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

## The Rev. Alfred Wrigley: *Examples and Problems in Pure and Mixed Mathematics: Second Edition. Altered, Corrected and Enlarged.*

Published $\text {1847}$, **Longman, Brown, Green, and Longmans**.

### Subject Matter

- Mathematical exercises

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

### Contents

- PREFACE to THE SECOND EDITION.

In preparing this Edition for the press the utmost care has been taken to ensure accuracy to as great a degree as possible. With this view, all the examples contained in the first Edition, and now reprinted, have been again worked out.

The additional matter, which amounts to about one-third of the whole work, consists (1) of Theory of Equations, Hydrostatics and Hydrodynamics ; (2) of Summation and Interpolation of Series, Interest and Annuities, Chances, &c. in Algebra ; of Rotation of Bodies, &c. in Dynamics ; (3) of Problems in Mechanics involving the Differential and Integral Calculus ; (4) of a large increase of examples in all of the subjects, except Geometrical Deductions, that occur in the first Edition, especially in Arithmetic, Algebra, Trigonometry and Mechanics ; (5) of answers to Conic Sections, Exs. 20 -- 46, 170 -- 199.

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, used throughout this work, 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 9, 1847.

- ARITHMETIC.

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

- ALGEBRA. PART I.

- 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 Quadratic Equations

- 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. Scales of Notation
- 22. Logarithms:
- I. Multiplication, Division, Proportion
- II. Involution
- III. Evolution
- IV. Exponential Equations, &c.

- 23. Interest and Annuities
- 24. Chances or Probabilities

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

- GEOMETRICAL DEDUCTIONS

- 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.
- 7. Solutions of Equations
- 8. Subsidiary Angles

- ANALYTICAL GEOMETRY AND CONIC SECTIONS.

- 1. Application of Algebra to Geometry
- 2. Straight Line, &c.
- 3. Circle
- 4. Parabola
- 5. Ellipse
- 6. Hyperbola
- 7. Section of the Cone, and General Problems
- 8. Equations to Curves
- 9. Loci, &c.

- STATICS.

- 1. Forces acting in one Plane, through one point
- 2. Forces acting in one Plane, not through one point
- 3. Forces which do not act in the same plane
- 4. The Centre of Gravity
- 5. Centre of Gravity requiring the Integral Calculus
- 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. Specific Gravity
- 4. Equilibrium of Floating Bodies
- 5. Elastic Fluids
- 6. Machines, &c.

- HYDRODYNAMICS

- ANSWERS.

- Arithmetic
- Algebra. Part I.
- Algebra. Part II.
- Mensuration
- Trigonometry
- Analytical Geometry of Two Dimensions
- Statics
- Dynamics
- Hydrostatics
- Hydrodynamics