CONTENTS. page Questions on general principles, Questions on logarithms and plane trigonometry, Questions on hights and distances, navigation and surveying, Questions on conic sections and spherical trigonometry, General principles of arithmetic, General principles of algebra, General principles of geometry, General principles of logarithms, General principles of plane trigonometry, General principles of mensuration, General principles of hights and distances, Ceneral principles of navigation General principles of surveying, General principles of conic sections, General principles of spherical trigonometry, General principles of mechanics, Solutions in algebra, including reduction of simple equations, prob- lems in simple equations, involution, Examples of fractions containing powers, Reduction of radical quantities, Multiplication and division of radical quantities, Involution of radical quantities, Examples in radical quantities, Reduction of equations by involution, Examples of quadratic equations, Problems producing quadratic equations, Problems containing two or more unknown quantities, Examples of geometrical ratio, . Problems in geometrical progression, Problems in geometrical progression, Division by compound divisors, Involution and expansion of binomials, Promiscuous examples in binomials, Evolution of compound quantities, 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, Theory and construction of logarithms, Multiplication, division, involution, and evolution by logarithms, 236 Compound interest by logarithms, Increase of population by logarithms, Different systems of logarithms, Computation of common or Brigg's logarithms, Various explanations in trigonometry, Solutions of oblique angled triangles, Expressions for the area of a triangle in terms of the sides, Particular solutions of triangles, Areas of figures bounded by right lines, 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, Promiscuous examples of hights and distances, Laying out, dividing lands, and levelling, Composition and resolution of motion, Questions for practice on the lever, Questions for practice on the pulley, wheel, and axle, Questions on the inclined plane and screw, Table of circular segments, the compass, Table of logarithms of numbers, Table of logarithmic sines, &c. 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 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 ad. dition? 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 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 numer. ator 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 |