Elements of Algebra: Including Sturms' Theorem |
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Page 12
... figures . For , if it were re- quired to express the product of 5 by 6 , we could not write 56 , without confounding ... figure is then placed before it , to show how many times it is taken . Thus , The number 5 is called the co ...
... figures . For , if it were re- quired to express the product of 5 by 6 , we could not write 56 , without confounding ... figure is then placed before it , to show how many times it is taken . Thus , The number 5 is called the co ...
Page 45
... figures of the quotient are obtained by trial , while in algebraical division the quotient obtained by dividing the first term of the partial divi- dend by the first term of the divisor , is always one of the terms of the quotient ...
... figures of the quotient are obtained by trial , while in algebraical division the quotient obtained by dividing the first term of the partial divi- dend by the first term of the divisor , is always one of the terms of the quotient ...
Page 92
... figures ; the sum of these figures is 11 ; the figure in the place of units is double that in the place of hundreds ; and when 297 is added to this number , the sum obtained is expressed by the figures of this number re- versed . What ...
... figures ; the sum of these figures is 11 ; the figure in the place of units is double that in the place of hundreds ; and when 297 is added to this number , the sum obtained is expressed by the figures of this number re- versed . What ...
Page 108
... figure of a higher denomination than tens . The numbers of the last line , 1 , 4 , 9 , 16 , & c . , and all other ... figures : the square roots of all other numbers expressed by one or two figures will be found between two whole ...
... figure of a higher denomination than tens . The numbers of the last line , 1 , 4 , 9 , 16 , & c . , and all other ... figures : the square roots of all other numbers expressed by one or two figures will be found between two whole ...
Page 109
... figure of a less denomination than hundreds , nor of a higher name than thousands . Let us now take any number , as 78 , and square it . We have 78 = 70 + 8 ; that is , equal to 7 tens , or 70 , plus 8 units . Seven tens , or 70 squared ...
... figure of a less denomination than hundreds , nor of a higher name than thousands . Let us now take any number , as 78 , and square it . We have 78 = 70 + 8 ; that is , equal to 7 tens , or 70 , plus 8 units . Seven tens , or 70 squared ...
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Common terms and phrases
affected algebraic quantities arithmetical means arithmetical progression binomial called co-efficient common difference consequently contain contrary signs cube root Cx² decimal deduced denominator denote divide dividend division entire number enunciation equa equal equation involving example exponent expression extract the square factors figure find the values formula fourth fraction given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm monomial multiplicand multiplied negative nth root number of terms obtain operation ounces perfect square permutations problem proportion proposed equation quan quotient radical sign Reduce remainder result rule satisfy second degree second member second term simplest form square root substituted subtract suppose supposition take the equation third tion tities total number transposing unity unknown quantity whence whole number ах
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.