PROBLEMS PRODUCING QUADRATIC EQUATIONS.

117. What number is it, whose half multiplied by its third part, gives 864?

Ans. 72.

118. It is required to find a number, such that if we first add it to 94, then subtract it from 94, and afterwards multiply this remainder by the former sum, the product may be 8512. What number is it?

Ans. 18. 119. What two numbers are those whose product is 144,

and whose quotient is 9?

120. What two numbers are

=a, and whose quotient is =b?

Ans. 36 and 4. those whose product is

Ans. √ab and √

121. A gentleman left L.210 to three servants, to be divided in geometrical progression, so that the first shall have L.90 more than the last. Find their legacies.

Ans. L.120, L.60, L.30.

122. A certain capital yields 4 per cent.; if we multiply the number of pounds in the capital by the number of pounds in the interest for five months, we obtain 1170413. What is the capital? Ans. 2650.

123. There are two numbers, one of which is greater than the other by 8, and whose product is 240. What numbers are they? Ans. 12 and 20. 124. It is required to find a number, whose square exceeds its simple power by 306?

Ans. 18.

125. It is required to find a number, such that if we multiply its third part by its fourth part, and to the product add five times the number required, this sum exceeds the number 200 by as many as the number sought is less than 280?

126. A person buys some pieces of cloth, at for L.60. Had he got 3 more pieces for the each piece would have cost him a pound less. pieces did he buy?

Ans. 48. equal prices, same sum, How many

Ans. 12.

127. A person dies, leaving children, and a fortune of L.46,800, which, by the will, is to be divided equally among them. It happens, however, that immediately after the death of the father, two of his children also die. If, consequently, each child receives L.1950 more than he or she was formerly entitled to by the will, how many children were there? Ans. Eight.

128. Two retailers jointly invest L.500 in business, to which each contributes a certain sum; the one let his money remain five months, the other only two, and each received L.450 capital and profit. How much did each advance ? Ans. One L.200, the other L.300. 129. What two numbers are those whose sum is 41, and the sum of whose squares 901? Ans. 26 and 15. 130. A capital of L.5000 stands at 4 cent. compound interest. What will it amount to in forty years? Ans. L.24005, 2s. 1d.

per

131. How long must L.3600 remain at 5 per cent. compound interest, so that it may become as much as L.5000, at 4 per cent. for twelve years? Ans. 16 years, 136 days. 132. What capital, at 4 per cent., will fifteen years hence be equal in value to L.4500, at 6 per cent., for nine years? Ans. L.4221.483.

133. A town contains 20,000 inhabitants, and we know that the population has regularly increased yearly. What was its population ten years ago? Ans. 14,882.

134. In how many years will the population of a place become ten times as great as it is at present, if the yearly increase amount to three persons in a hundred?

Ans. 78 years nearly. 135. What is the present value of an annuity of L.20, to continue for forty years, reckoning interest at the rate of 6 per cent. per annum. Ans. L.300, 18s. 6d.

136. What annuity, improved at the rate of 4 per cent. per annum, compound interest, will at the end of twelve years amount to L.500, 17s. 2d.? Ans. L.33, 6s. 8d.

A SYSTEM

OP

PRACTICAL MATHEMATICS,

PART II.

CONTAINING

LOGARITHMIC ARITHMETIC, TRIGONOMETRY, MENSURATIon of HEIGHTS AND DISTANCES, NAVIGATION, MENSURATION OF SURFACES AND SOLIDS, LAND-SURVEYING, SPECIFIC GRAVITY, AND GAUGING.

WITH A COPIOUS AND HIGHLY ACCURATE SET OF

STEREOTYPED LOGARITHMIC TABLES.

BEING PART SECOND OF

No. XVI.

OF

A NEW SERIES OF SCHOOL-BOOKS.

BY THE

SCOTTISH SCHOOL-BOOK ASSOCIATION.

Published for the Association, by
WILLIAM WHYTE AND CO.

BOOKSELLERS TO THE QUEEN DOWAGER,

13, GEORGE STREET, EDINBURGH.

HOULSTON AND STONEMAN, LONDON; W. GRAPEL, AND G. H. AND J. SMYTH, LIVERPOOL; ABEL HEYWOOD, MANCHESTER; FINLAY AND CHARLTON, NEWCASTLE.

MDCCCXLVI.

EDINBURGH:

ANDREW JACK, PRINTER,

NIDDRY STREET.

PREFACE

In publishing" Part II. of a System of Practical Mathematics," the Committee beg to state, that they have used every effort in their power to secure perfect accuracy in the Answers to the questions, which are all given as they can be obtained from the Tables at the end of the volume. This is a very important point to both Teacher and Student; and yet it is one that has very generally been overlooked in Treatises on Practical Mathematics.

The article on LOGARITHMS contains all that is necessary, to be known in regard to their practical applications to common numerical calculations.

The article on TRIGONOMETRY embraces the modern improvements in the science. By adopting the definitions of the trigonometrical ratios, now used in all theoretical treatises on the subject, it became necessary to demonstrate all the Rules in a different manner from that followed in other practical treatises on the subject; and the consequence is, that the demonstrations have thereby been greatly simplified. The method of surveying by Rectangular Co-ordinates, here given for the first time, will be found very useful in extensive surveys, and also in Marine Surveying. The rule for finding the angles of a triangle when the three sides are given, is new.

The articles on MENSURATION OF SURFACES and SOLIDS, LAND SURVEYING, and SPECIFIC GRAVITIES, contain clear and perspicuous Rules, illustrated by suitable Examples, and a collection of Exercises, sufficiently numerous to render the Pupil expert in performing the various calculations, and the Practical Measurer acquainted with the most approved methods of taking dimensions.