Ray's Algebra, Part First: On the Analytic and Inductive Methods of Instruction, with Numerous Practical Exercises, Designed for Common Schools and Academies, Part 1 |
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Page 30
... evident . ART . 46. Each of the literal factors of any simple quantity or term is called a dimension of that term ; and the degree of any term depends on the number of its literal factors . REVIEW . - 38 . Thus , ax consists of two ...
... evident . ART . 46. Each of the literal factors of any simple quantity or term is called a dimension of that term ; and the degree of any term depends on the number of its literal factors . REVIEW . - 38 . Thus , ax consists of two ...
Page 33
... a , thus : 3a 4a 5a 12a REVIEW . - 53 . What is algebraic addition ? When quantities are simi . lar , and have the same sign , how are they added together ? It is evident that the sum of 3 times a EXAMPLES IN NOTATION . 33.
... a , thus : 3a 4a 5a 12a REVIEW . - 53 . What is algebraic addition ? When quantities are simi . lar , and have the same sign , how are they added together ? It is evident that the sum of 3 times a EXAMPLES IN NOTATION . 33.
Page 34
... evident that the sum of 3 times a , 4 times a , and 5 times a , would be 12 times a , or 12a , whatever a might represent . 2. In the same manner the sum of —3a , —4a , and —5a -3a would be -12a . Hence , the RULE , -4a -5a -12a FOR ...
... evident that the sum of 3 times a , 4 times a , and 5 times a , would be 12 times a , or 12a , whatever a might represent . 2. In the same manner the sum of —3a , —4a , and —5a -3a would be -12a . Hence , the RULE , -4a -5a -12a FOR ...
Page 35
... evident , the true result will be found , by + 10c adding the positive quantities into one sum , and the -4c negative quantities into another , and then taking -3c their difference . It is thus found that he received + 18c 25c , and ...
... evident , the true result will be found , by + 10c adding the positive quantities into one sum , and the -4c negative quantities into another , and then taking -3c their difference . It is thus found that he received + 18c 25c , and ...
Page 36
... evident that the question is impossible . But if we suppose that James had a certain sum of money before he received the 5c , we may inquire how much less money he had after the operation , than before it ; or , in other words , what ...
... evident that the question is impossible . But if we suppose that James had a certain sum of money before he received the 5c , we may inquire how much less money he had after the operation , than before it ; or , in other words , what ...
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Common terms and phrases
acre added algebraic quantities apples arithmetical progression arithmetical series binomial Binomial Theorem bought bushels coefficient common difference complete equation Completing the square cost Divide the number dividend division dollars entire quantity equal EQUATIONS CONTAINING exactly divide exponent expressed extract the square Find a number Find the cube Find the product Find the square Find the sum find the value following examples fraction geometrical progression geometrical series Give an example greater greatest common divisor Hence least common multiple lemons less number letter minus monomial negative quantity number of places number of terms oranges perfect square polynomial positive quantity preceding principle proportion pupil quan question quotient radical sign ratio reduced remainder represent the number required the numbers required to find result second degree second power solution solving square root three numbers tities Transposing twice unknown quantity whole number yards
Popular passages
Page 60 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 106 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 178 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 235 - In any proportion the product of the means is equal to the product of the extremes.
Page 124 - 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 equal to 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Let x be the number of leaps taken by the hound.
Page 217 - If, then, any problem furnishes an equation in which the known term is negative, and greater than the square of half the coefficient of the first power of the unknown quantity, we infer, that the conditions of the problem are incompatible with each other.
Page 64 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 81 - The least Common Multiple of two or more quantities is the least quantity that will contain them exactly. Thus, 6 is the least common multiple of 2 and 3 ; and lOxy is the least common multiple of 2x and by. NOTE. — LCM stands for least common multiple.
Page 232 - If we compare the numbers 2 and 6, by the first method, we say that 2 is 4 less than 6, or that 6 is 4 greater than 2. If we compare 2 and 6 by the second method, we say that 6 is equal to three times 2, or that 2 is one third of 6.