The elements of algebraDeighton, 1841 - 305 páginas |
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Página 76
... side to the other , if their signs be changed , and the two sides will still be equal . Let a + 10 = 15 , then by subtracting 10 from each side , + 10-10 = 15 10 ( Art . 80 ) , or æ = 15 – 10 . - - Let x − 4 = 6 , by adding 4 to each side ...
... side to the other , if their signs be changed , and the two sides will still be equal . Let a + 10 = 15 , then by subtracting 10 from each side , + 10-10 = 15 10 ( Art . 80 ) , or æ = 15 – 10 . - - Let x − 4 = 6 , by adding 4 to each side ...
Página 77
... side , and the rational quantities the other , and then raising both sides to that power which will rationalize the surd . α Thus , if √a + a - b = c , by transposition √ a + x = b + c , and a + x = ( b + c ) . ( Art . 81 ) . If the ...
... side , and the rational quantities the other , and then raising both sides to that power which will rationalize the surd . α Thus , if √a + a - b = c , by transposition √ a + x = b + c , and a + x = ( b + c ) . ( Art . 81 ) . If the ...
Página 78
... side of an equation be raised to the same power , the results will be equal . ( Art . 81. ) Let x = 9 ; then x = 9x9 = 81 . Also , if the same root be extracted on both sides , the results will be equal . Let x 81 ; then a 9 ( Art . 138 ) ...
... side of an equation be raised to the same power , the results will be equal . ( Art . 81. ) Let x = 9 ; then x = 9x9 = 81 . Also , if the same root be extracted on both sides , the results will be equal . Let x 81 ; then a 9 ( Art . 138 ) ...
Página 79
... side of the equation , and the known quantities to the other ( Art . 181 ) ; divide both sides by the coefficient , or sum of the coefficients , of the unknown quantity , and the value required is obtained . Ex . 1. To find the value of ...
... side of the equation , and the known quantities to the other ( Art . 181 ) ; divide both sides by the coefficient , or sum of the coefficients , of the unknown quantity , and the value required is obtained . Ex . 1. To find the value of ...
Página 80
... sides by this number , 70x + 80 − 45x + 60 = 24x + 8 - - 116+ 32x , 70x – 45x – 24x – 32x = 8 – 116 – 80 – 60 , - - – 31x = - 248 - or 31 248 - 248 .. x = = 8 . 31 Ex . 7. √a + x + √ a − x = 2√x ; required a . √ a + x = 2 √ x ...
... sides by this number , 70x + 80 − 45x + 60 = 24x + 8 - - 116+ 32x , 70x – 45x – 24x – 32x = 8 – 116 – 80 – 60 , - - – 31x = - 248 - or 31 248 - 248 .. x = = 8 . 31 Ex . 7. √a + x + √ a − x = 2√x ; required a . √ a + x = 2 √ x ...
Términos y frases comunes
a²x² algebraical quantities annuity Arithmetical Progression ax² binomial Binomial Theorem coefficient common denominator contains continued fraction cube root difference digits divided divisible divisor equal expressed Extract the square factors find the number Find the value fraction given greater Greatest Common Measure Hence impossible roots last term Least Common Multiple less lowest terms multiplied negative number of terms numerator and denominator odd number original equation permutations Present Value probability proposed equation proposed quantity prove quadratic quadratic equation quadratic surds quan quotient ratio Reduce to lowest remainder represented Required the value rule shew shillings signs square root substituted subtracted suppose supposition surd unknown quantity vulgar fraction whole number
Pasajes populares
Página 91 - This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE.
Página 87 - A laborer agreed to serve for 36 days on condition that for every day he worked he should receive $1.25, and for every day he was absent he should forfeit 50 cents.
Página 110 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.
Página 79 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Página 49 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Página 125 - Progression may be found by multiplying the sum of the first and last terms by half the number of terms.
Página 113 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Página 106 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.
Página 24 - The sign of equality, called equal, or equal to, signifies that the quantities between which it is placed are equal to each other.
Página 15 - Multiply as in whole numbers, and point off as many decimal places in the product as there are in both multiplicand and multiplier. DIVISION. Divide as in whole numbers, and point off...