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 sider |
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Resultat 1-5 av 17
Side 31
... consequent reduction . Suppose 6b is to be added to -4b . The sum is a - 4b + 6b . But this expression may be rendered more simple . As it now stands , 4b is to be subtracted from a , and 6b added.- But the amount will be the same , if ...
... consequent reduction . Suppose 6b is to be added to -4b . The sum is a - 4b + 6b . But this expression may be rendered more simple . As it now stands , 4b is to be subtracted from a , and 6b added.- But the amount will be the same , if ...
Side 177
... consequent , and the ratio , any two being given , the other may be found . Let a = the antecedent , c = the consequent , r = the ratio . α By definition == ; that is , the ratio is equal to the antece- dent divided by the consequent ...
... consequent , and the ratio , any two being given , the other may be found . Let a = the antecedent , c = the consequent , r = the ratio . α By definition == ; that is , the ratio is equal to the antece- dent divided by the consequent ...
Side 178
... consequent . 1 1 α b The reciprocal ratio , is or - 1 1 1 b b α b -- a 1 that is , the consequent b divided by the antecedent a . Hence a reciprocal ratio is expressed by inverting the frac- tion which expresses the direct ratio ; or ...
... consequent . 1 1 α b The reciprocal ratio , is or - 1 1 1 b b α b -- a 1 that is , the consequent b divided by the antecedent a . Hence a reciprocal ratio is expressed by inverting the frac- tion which expresses the direct ratio ; or ...
Side 179
... consequent of each pre- ceding couplet , is the antecedent of the following one , the ratio of the first antecedent to the last consequent , is equal to that which is compounded of all the intervening ratios . * Thus , in the series of ...
... consequent of each pre- ceding couplet , is the antecedent of the following one , the ratio of the first antecedent to the last consequent , is equal to that which is compounded of all the intervening ratios . * Thus , in the series of ...
Side 180
... consequent , the de- nominator . It will be easy , then , to derive from the proper- ties of fractions , the changes produced in ratios by varia- tions in the quantities compared . For the ratio of the two quantities is the same as the ...
... consequent , the de- nominator . It will be easy , then , to derive from the proper- ties of fractions , the changes produced in ratios by varia- tions in the quantities compared . For the ratio of the two quantities is the same as the ...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ... Jeremiah Day Uten tilgangsbegrensning - 1853 |
An Introduction to Algebra: Being the First Part of a Course of Mathematics ... Jeremiah Day Uten tilgangsbegrensning - 1819 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 265 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Side 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.
Side 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.
Side 40 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
Side 85 - If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means.
Side 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.
Side 60 - The Value of a fraction is the quotient of the numerator divided by the denominator.
Side 61 - ... produce the same effect on the value of the fraction, as multiplying the numerator. In all cases...