The Elements of AlgebraHarper & Bros., 1856 - 268 σελίδες |
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Σελίδα 21
... examples of this kind admit of proof . The results are proved to be correct when they fulfill all QUEST .-- What is a coefficient ? How is an algebraic problem solv . ed ? How is an equation reduced ? the conditions of the problem . In ...
... examples of this kind admit of proof . The results are proved to be correct when they fulfill all QUEST .-- What is a coefficient ? How is an algebraic problem solv . ed ? How is an equation reduced ? the conditions of the problem . In ...
Σελίδα 46
... examples are designed to exercise the pupil upon the preceding definitions and remarks . ( 36. ) Examples in which words are to be translated into algebraic symbols . Ex . 1. What is the algebraic expression for the fol- lowing ...
... examples are designed to exercise the pupil upon the preceding definitions and remarks . ( 36. ) Examples in which words are to be translated into algebraic symbols . Ex . 1. What is the algebraic expression for the fol- lowing ...
Σελίδα 47
... Examples in which the algebraic signs are to be translated into common language . Ex . 1 . nx a + b · + mx = · d Ans . The quotient arising from dividing the sum of a and b by c , increased by the product of m and x , is equal to the ...
... Examples in which the algebraic signs are to be translated into common language . Ex . 1 . nx a + b · + mx = · d Ans . The quotient arising from dividing the sum of a and b by c , increased by the product of m and x , is equal to the ...
Σελίδα 53
... following terms : 11bc + 4ad - 8x 8x + 7bc - 2ad 2cd - 2ad - 2bc . QUEST . - Give the rule . What is the most convenient mode of ar ranging the terms ? These terms may be written thus : Sum , 11bc ADDITION . 53 Examples.
... following terms : 11bc + 4ad - 8x 8x + 7bc - 2ad 2cd - 2ad - 2bc . QUEST . - Give the rule . What is the most convenient mode of ar ranging the terms ? These terms may be written thus : Sum , 11bc ADDITION . 53 Examples.
Σελίδα 60
... Examples . Ex . 1. From 7x + 4y take 3x2 - 2y . Ans . 4x2 + 6y . ( 4. ) ( 2. ) ( 3. ) From 5a2 - 2b 5xy + 8x - 2 x2 + 2xy + y ' Take 2a2 + 5b 3xy - 8x - 7 x2 - 2xy + y2 Rem . 3a2 - 7b ( 5. ) ( 6. ) ( 7. ) From 3a2 + ax + 2x2 10-8x - 3xy ...
... Examples . Ex . 1. From 7x + 4y take 3x2 - 2y . Ans . 4x2 + 6y . ( 4. ) ( 2. ) ( 3. ) From 5a2 - 2b 5xy + 8x - 2 x2 + 2xy + y ' Take 2a2 + 5b 3xy - 8x - 7 x2 - 2xy + y2 Rem . 3a2 - 7b ( 5. ) ( 6. ) ( 7. ) From 3a2 + ax + 2x2 10-8x - 3xy ...
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.