The Elements of AlgebraHarper & Bros., 1856 - 268 σελίδες |
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Σελίδα 43
... , multi- plied by itself a certain number of times , will produce the given quantity . QUEST . - What is an exponent ? What is a root of a quantity ? ✓ The symbol is called the radical sign , and DEFINITIONS . 43 Exponent-Root.
... , multi- plied by itself a certain number of times , will produce the given quantity . QUEST . - What is an exponent ? What is a root of a quantity ? ✓ The symbol is called the radical sign , and DEFINITIONS . 43 Exponent-Root.
Σελίδα 59
... given , we first The result , then , must be 10 . operation on the numbers as they subtract 8 from 15 and obtain 7. This result is too small by 3 , because the number 8 is larger by 3 thar the number which was required to be subtracted ...
... given , we first The result , then , must be 10 . operation on the numbers as they subtract 8 from 15 and obtain 7. This result is too small by 3 , because the number 8 is larger by 3 thar the number which was required to be subtracted ...
Σελίδα 60
... given in the subtrahend . ( 48. ) Hence we deduce the following general RULE . Conceive the signs of all the terms of the subtra- hend to be changed from + to — or from — to + , and then collect the terms together as in the several ...
... given in the subtrahend . ( 48. ) Hence we deduce the following general RULE . Conceive the signs of all the terms of the subtra- hend to be changed from + to — or from — to + , and then collect the terms together as in the several ...
Σελίδα 71
... given in multiplication have been confined to positive quantities , and the pro- ducts have all been positive . We must now establish a general rule for the signs of the product . First . If + a is to be multiplied by + b , this signi ...
... given in multiplication have been confined to positive quantities , and the pro- ducts have all been positive . We must now establish a general rule for the signs of the product . First . If + a is to be multiplied by + b , this signi ...
Σελίδα 78
... given , that is , the divisor ; and it is required to find the other factor , which we call the quotient . CASE I. ( 70. ) When the divisor and dividend are both mo- omials . Suppose we have 72 to be divided by 8. We must find such a ...
... given , that is , the divisor ; and it is required to find the other factor , which we call the quotient . CASE I. ( 70. ) When the divisor and dividend are both mo- omials . Suppose we have 72 to be divided by 8. We must find such a ...
Συχνά εμφανιζόμενοι όροι και φράσεις
A's share apples arithmetical means arithmetical progression bers binomial binomial theorem brandy cents coefficient common denominator common difference complete equation Completing the square cube denotes digits Divide the number dividend divisor dollars equal Examples exponent extract the square factor Find the square Find the sum find the value Find two numbers following RULE four quantities fourth power gallons geometrical progression Give the rule Given greater number Hence horse last term least number Let x represent letters lowest terms metical miles per hour mixed quantity monomial multiplied number of terms obtain paid pears perfect square polynomial preceding problem Prob QUEST.-Give the rule QUEST.-How QUEST.-What quotient radical quantities receive Reduce remainder represent the number Required the square result second degree second power second term shillings solved square root subtract tion Transposing twice units unknown quantity values of x Whence worth yards
Δημοφιλή αποσπάσματα
Σελίδα 75 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Σελίδα 96 - To reduce fractions to a common denominator. RULE. Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Σελίδα 73 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Σελίδα 94 - To reduce a mixed number to an improper fraction, — RULE : Multiply the whole number by the denominator of the fraction, to the product add the numerator, and write the result over the denominator.
Σελίδα 85 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...
Σελίδα 134 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Σελίδα 76 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Σελίδα 225 - Three quantities are in proportion when the first has the same ratio to the second, that the second has to the third ; and then the middle term is said to be a mean proportional between the other two.
Σελίδα 192 - Multiply the divisor thus increased by the last term of the root, and subtract the product from the last remainder.
Σελίδα 174 - RULE. 1. Separate the given number into periods of two figures, each, beginning at the units place.