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 14
... Divide $ 1000 among A , B , and C ; so that B shall have $ 72 more than A , and C shall have $ 172 more than A. By the statement , B's share is equal to A's and $ 72 be- sides . We may write it thus , A's + $ 72 . C's share is equal to ...
... Divide $ 1000 among A , B , and C ; so that B shall have $ 72 more than A , and C shall have $ 172 more than A. By the statement , B's share is equal to A's and $ 72 be- sides . We may write it thus , A's + $ 72 . C's share is equal to ...
Page 16
... together , Dividing by 10 , C + 3C + 6C - 70 . B's is three times as A's is twice B's ; or 10C = 70 . C = 7 . C's age = 7 years . much , or 21 years . 42 years . Proof , 70 §7 . We very often wish to state that we 16 ALGEBRA .
... together , Dividing by 10 , C + 3C + 6C - 70 . B's is three times as A's is twice B's ; or 10C = 70 . C = 7 . C's age = 7 years . much , or 21 years . 42 years . Proof , 70 §7 . We very often wish to state that we 16 ALGEBRA .
Page 17
... Dividing by 2 , 130 more . The successful candidate had A = 339 . 339 . The unsuccessful one , 130 less = 209 . Proof 548 . §9 . Des Cartes , * a Frenchman , who wrote about 1637 , used the ... divide $ 300 among 2 * PRELIMINARY REMARKS . 17.
... Dividing by 2 , 130 more . The successful candidate had A = 339 . 339 . The unsuccessful one , 130 less = 209 . Proof 548 . §9 . Des Cartes , * a Frenchman , who wrote about 1637 , used the ... divide $ 300 among 2 * PRELIMINARY REMARKS . 17.
Page 18
... divide $ 300 among A , B , and C ; so that A may have twice as much as B , and C may have as much as A and B ... Dividing by 6 , x = 50 . Therefore , B's share is $ 50 . A's is twice as much , or $ 100 . C's as much as both , or $ 150 ...
... divide $ 300 among A , B , and C ; so that A may have twice as much as B , and C may have as much as A and B ... Dividing by 6 , x = 50 . Therefore , B's share is $ 50 . A's is twice as much , or $ 100 . C's as much as both , or $ 150 ...
Page 23
... dividing that co - efficient . Thus , 8x divided by 2 = 4x . 12x divided by 4 = 3x , & c . §32 . In 1661 , Rev. William Oughtred of England , pub- lished a work , in which he introduced the sign X to repre- sent multiplication . Thus ...
... dividing that co - efficient . Thus , 8x divided by 2 = 4x . 12x divided by 4 = 3x , & c . §32 . In 1661 , Rev. William Oughtred of England , pub- lished a work , in which he introduced the sign X to repre- sent multiplication . Thus ...
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.