Elements of Algebra: Tr. from the French of M. Bourdon, for the Use of the Cadets of the U. S. Military Academy, Τόμος 1E. B. Clayton, 1831 - 389 σελίδες |
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Σελίδα 3
... gives an idea of the brevity of algebraic language . 8th . The sign √ , which is prefixed to a number , when we wish to indicate that a certain root of it is to be extracted . 3 Thus a is read , the third or cube root of a ; b the ...
... gives an idea of the brevity of algebraic language . 8th . The sign √ , which is prefixed to a number , when we wish to indicate that a certain root of it is to be extracted . 3 Thus a is read , the third or cube root of a ; b the ...
Σελίδα 7
... gives for the first frac- b2 + bm tion . In like manner , by multiplying the two terms of the second a + m b + m ab ... give the beginner a clear idea of the object of algebra . By reflecting upon the solutions of these questions , he ...
... gives for the first frac- b2 + bm tion . In like manner , by multiplying the two terms of the second a + m b + m ab ... give the beginner a clear idea of the object of algebra . By reflecting upon the solutions of these questions , he ...
Σελίδα 11
... give particular values to a and b ; but as it cannot be effected in the present condition of the quantities , it will be the same thing if we first add 2 a2 + b2 to 3 a2 4 ab , and then subtract 3 ab from this sum : this gives 3 a2 - 4 ...
... give particular values to a and b ; but as it cannot be effected in the present condition of the quantities , it will be the same thing if we first add 2 a2 + b2 to 3 a2 4 ab , and then subtract 3 ab from this sum : this gives 3 a2 - 4 ...
Σελίδα 15
... gives a d + bd + cd . In like manner , to multiply a + b + c by f , is to take ƒ times each of the parts of the multiplicand , and add together the partial products . Hence , ( a + b + c ) ( d + f ) = ad + bd + cd + af + bf + cf ...
... gives a d + bd + cd . In like manner , to multiply a + b + c by f , is to take ƒ times each of the parts of the multiplicand , and add together the partial products . Hence , ( a + b + c ) ( d + f ) = ad + bd + cd + af + bf + cf ...
Σελίδα 16
... gives c a - c b , or a c - bc . In like manner , the product of a - b by d , is a d - b d ; and as we have just seen that this last product should be subtracted from the preceding a c - bc , it is necessary to change the signs of a d ...
... gives c a - c b , or a c - bc . In like manner , the product of a - b by d , is a d - b d ; and as we have just seen that this last product should be subtracted from the preceding a c - bc , it is necessary to change the signs of a d ...
Συχνά εμφανιζόμενοι όροι και φράσεις
absolute numbers affected algebraic algebraic quantities arithmetical binomial binomial formula coefficient common factor consequently contains contrary signs cube root deduce denote difference divide dividend division entire functions entire number entire polynomials enunciation equa equal equation involving example exponent expression extract formula fraction given number gives greater greatest common divisor greyhound Hence hypothesis infinite number logarithm manner method monomial multiplied necessary negative nomials nth root number of terms obtain perfect square performing positive preceding prime principle problem proposed equation proposed polynomials question quotient radical rational and entire reduced relative divisor remainder resolved result rule second degree second member second term solution square root substituting subtract suppose take the equation tion transformations unity unknown quantities verified whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 26 - In the first operation we meet with a difficulty in dividing the two polynomials, because the first term of the dividend is not exactly divisible by the first term of the divisor. But if we observe that the co-efficient 4...
Σελίδα 5 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Σελίδα 67 - It is founded on the following principle. The square root of the product of two or more factors, is equal to the product of the square roots of those factors.
Σελίδα 304 - 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.
Σελίδα 119 - There are other problems of the same kind, which lead to equations of a degree superior to the second, and yet they may be resolved by the aid of equations of the first and second degrees, by introducing unknown auxiliaries.
Σελίδα 14 - ... first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend.
Σελίδα 69 - 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.
Σελίδα 133 - 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.
Σελίδα 237 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Σελίδα 201 - ... multiply the last term by the ratio, subtract the first term from this product, and divide the remainder by the ratio diminished by unity.