CONTENTS.

5

8

.

9

page

QUESTIONS on general principles,

1

Questions on arithmetic,

ib.

Questions on algebra,

2

Questions on geometry,

Questions on logarithms and plane trigonometry,

7

Questions on mensuration,

Questions on hights and distances, navigation and surveying, .

Questions on conic sections and spherical trigonometry,

10

Questions on mechanics,

11

Supplementary questions,

14

General principles of arithmetic,

17

General principles of algebra,

23

General principles of geometry,

33

General principles of logarithms,

58

General principles of plane trigonometry,

60

General principles of mensuration,

62

General principles of hights and distances,

66

Ceneral principles of navigation

67

General principles of surveying,

63

General principles of conic sections,

71

General principles of spherical trigonometry,

75

General principles of mechanics,

78

Solutions in arithmetic,

89

Solutions in algebra, including reduction of simple equations, prob-

lems in simple equations, involution,

101

Multiplication of powers,

103

Examples of fractions containing powers,

104

Reduction of radical quantities,

104

Addition and subtraction of radical quantities,

105

.

1

Multiplication and division of radical quantities,

106

Involution of radical quantities,

107

Examples in radical quantities,

108

Reduction of equations by involution,

111

Examples of quadratic equations,

117

Problems producing quadratic equations,

123

Problems containing two or more unknown quantities,

129

Solutions by substitution,

142

Examples of geometrical ratio,

143

Examples of proportion,

145

Arithmetical progression,

150

Problems in geometrical progression,

152

Geometrical progression,

155

Problems in geometrical progression,

156

Division by compound divisors,

162

Greatest common measure,

164

Involution and expansion of binomials,

166

Promiscuous examples in binomials,

169

Evolution of compound quantities,

173

Roots of binomial surds,

175

Infinite series, including indeterminate co-efficients, summation of

series, recurring series, and method of differences,

176

Composition and resolution of the higher equations,

191

Newton's method of approximation,

193

Application of algebra to geometry,

196

Equation of curves,

215

Geometry,

218

History of logarithms,

221

Theory and construction of logarithms,

228

Multiplication, division, involution, and evolution by logarithms, 236

Compound interest by logarithms,

238

Increase of population by logarithms,

241

Exponential equations,

244

Different systems of logarithms,

246

Computation of common or Brigg's logarithms,

255

Various explanations in trigonometry,

259

Solutions of right angled triangles,

262

.

286

288

291

294

308

311

315

321

323

327

.

328

330

331

Solutions of oblique angled triangles,

Trigonometrical analysis,

Theorems for practice,

Expressions for the area of a triangle in terms of the sides,

Particular solutions of triangles,

Various explanations,

Areas of figures bounded by right lines,

Reduction of the formulæ,

The quadrature of the circle and its parts,

Promiscuous examples of areas,

Solids bounded by plane surfaces,

The cylinder, cone, and sphere,

Promiscuous examples of solids,

Hights and distances,

Promiscuous examples of hights and distances,

Navigation,

Examples for practice,

Parallel sailing,

Middle latitude sailing,

Mercator's Sailing,

Traverse Sailing,

Oblique Sailing,

Current Sailing,

Surveying,

Laying out, dividing lands, and levelling,

Mechanics,

Questions for practice,

Composition and resolution of motion,

Questions for practice,

Collision of Bodies,

Questions for practice on the lever,

Questions for practice on the pulley, wheel, and axle,

Questions on the inclined plane and screw,

The motions of bodies on inclined planes,

Questions on the pendulum,

Remarks on the tables,

Table of square roots and cube roots,

332

333

335

338

339

1

340

343

344

345

349

350

.

Q

Table of circular segments,
Table of logarithmic sines, &c. to every point and quarter point of

the compass,

Table of logarithms of numbers,

Table of logarithmic sines, &c.

Table of meridional parts,

Supplementary principles,

461

Remarks on arithmetic,

464

Additional solutions,

466

Remarks on the canon,

466

Applications of mechanics,

467

Amusing problems,

468

Latin translations from the Greek Anthology,

471

.

axion

kinds

QUESTIONS FOR EXAMINATION.

INTRODUCTION.

What is mathematics? What is quantity ? On what is mathe. matics based? What are pure, and what are mixed mathematics ? What are definitions ? What is a complete definition? What is an axiom? What is a theorem? What is a problem? Of what two kinds is demonstration ? What is a lemma ? What is a corollary? What is a postulate ? When is a quantity given ? How may a quan. tity be given in geometry? When are two propositions contrary to each other? When is one proposition the converse of another ?

ARITHMETIC.

What is arithmetic? What are its five principal rules? What is numeration ? What is simple addition ? What is simple subtrac. tion? What is the ininuend? What is the subtrahend? What is the difference between the minuend and subtrahend called? What is simple multiplication? What is the multiplicand? What is the multiplier ? What is the product? What are the factors ? What is resolving a given number into factors ? What is a composite num. ber? What is the rule for performing simple multiplication? What is simple division? What is the dividend ? What is the divisor ? What is the quotent? What is the remainder ? What is the rule for performing simple division? What is short division? What is compound addition? What is the rule for performing compound addition? What is compound subtraction ? What is the rule for ferforming compound subtraction? What is compound multiplication ? What is the rule for performing compound multiplication? What is compound division? What is the rule for performing compound di. vision? What is reduction? Of how many kinds is it? What is reduction descending? What is reduction ascending ? What are fractions ? What is a vulgar fraction? What is every fraction an instance of? What effect has multiplying the numerator on the value of the fraction? What multiplying the denominator ? If both numerator and denominator be multiplied or divided by the same number, how will the value of the fraction be affected ? How are several fractions reduced to a common denominator? What is a proper frac. tion? What is an improper fraction ? What is a compound fraction ? What is a mixed fraction? How may vulgar fractions be added, subtracted, multiplied, or divided ? What is a decimal fraction? What is centage? What is commission ? What is duty ? What is inter