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

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

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Page 87 - 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.
Page 115 - 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.
Page 129 - Express the area of a triangle in terms of the coordinates of its angular points a, b ; a', V ; a", b", 40.
Page 54 - 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?
Page 50 - 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.
Page 61 - 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.
Page 85 - 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.
Page 60 - 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.
Page 14 - 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.
Page 59 - 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.

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