Ray's Algebra, Part First: On the Analytic and Inductive Methods of Instruction, with Numerous Practical Exercises, Designed for Common Schools and Academies |
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Page 31
... prime ; a " is read , a second ; a " " is read , a third , and so on . EXAMPLES . The following examples are intended to exercise the learner in the use and meaning of the signs . Of xyz ? 48. For REVIEW . - 46 . What is the dimension ...
... prime ; a " is read , a second ; a " " is read , a third , and so on . EXAMPLES . The following examples are intended to exercise the learner in the use and meaning of the signs . Of xyz ? 48. For REVIEW . - 46 . What is the dimension ...
Page 68
... prime or composite ; and every composite number is the product of two or more prime numbers . The following is a list of the prime numbers under 100 : 1 , 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 ...
... prime or composite ; and every composite number is the product of two or more prime numbers . The following is a list of the prime numbers under 100 : 1 , 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 ...
Page 69
... prime factors of 210 ?. 4. Resolve 4290 into its prime factors .. Ans . 2 , 3 , 5 , 11 , 13 . ART . 89. — A prime quantity , in Algebra , is one which is exactly divisible only by itself and by unity . Thus , a , b , and b + c are prime ...
... prime factors of 210 ?. 4. Resolve 4290 into its prime factors .. Ans . 2 , 3 , 5 , 11 , 13 . ART . 89. — A prime quantity , in Algebra , is one which is exactly divisible only by itself and by unity . Thus , a , b , and b + c are prime ...
Page 70
... prime factors . No general rule can be given , for this case . When the given quantity does not consist of more than three terms , the pupil will generally be able to accomplish it , if he is familiar with the theorems in the preceding ...
... prime factors . No general rule can be given , for this case . When the given quantity does not consist of more than three terms , the pupil will generally be able to accomplish it , if he is familiar with the theorems in the preceding ...
Page 72
... prime factors , when one of them is a monomial , and the other a polyno- mial ? 94. When can a trinomial be separated into two binomial factors ? What are the factors of m2 + 2mn + n2 ? Of c2 - 2cdd2 ? When can a bi- nomial be separated ...
... prime factors , when one of them is a monomial , and the other a polyno- mial ? 94. When can a trinomial be separated into two binomial factors ? What are the factors of m2 + 2mn + n2 ? Of c2 - 2cdd2 ? When can a bi- nomial be separated ...
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added algebraic quantities apples arithmetical progression arithmetical series binomial bushels called cents a piece coefficient common difference complete equation Completing the square denotes Divide the number dividend division dollars entire quantity equal exactly divide exponent expression extract the square find the greatest Find the product Find the square Find the sum find the value following examples fourth fraction geometrical progression geometrical series Give an example greater greatest common divisor Hence last term least common multiple lemon letter minus monomial negative quantities number of terms peaches perfect square polynomial positive quantity pound of coffee preceding prime factors principle proportion pupil quan question quotient ratio Reduce remainder represent the cost represent the number required the numbers required to find result rule second degree solution square root subtracted theorem three numbers tion tities transposing unknown quantity whole number
Popular passages
Page 100 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 22 - Required the distance from A to B, from B to C, and from C to D.
Page 176 - 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 136 - In any proportion, the product of the means is equal to the product of the extremes.
Page 122 - 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 62 - 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 78 - To find the greatest common divisor of three or more quantities, first find the greatest common divisor of two of them ; then, of that divisor and one of the other quantities, and so on. The last divisor thus found, will be the greatest common divisor sought.
Page 59 - 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.
Page 137 - A farmer has 2 horses, and a saddle worth 25 dollars ; now, if the saddle be put on the first horse, his value will be double that of the second ; but, if the saddle be put on the second horse, his value will be three times that of the first.
Page 219 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space.