# The first principles of algebra, for the use of the boys of the Royal hospital schools, Greenwich

### Contents

 DEFINITIONS c 1 MULTIPLICATION 17 FRACTIONS 37 INVOLUTION 50 QUADRATIC EQUATIONS 98
 RATIOS 111 ARITHMETICAL PROGRESSION 118 FRACTIONAL INDICES AND SURDS 130 MULTIPLICATION AND DIVISION OF SURDS 136

### Popular passages

Page 116 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 91 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days ; how many days would the man alone be in drinking it ? Ans.
Page 118 - If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents.
Page 91 - A hare is 50 leaps before a greyhound, and takes 4 leaps to- the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.
Page 23 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 23 - The square of the sum of two quantities is equal to the square nf the first, plus twice the product of the first by the second, plus the square of the second.
Page 23 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second.
Page 1 - The Sign of Subtraction, — , is read minus. It denotes that the quantity to which it is prefixed is to be subtracted. Thus, a — b, denotes that b is to be subtracted from a.
Page 128 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Page 62 - First, if necessary, clear of fractions ; then transpose all the terms containing the unknown quantity to one side of the equation, and the known quantities to the other.