## Gradations in Algebra in which the First Principles of Analysis are Inductively Explained: Illustrated by Copious Exercises, and Made Suitable for Primary Schools |

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### Common terms and phrases

A's share added Algebra answer apples asked becomes bought called cents chaise changed co-efficient common compound quantity condition contained cost course denominator denotes difference Divide dividend division divisor dollars equal evident EXAMPLES expressed factor figures find the value Forming the equation four fourth fraction gallons gave give Given greater half Hence horse kind known less letter literal lowest terms man's manner means method minus Multiply obtain operation paid pears performed person pocket pounds principle PROBLEMS proportion pupil question quotient ratio receive Reduce remainder represents result rule share sheep shillings shown sides simple quantity sort stand Substituting subtract Suppose third Transposing Transposing and uniting twice Unite the terms Uniting terms unknown quantity vinculum whole wine wish worth writing written yards

### Popular passages

Page 57 - A man driving his geese to market, was met by another, who said, good morrow, master, with your hundred geese...

Page 139 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.

Page 121 - Prove that the square of the sum of any two numbers equals the square of the first number, plus twice the product of the two numbers, plus the square of the second number.

Page 82 - A sum of money was divided between two persons, A and B, so that the share of A was to that of B as 5 to 3.

Page 45 - A person, at the time he was married, was 3 times as old as his wife ; but after they had lived together 15 years, he was only twice as old ; what were their ages on their wedding day ? Ans.

Page 80 - Prob. 14. A ship and a boat are descending a river at the same time. The ship passes a certain fort, when the boat is 13 miles below. The ship descends five miles, while the boat descends three. At what distance below the fort will they be together ? Ans.

Page 100 - There is a certain number, consisting of two digits, the sum of which digits is 5 ; and if 9 be added to the number itself the digits will be inverted ; what is the number?

Page 79 - Two men commenced trade together ; the first put in $40 more than the second, and the stock of the first was to that of the second as 5 to 4 ; what was the stock of each ? Ans. $200, and $160.

Page 55 - A post is one-fourth of its length in the mud, one-third in the water, and 10 feet above the water ; what is its whole length ? Ans. 24 feet.

Page 72 - ... 5, respectively ? Ans. 10 and 2 30. A person in play lost a fourth of his money, and then won back 3s., after which he lost a third of what he now had, and then won back 2s. ; lastly, he lost a seventh of what he then had, and after this found he had but 12s. remaining ; what had he at first ? Ans. 20s.