problems, in which logarithms may conveniently be used, have been solved with the aid of tables, in which the logarithms consist of six figures. The Logarithmic Tables here used, were edited by the Rev. J. Cape, M.A., &c., Professor of Mathematics in the Honourable East India Company's Military Seminary, Addiscombe.

As in many calculations, logarithms are used rather for convenience than from necessity, the answers obtained will slightly vary, (1) according as logarithms are used or not, (2) according as the tabulated logarithm consists of five, six or seven figures, more or less, and (3) according to the extent of the use made of 'proportional parts.' This variation is generally very small, and an indication of the cause of it will be sufficient to explain the disparity between the answers to some questions obtained on different occasions or by different persons.

Great assistance has been derived from Barlow's Tables of Squares, Cubes, Square Roots, &c., edited by Professor De Morgan, 1840.

In preparing for the first Edition of this Work, the Rev. W. H. Johnstone, M.A. was associated with the author. Other engagements have prevented Mr. Johnstone from contributing his able assistance towards the present volume ; for which accordingly, with all its imperfections, the author is solely responsible.

- November 15, 1857.

- ADVERTISEMENT.

The Seventh Edition is a reprint of the Sixth corrected.

Clapham Grammar School,

- November 1865.

- ARITHMETIC.

- 1. Vulgar Fractions
- 2. Decimal Fractions
- 3. Duodecimals
- 4. Practice
- 5. Rule of Three Direct
- 6. Rule of Three Inverse
- 7. Double Rule of Three, Compound Proportion
- 8. Simple Interest
- 9. Compound Interest
- 10. Discount
- 11. Stocks
- 12. Single Fellowship
- 13. Double Fellowship
- 14. Extraction of Roots

- ALGEBRA.

- 1. Multiplication
- 2. Division
- 3. Greatest Common Measure
- 4. Least Common Multiple
- 5. Fractions
- 6. Involution and Evolution
- 7. Surds
- 8. Equations:
- I. Simple Equations
- II. Simultaneous Equations of the First Degree
- III. Problems in Equations of the First Degree
- IV. Pure Quadratic Equations
- V. Adfected Quadratic Equations
- VI. Simultaneous Equations of the 2nd, 3rd, &c. Degrees
- VII. Problems in Equations of the 2nd and higher Degrees

- 9. Inequalities
- 10. Ratio, Proportion, and Variation
- 11. Arithmetical Progression
- 12. Geometrical Progression
- 13. Harmonical Progression
- 14. Piles of Balls and Shells
- 15. Permutations and Combinations
- 16. Binomial and Multinomial Theorems
- 17. Indeterminate Coefficients
- 18. Reversion of Series
- 19. Summation of Series
- 20. Interpolation of Series
- 21. Chances or Probabilities
- 22. Scales of Notation
- 23. Logarithms
- 24. Exponential Equations, &c.
- 25. Interest and Annuities

- THEORY OF EQUATIONS
- 1. Formation of Equations, &c.
- 2. Transformations, &c.
- 3. Symmetrical Functions
- 4. Reciprocal or Recurring Equations
- 5. Equations having Equal Roots
- 6. Cubic Equations
- 7. Biquadratic Equations
- 8. Limits in the Roots of Equations
- 9. Rational Roots
- 10. Sturm's Theorem
- 11. Methods of Approximation

- GEOMETRY: Miscellaneous Theorems and Problems

- MENSURATION.
- 1. Areas of Plane Figures
- 2. Surfaces and Contents of Solids
- 3. Measurement of Shot, Shells and Powder

- TRIGONOMETRY.

- 1. Trigonometrical Formulae, &c.
- 2. Properties of Plane Figures
- 3. Trigonometrical Tables
- 4. Solution of Plane Triangles
- 5. Heights and Distances
- 6. Expansions, Series, &c.

- APPLICATION OF ALGEBRA TO GEOMETRY.

- ANALYTICAL GEOMETRY AND CONIC SECTIONS.

- 1. Straight Line, &c.
- 2. Circle
- 3. Parabola
- 4. Ellipse
- 5. Hyperbola
- 6. Section of the Cone, and General Problems
- 7. Loci

- STATICS.

- 1. Forces acting in one Plane, through one point
- 2. Forces acting in one Plane, but not through one point
- 3. Forces which do not act in the same Plane
- 4. The Centre of Gravity
- 5. Centre of Parallel Forces
- 6. Guldinus' Properties
- 7. Machines:
- I. Lever
- II. Wheel and Axle
- III. Pulleys
- IV. Inclined Plane
- V. Screw

- 8. Friction

- DYNAMICS.
- 1. Collision or Impact of Bodies
- 2. Uniformly Accelerated Mction and Gravity
- 3. Motion upon a Curve, and Simple Pendulum
- 4. Projectiles
- 5. Rotation of Bodies:
- I. Moment of Inertia
- II. Centre of Oscillation
- III. D'Alembert's Principle, &c.

- HYDROSTATICS

- 1. Pressure on Surfaces
- 2. Centre of Pressure
- 3. Equilibrium of two fluids in a bent tube
- 4. Specific Gravity
- 5. Equilibrium of Floating Bodies
- 6. Elastic Fluids
- 7. Instruments and Machines

- HYDRODYNAMICS

- Efflux of Fluid from Vessels
- Resistances

- ANSWERS.

- Arithmetic
- Algebra
- Logarithms
- Theory of Equations
- Mensuration
- Trigonometry
- Application of Algebra to Geometry
- Analytical Geometry of Two Dimensions
- Statics
- Dynamics
- Hydrostatics
- Hydrodynamics