## Gradiations in Algebra: In which the First Principles of Analysis are Inductively Explained ... |

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### Common terms and phrases

a-Hb A's share added ALGEBRAICAL QUANTITIES answer apples arithmetic barley bought bushels called cents apiece chaise change the sign co-efficient compound quantity denotes difference digits Divide the number dividend division dollars earponent equal EQUATIONS.—SECTION equivalent fraction example factor find ac find the value Find two numbers Forming the equation gallons gentleman Given greater half harness improper fraction last member left pocket less letter literal quantities lowest terms manner merator method minus multiply the numerator number of yards numeral quantities obtain paid pears person principle proportion pupil purse quan question quotient ratio receive Reduce remainder represents saddle sheep shillings simple fraction simple quantity Substituting subtract 13 third tity Transposing and dividing Transposing and uniting Transposition twice Unite the terms UNITING FRACTIONS Uniting terms unknown quantity vinculum vulgar fraction Whence whole number whole quantity wine worth

### 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.