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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Page 9
... manner as to make the operations of one illustrate the principles of the other . In order that this method of treating the subject might pre- serve its chief advantage , especially in the initiatory course of the study ; the work has ...
... manner as to make the operations of one illustrate the principles of the other . In order that this method of treating the subject might pre- serve its chief advantage , especially in the initiatory course of the study ; the work has ...
Page 20
... manner . Thus , 4 + 3 may be united into 7. 9-4 may be united into 5. 6—2 + 5 may be united into 9 . EXAMPLES . Unite , as much as possible , the terms in each of the fol- lowing compound quantities . 1. a + b + 8—4 + 2a + 6 + 3b - b + ...
... manner . Thus , 4 + 3 may be united into 7. 9-4 may be united into 5. 6—2 + 5 may be united into 9 . EXAMPLES . Unite , as much as possible , the terms in each of the fol- lowing compound quantities . 1. a + b + 8—4 + 2a + 6 + 3b - b + ...
Page 24
... manner as not to destroy the equation . §38 . The operation of managing an equation , so as to bring the unknown quantity to stand equal to a known quantity , is called solving or reducing the equation . EQUATIONS . - SECTION 1 ...
... manner as not to destroy the equation . §38 . The operation of managing an equation , so as to bring the unknown quantity to stand equal to a known quantity , is called solving or reducing the equation . EQUATIONS . - SECTION 1 ...
Page 26
... manner as if the answer were al- ready found , and you were required to see if it is right . In order to do this , it is customary to represent the unknown quantity by x , y , or some other final letters of the alphabet . §41 . When the ...
... manner as if the answer were al- ready found , and you were required to see if it is right . In order to do this , it is customary to represent the unknown quantity by x , y , or some other final letters of the alphabet . §41 . When the ...
Page 27
... manner similar to the three questions above ; beginning the statement by making a the answer to the question . And in recitation , the whole of it is to be recited . 4. A father once said , that his age was six times that of his son ...
... manner similar to the three questions above ; beginning the statement by making a the answer to the question . And in recitation , the whole of it is to be recited . 4. A father once said , that his age was six times that of his son ...
Common terms and phrases
A's share a²-2ab+b² 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 equal fractions EQUATIONS.-SECTION EXAMPLES exponent factor find the value Find two numbers find x Forming the equation gallons gentleman Given greater 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 pears person principle proportion pupil purse quan question quotient ratio receive Reduce remainder represents rule saddle sheep shillings simple fraction simple quantity Substituting third tity Transposing and dividing Transposing and uniting twice Unite the terms UNITING FRACTIONS Uniting terms unknown quantity vinculum vulgar fraction Whence whole number whole quantity whole x's 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.