Elements of Algebra: Including Sturms' Theorem |
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Page 74
... My horse and saddle together are worth $ 132 , and the horse is worth ten times as much as the saddle : what is the value of the horse ? Ans . $ 120 . 23. The rent of an estate is this year 8 74 [ CHAP . IV . ELEMENTS OF ALGEBRA .
... My horse and saddle together are worth $ 132 , and the horse is worth ten times as much as the saddle : what is the value of the horse ? Ans . $ 120 . 23. The rent of an estate is this year 8 74 [ CHAP . IV . ELEMENTS OF ALGEBRA .
Page 75
... ten feet above the water what is the whole length of the post ? Ans . 24 feet . 26. After paying and of my money , I had 66 guineas left in my purse : how many guineas were in it at first ? Ans . 120 . 27. A person was desirous of ...
... ten feet above the water what is the whole length of the post ? Ans . 24 feet . 26. After paying and of my money , I had 66 guineas left in my purse : how many guineas were in it at first ? Ans . 120 . 27. A person was desirous of ...
Page 108
... ten numbers are , once . 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , and their squares , 1 , 4 , 9 , 16 , 25 , 36 , 49 ... tens . The numbers of the last line , 1 , 4 , 9 , 16 , & c . , and all other numbers which can be produced by the ...
... ten numbers are , once . 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , and their squares , 1 , 4 , 9 , 16 , 25 , 36 , 49 ... tens . The numbers of the last line , 1 , 4 , 9 , 16 , & c . , and all other numbers which can be produced by the ...
Page 109
... tens and a certain number of units . Thus 64 is made up of 6 tens and 4 units , and may be expressed under the form 60+ 4 = 64 . Now , if we represent the tens by a and the units by b , we shall have and and consequently , a + b = 60+ 4 ...
... tens and a certain number of units . Thus 64 is made up of 6 tens and 4 units , and may be expressed under the form 60+ 4 = 64 . Now , if we represent the tens by a and the units by b , we shall have and and consequently , a + b = 60+ 4 ...
Page 110
... tens . Now , the square of the tens must be found in the two left- hand figures which we will separate from the other two , by placing a point over the the place of units , and another over the place of hundreds . These parts , of two ...
... tens . Now , the square of the tens must be found in the two left- hand figures which we will separate from the other two , by placing a point over the the place of units , and another over the place of hundreds . These parts , of two ...
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Common terms and phrases
affected algebraic quantities arithmetical arrangements becomes binomial called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator divide dividend division entire number enunciation equa equal equation involving example exponent factors figure formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm method monomial multiply nth root number of terms obtain operation ounces perfect square positive roots preceding problem progression proposed equation quan quotient real roots Reduce remainder resolved result rule second degree second member second term simplest form square root substituted subtract superior limit suppose take the equation taken third tion tities transformed transposing unity unknown quantity whence whole number
Popular passages
Page 30 - 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 275 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 27 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Page 179 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 180 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 90 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 346 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to , the number of permanences.
Page 34 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 108 - 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 202 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.