CONTENTS.

QUESTIONS on general principles,

Questions on arithmetic,

Questions on algebra,

Questions on geometry,

Questions on logarithms and plane trigonometry,

Questions on mensuration,

Questions on hights and distances, navigation and surveying,

Questions on conic sections and spherical trigonometry,

page

ib.

2

5

7

8

10

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

lems in simple equations, involution,

101

103

104

104

105

Infinite series, including indeterminate co-efficients, summation of

series, recurring series, and method of differences,

Composition and resolution of the higher equations,

Newton's method of approximation,

Application of algebra to geometry,

176

191

193

196

Multiplication, division, involution, and evolution by logarithms,

236

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

283

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

354

Table of circular segments,

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

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 subtraction? What is the minuend? 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 number? 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 performing 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 division? 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 fraction? 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