A collection of examples in pure and mixed mathematics, with hints and answers, by A. Wrigley and W.H. Johnstone. By A. Wrigley

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Page 74 - 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 36 - ... of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space.
Page 141 - V up a smooth plane inclined at an angle of 30° to the horizon, and 2 V the other with a velocity -^- at an elevation of 60°.
Page 40 - 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 151 - A beam, 30 feet long, balances itself on a point at one-third of its length from the thicker end ; but when a weight of 10 Ibs. is suspended from the smaller end, the prop must be moved 2 feet towards it, in order to maintain the equilibrium.
Page 73 - 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 107 - The product of all the straight lines that can be drawn from one of the angles of a regular polygon of n sides inscribed in a circle whose radius is a to all the other angular points is па"'1. 8. If £>,, рг, •••i>2„_, , p...
Page 104 - Wanting to know my distance from an inaccessible object 0, on the other side of a river; and having no instrument for taking angles, but only a chain or cord for measuring distances; from each of two stations, A and B, which were taken at 500 yards asunder, I measured in a direct line from the object 0 100 yards, viz. AC and BD each equal to...
Page 100 - 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 35 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then, filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left.

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