Elements of algebra1870 |
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Page 59
... equation , we shall have ( a + b ) 2 = ( 20 + 7 ) 2 , or a2 + 2ab + b2 = 400 + 280 + 49 = 729 . Hence the square of ... complete divisor by the last figure of the root thus obtained , subtract the product from the dividend , and to the ...
... equation , we shall have ( a + b ) 2 = ( 20 + 7 ) 2 , or a2 + 2ab + b2 = 400 + 280 + 49 = 729 . Hence the square of ... complete divisor by the last figure of the root thus obtained , subtract the product from the dividend , and to the ...
Page 70
... equation . Thus , the square root of the first line gives a . Subtracting the square of this from the second member ... complete square , such as ( a + b + c + d + ...... .. ) 2 . When the given quantity is not a complete square , the ...
... equation . Thus , the square root of the first line gives a . Subtracting the square of this from the second member ... complete square , such as ( a + b + c + d + ...... .. ) 2 . When the given quantity is not a complete square , the ...
Page 73
... Equations of the second degree are divided into two classes , complete and incomplete . A complete equation involves the first and second powers of the un- known quantity and the known terms . An incomplete equation involves the second ...
... Equations of the second degree are divided into two classes , complete and incomplete . A complete equation involves the first and second powers of the un- known quantity and the known terms . An incomplete equation involves the second ...
Page 77
... equations of the first degree , the only difficulty being to obtain the value of x from the equation x2 - ax = b . The first member being a binomial , is not a EQUATIONS OF THE SECOND DEGREE . 77 Of Complete Equations of the Second ...
... equations of the first degree , the only difficulty being to obtain the value of x from the equation x2 - ax = b . The first member being a binomial , is not a EQUATIONS OF THE SECOND DEGREE . 77 Of Complete Equations of the Second ...
Page 83
... equation from radicals would , in this case , be very complicated ; but the ... complete equation of the second degree can be reduced to the form x2 + ax ... EQUATIONS OF THE SECOND DEGREE . 83 Discussion of Equations of the Second Degree.
... equation from radicals would , in this case , be very complicated ; but the ... complete equation of the second degree can be reduced to the form x2 + ax ... EQUATIONS OF THE SECOND DEGREE . 83 Discussion of Equations of the Second Degree.
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Common terms and phrases
algebraic algebraic quantities binomial clearing the equation Cloth coefficient complete equation completing the square continued fraction cube root Decompose denotes dividend divisor equal equation of fractions EXAMPLES exponent expression Extract the square factors Find the numerical Find the sum find the values Find two numbers following rule fourth powers given equation given number greater greatest common measure Hence inequality last term least common multiple less lettered logarithm mixed quantity monomial multiplicand Multiply negative nth root number of permutations number of terms numerical value obtain original equation perfect square polynomial positive preceding quotient radical sign real roots remainder Required the square Required the sum second degree second member second term shillings simplest form square root substitution subtract third Transform transposing travelled unknown quantity values of x whence whole number zero
Popular passages
Page 59 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 12 - 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 12 - 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.
Page 59 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 43 - A footman agreed to serve his master for £8 a year and a livery, but was turned away at the end of 7 months, and received only £2 13s.
Page 89 - ... that the intensity of light varies inversely as the square of the distance.
Page 54 - 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...
Page 88 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Page 42 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days ; how many days would the man alone be in drinking it ? Ans.