## A collection of problems and examples adapted to the 'Elementary course of mathematics'. |

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acting angle arithmetical axis ball base beam body centre circle common concave containing convex course cylinder described determine difference direction distance Divide double elastic equal equation Express extremity fall feet fixed fluid focal length focus force four geometrical given given weight greater half horizontal immersed inches incident inclined plane inscribed known lens less means measured miles mirror move Multiply object observed opposite parallel passing person placed plane position pressure prism Problems progression projected proportion Prove pully quantities radii radius ratio rays receiver reflected refracted respectively rest shew shillings sides space specific gravity sphere square string supposing surface taken third tower triangle twice uniform velocity vertical vessel weight whole

### Popular passages

Page 23 - A man travelled 105 miles, and then found that if he had not travelled so fast by 2 miles an hour, he should have been 6 hours longer in performing the journey.

Page 22 - B, can perform a piece of work together in 16 days. They work together for 4 days, when A being called off, B is left to finish it, which he does in 36 days more. In what time would each do it separately ? Ans. A in 24 days, B in 48 days.

Page 22 - There is a cistern, into which water is admitted by three cocks, two of which are of exactly the same dimensions. When they are all open, five-twelfths of the cistern is filled in four hours; and if one of the equal cocks be stopped, seven-ninths of the cistern is filled in ten hours and forty minutes.

Page 52 - A person standing at the edge of a river observes that the top of a tower on the edge of the opposite side subtends an angle of 55° with a line drawn from his eye parallel to the horizon ; receding backwards 30 feet, he then finds it to subtend an angle of 48°. Determine the breadth of the river. log. sin 7° = 9.08589 log.

Page 32 - 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 89 - A descends alone ; the pressure of the atmosphere is equal to that of a column of water...

Page 21 - Fifteen guineas should weigh four ounces ; but a parcel of light gold having been weighed and counted, was found to contain 9 more guineas than was supposed from the weight ; and a part of the whole, exceeding the half by four guineas and a half, was found to be 1-^ oz.

Page 31 - If the first has to the second the same ratio which the third has to the fourth...

Page 24 - For every yard of the better sort he gave as many shillings as he had yards in all ; and for every yard of the worse as many shillings as there were yards of the better sort more than of the worse. And the whole price of the better sort was to the whole price of the worse as 72 to 7. How many yards had he of each ? Ans.

Page 94 - There are three plane reflectors, two of which are at right angles to each other, and a ray of light is incident upon the third, and reflected successively by each of them...