An Introduction to Algebra: Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American CollegesHowe & Deforest, 1814 - 303 páginas |
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Página 36
... changed from + to - . Again , if m - n is subtracted from b , the remainder is , b - m + n For the less the quantity ... changed , from to , or from to + , and then proceed as in addi tion . - The signs are to be changed , in the ...
... changed from + to - . Again , if m - n is subtracted from b , the remainder is , b - m + n For the less the quantity ... changed , from to , or from to + , and then proceed as in addi tion . - The signs are to be changed , in the ...
Página 46
... changed in- to So that b- ( 4xa ) is b - 4a . And aX - 4 is there- fore - 4a . Again , suppose the multiplicand is a , and the multiplier ( 6-4 ) . As ( 6-4 ) is equal to 2 , the product will be equal to 2a . This is less than the ...
... changed in- to So that b- ( 4xa ) is b - 4a . And aX - 4 is there- fore - 4a . Again , suppose the multiplicand is a , and the multiplier ( 6-4 ) . As ( 6-4 ) is equal to 2 , the product will be equal to 2a . This is less than the ...
Página 62
... changed . ab By Art . 123 , 7 = + a . But ab - bc . And + a - c . -ab = -α . b -ab + bc But b -a + c . That is , by changing all the signs of the numerator , the value of the fraction is changed from positive to negative 62 ALGEBRA .
... changed . ab By Art . 123 , 7 = + a . But ab - bc . And + a - c . -ab = -α . b -ab + bc But b -a + c . That is , by changing all the signs of the numerator , the value of the fraction is changed from positive to negative 62 ALGEBRA .
Página 63
... changed ; the value of the frac tion will be changed , from positive to negative , or from nega- tive to positive . From this is derived another important principle . As each of the changes mentioned here is from positive to neg- ative ...
... changed ; the value of the frac tion will be changed , from positive to negative , or from nega- tive to positive . From this is derived another important principle . As each of the changes mentioned here is from positive to neg- ative ...
Página 81
... changed , without affecting the equality . Thus , if we have Then by transposition Or , inverting the members x - b - d - a -d + a = -x + b -x + b = d + a . 178. If all the terms on one side of an equation be trans- posed , each member ...
... changed , without affecting the equality . Thus , if we have Then by transposition Or , inverting the members x - b - d - a -d + a = -x + b -x + b = d + a . 178. If all the terms on one side of an equation be trans- posed , each member ...
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Términos y frases comunes
12 rods abscissa added algebraic antecedent applied arithmetic become binomial calculation called Clearing of fractions co-efficients Completing the square compound quantity consequent cube root cubic equation curve demonstration denominator diminished dividend division divisor dollars equa equal quantities errour Euclid exponents expressed Extracting and transp factors fourth geometrical geometrical progression given quantity greater Hence inches infinite series inverted involution last term less letters manner mathematics Mult multiplicand negative quantity notation nth power nth root number of terms ordinate parallelogram perpendicular positive prefixed principle Prob Prod proportion proposition quadratic equation quan quotient radical quantities radical sign ratio reciprocal Reduce the equation remainder rule SECTION sides square root substituted subtracted subtrahend supposed supposition theorem third tion tity Transposing transposition triangle twice uniting terms unknown quantity varies vulgar fraction whole
Pasajes populares
Página 214 - In an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Página 188 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Página 265 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Página 227 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Página 189 - If four quantities are proportional, THE ORDER OF THE MEANS, OR OF THE EXTREMES, OR OF THE TERMS OF BOTH COUPLETS, MAY BE INVERTED, WITHOUT DESTROYING THE PROPORTION.
Página 40 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
Página 85 - If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means.
Página 187 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c., are all equal ; the quantities are said to be in continued proportion.
Página 60 - The Value of a fraction is the quotient of the numerator divided by the denominator.
Página 61 - ... produce the same effect on the value of the fraction, as multiplying the numerator. In all cases...