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 σελίδες |
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Σελίδα 56
... denominator . Div . ab By ac dhx dy ahm - 3ay ab ab + bx by 2am 2xy Quot . or ac ab b c & hm b - 3y am ---- xy These reductions are made upon the principle , that à given divisor is contained in a given dividend , just as many times ...
... denominator . Div . ab By ac dhx dy ahm - 3ay ab ab + bx by 2am 2xy Quot . or ac ab b c & hm b - 3y am ---- xy These reductions are made upon the principle , that à given divisor is contained in a given dividend , just as many times ...
Σελίδα 60
... denominator is a divisor . According to the common definition in arithmetic , the denominator shows into what parts an integral unit is sup- posed to be divided ; and the numerator shows how many of these parts belong to the fraction ...
... denominator is a divisor . According to the common definition in arithmetic , the denominator shows into what parts an integral unit is sup- posed to be divided ; and the numerator shows how many of these parts belong to the fraction ...
Σελίδα 61
... denominator , the value is less than a unit ; and when the numerator is greater than the denominator , the val ue is greater than a unit . The calculations in fractions depend on a few general principles , which will here be stated in ...
... denominator , the value is less than a unit ; and when the numerator is greater than the denominator , the val ue is greater than a unit . The calculations in fractions depend on a few general principles , which will here be stated in ...
Σελίδα 62
... denominator , and taking the pro- duct for a numerator . Thus a = α ab ad + ah 6adh 1 b of each of these is a . dx + hx So d + h = X & c . For the quotient d + h 6dh ' 2drr + 2dr And r + 1 = 2dr 142. There is nothing perhaps , in the ...
... denominator , and taking the pro- duct for a numerator . Thus a = α ab ad + ah 6adh 1 b of each of these is a . dx + hx So d + h = X & c . For the quotient d + h 6dh ' 2drr + 2dr And r + 1 = 2dr 142. There is nothing perhaps , in the ...
Σελίδα 63
... denominator to be chan- ged . ab As before b = + a . But ab 143. We have , then , this general proposition ; If the sign prefixed to a fraction , or all the signs of the numerator , or all the signs of the denominator be changed ; the ...
... denominator to be chan- ged . ab As before b = + a . But ab 143. We have , then , this general proposition ; If the sign prefixed to a fraction , or all the signs of the numerator , or all the signs of the denominator be changed ; the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 265 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Σελίδα 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.
Σελίδα 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.
Σελίδα 40 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
Σελίδα 85 - If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means.
Σελίδα 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.
Σελίδα 60 - The Value of a fraction is the quotient of the numerator divided by the denominator.
Σελίδα 61 - ... produce the same effect on the value of the fraction, as multiplying the numerator. In all cases...