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

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

Published $\text {1862}$, Longman, Brown, Green, and Longmans.


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 Sixth Edition is a reprint of the Fifth corrected.

January 1862.




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