# Collection of Examples and Problems in Pure and Mixed Mathematics: With Answers and Occasional Hints

Longman, Brown, Green, Longmans, and Roberts, 1862 - 294 pàgines

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### Continguts

 Compound Interest 14 Discount 15 Stocks lS 12 Single Fellowship 16 Double Fellowship 17 Multiplication 18 Division 19 Least Common Multiple 20 Involution and Evolution 24 Surds 26 I Simple Equations 32 6 8 21 22 24 13 35 Simultaneous Equations of the First Degree 38 Pure Quadratic Equations 40 Simultaneous Equations of the 2nd 3rd c Degrees 44 Problems in Equations of the 2nd and higher Degrees 47 Inequalities 48 Sec Page 11 Arithmetical Progression 49 Geometrical Progression 53 Harmonical Progression 55 Piles of Balls and Shells 56 Permutations and Combinations 57 Binomial and Multinomial Theorems 59 Indeterminate Coefficients 62 Reversion of Series 63 Interpolation of Series 65 Scales of Notation 67 Logarithms 68
 Rational Roots 79 Miscellaneous Theorems and Problems 81 Areas of Plane Figures 91 Surfaces and Contents of Solids 96 Mensuration of Shot Shells and Powder 101 PLANE TRIGONOMETRY 1 Trigonometrical Formula Sc 103 Properties of Plane Figures 109 Trigonometrical Tables 113 6 8 13 119 APPLICATION OF ALGEBRA TO GEOMETRY 121 Circle 127 Ellipse 134 Hyperbola 141 Loci 147 Forces which do not act in the same Plane 158 Centre of Parallel Forces 165 V 174 Sec Page 199 HYDRODYNAMICS 214 Arithmetic 221 Algebra 229 Logarithms 256 264 264 Application of Algebra to Geometry 274 Analytical Geometry and Conic Sections 280 Dynamics 291 Hydrostatics 3 305

### Passatges populars

Pàgina 85 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Pàgina 113 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Pàgina 127 - Express the area of a triangle in terms of the coordinates of its angular points a, b ; a', V ; a", b", 40.
Pàgina 52 - A and B set out to meet each other. A went 3 miles the first day, 5 the second, 7 the third, and so on. B went 4 miles the first day, 6 the second, 8 the third, and so on. In how many days did they meet?
Pàgina 48 - A detachment of an army was marching in regular column, with 5 men more in depth than in front ; but upon the enemy coming in sight, the front was increased by 845 men ; and by this movement the detachment was drawn up in 5 lines. Required the number of men.
Pàgina 59 - C^. 27. A person wishes to make up as many different parties as he can out of 20 friends, each party consisting of the same number ; how many should he invite at a time ? 28. When the No. of Combs. of 2n things taken r together is the greatest possible ; required r. 29. There are 4 regular polyhedrons marked, each face with a different symbol, and the numbers of their faces are 4, 6,8, 12 respectively; taking all of them together, how many different throws are possible ? 30.
Pàgina 83 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.
Pàgina 58 - At a game of cards, 3 being dealt to each person, any one can have 425 times as many hands as there are cards in the pack. How many cards are there 1 12.
Pàgina 12 - If 5 men and 7 boys can reap a field of corn of 125 acres in 15 days; in how many days will 10 men and 3 boys reap a field of corn of 75 acres, each boy's work being one-third of a man's ? 14.
Pàgina 57 - The number of balls in a triangular pile is to the number in a square pile, having the same number of balls in the side of the base, as 6 to 1 1 ; required the number in each pile.